{"id":58084,"date":"2025-08-16T02:20:07","date_gmt":"2025-08-15T18:20:07","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/58084.html"},"modified":"2025-08-16T02:20:07","modified_gmt":"2025-08-15T18:20:07","slug":"%e8%87%aa%e5%8a%a8%e9%a9%be%e9%a9%b6%e8%bd%a8%e8%bf%b9%e8%a7%84%e5%88%92%e7%ae%97%e6%b3%95-apollo-em-planner","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/58084.html","title":{"rendered":"\u81ea\u52a8\u9a7e\u9a76\u8f68\u8ff9\u89c4\u5212\u7b97\u6cd5\u2014\u2014Apollo EM Planner"},"content":{"rendered":"<h2>\u81ea\u52a8\u9a7e\u9a76\u8f68\u8ff9\u89c4\u5212\u7b97\u6cd5\u2014\u2014Apollo EM Planner<\/h2>\n<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u81ea\u52a8\u9a7e\u9a76\u8f68\u8ff9\u89c4\u5212\u7b97\u6cd5\u2014\u2014Apollo EM Planner<\/li>\n<li>\u4e00\u3001Apollo EM Planner \u662f\u4ec0\u4e48&#xff1f;<\/li>\n<li>\n<ul>\n<li>1.1 \u5b9a\u4e49\u4e0e\u6838\u5fc3\u601d\u60f3<\/li>\n<li>1.2 \u4e0e\u5176\u4ed6\u89c4\u5212\u5668&#xff08;\u5982 Lattice\u3001Hybrid A*&#xff09;\u7684\u533a\u522b<\/li>\n<li>1.3 Apollo EM Planner \u7684\u5178\u578b\u5e94\u7528\u573a\u666f<\/li>\n<\/ul>\n<\/li>\n<li>\u4e8c\u3001Apollo EM Planner \u7684\u539f\u7406&#xff08;\u53c2\u8003\u5b98\u65b9\u67b6\u6784\u89e3\u6790&#xff09;<\/li>\n<li>\n<ul>\n<li>2.1 \u89c4\u5212\u5668\u603b\u4f53\u67b6\u6784&#xff1a;EM \u8fed\u4ee3\u4f18\u5316\u601d\u60f3<\/li>\n<li>2.2 \u5750\u6807\u7cfb\u9009\u62e9&#xff1a;Frenet \u5750\u6807\u7cfb\u7684\u4f18\u52bf<\/li>\n<li>**2.3\u3000E-Step&#xff1a;\u8def\u5f84\u4f18\u5316\u9636\u6bb5**<\/li>\n<li>\n<ul>\n<li>**2.3.1 \u80cc\u666f\u95ee\u9898**<\/li>\n<li>**2.3.2 \u6838\u5fc3\u601d\u60f3**<\/li>\n<li>**2.3.3 Step-by-Step \u8fc7\u7a0b**<\/li>\n<li>\n<ul>\n<li>**Step 1 \u2014 SL \u6295\u5f71\u4e0e\u53ef\u884c\u533a\u57df\u751f\u6210**<\/li>\n<li>**Step 2 \u2014 \u52a8\u6001\u89c4\u5212&#xff08;DP&#xff09;\u641c\u7d22\u7c97\u8def\u5f84**<\/li>\n<li>**Step 3 \u2014 \u751f\u6210\u53ef\u884c\u8d70\u5eca&#xff08;Feasible Tunnel&#xff09;**<\/li>\n<li>**Step 4 \u2014 QP &#043; \u6837\u6761\u66f2\u7ebf\u5e73\u6ed1\u4f18\u5316**<\/li>\n<\/ul>\n<\/li>\n<li>**2.3.4 \u6570\u5b66\u5efa\u6a21**<\/li>\n<li>**2.3.5 \u53ef\u89c6\u5316\u793a\u610f**<\/li>\n<li>**2.3.6 \u7ed3\u679c\u610f\u4e49**<\/li>\n<\/ul>\n<\/li>\n<li>**2.4 M-Step&#xff1a;\u901f\u5ea6\u4f18\u5316\u9636\u6bb5**<\/li>\n<li>\n<ul>\n<li>**2.4.1 \u80cc\u666f\u95ee\u9898**<\/li>\n<li>**2.4.2 \u6838\u5fc3\u601d\u60f3**<\/li>\n<li>**2.4.3 Step-by-Step \u8fc7\u7a0b**<\/li>\n<li>\n<ul>\n<li>**Step 1 \u2014 ST \u6295\u5f71\u4e0e\u5b89\u5168\u533a\u57df\u751f\u6210**<\/li>\n<li>**Step 2 \u2014 \u52a8\u6001\u89c4\u5212&#xff08;DP&#xff09;\u641c\u7d22\u901f\u5ea6\u66f2\u7ebf**<\/li>\n<li>**Step 3 \u2014 \u751f\u6210\u901f\u5ea6\u8d70\u5eca&#xff08;Feasible ST Tunnel&#xff09;**<\/li>\n<li>**Step 4 \u2014 QP \u5e73\u6ed1\u901f\u5ea6\u66f2\u7ebf**<\/li>\n<\/ul>\n<\/li>\n<li>**2.4.4 E\u2013M \u4ea4\u4e92\u673a\u5236**<\/li>\n<li>**2.4.5 \u7ed3\u679c\u610f\u4e49**<\/li>\n<\/ul>\n<\/li>\n<li>**2.5 E-Step \u4e0e M-Step \u7684\u4ea4\u4e92\u673a\u5236**<\/li>\n<li>\n<ul>\n<li>**2.5.1 \u6982\u8ff0**<\/li>\n<li>**2.5.2 \u8fed\u4ee3\u6d41\u7a0b**<\/li>\n<li>**2.5.3 \u6267\u884c\u9891\u7387**<\/li>\n<li>**2.5.4 \u4ea4\u4e92\u673a\u5236\u7684\u4f18\u52bf**<\/li>\n<\/ul>\n<\/li>\n<li>\u4e09\u3001Apollo EM Planner \u7684\u5173\u952e\u6280\u672f\u7ec6\u8282<\/li>\n<li>\n<ul>\n<li>3.1 \u89c4\u5212\u95ee\u9898\u5efa\u6a21<\/li>\n<li>3.2 E-Step \u6838\u5fc3\u6280\u672f&#xff08;S\u2013L \u5e73\u9762&#xff09;<\/li>\n<li>\n<ul>\n<li>3.2.1 \u969c\u788d\u7269\u6295\u5f71\u4e0e\u5360\u636e\u533a\u751f\u6210<\/li>\n<li>3.2.2 \u52a8\u6001\u89c4\u5212\u7c97\u641c\u7d22<\/li>\n<li>3.2.3 \u4e8c\u6b21\u89c4\u5212\u5e73\u6ed1<\/li>\n<\/ul>\n<\/li>\n<li>3.3 M-Step \u6838\u5fc3\u6280\u672f&#xff08;S\u2013T \u5e73\u9762&#xff09;<\/li>\n<li>\n<ul>\n<li>3.3.1 S\u2013T \u6295\u5f71\u4e0e\u5b89\u5168\u533a\u6784\u5efa<\/li>\n<li>3.3.2 DP \u7c97\u901f\u5ea6\u66f2\u7ebf\u641c\u7d22<\/li>\n<li>3.3.3 \u5b89\u5168\u8d70\u5eca&#xff08;ST Tunnel&#xff09;\u751f\u6210<\/li>\n<li>3.3.4 QP \u5e73\u6ed1\u901f\u5ea6\u66f2\u7ebf<\/li>\n<\/ul>\n<\/li>\n<li>3.4 E\u2013M \u8fed\u4ee3\u673a\u5236<\/li>\n<li>\n<ul>\n<li>3.4.1 \u4ea4\u4e92\u6d41\u7a0b<\/li>\n<li>3.4.2 \u4f18\u52bf<\/li>\n<\/ul>\n<\/li>\n<li>3.5 \u6a21\u5757\u95f4\u6570\u636e\u4ea4\u4e92<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>\u4e00\u3001Apollo EM Planner \u662f\u4ec0\u4e48&#xff1f;<\/h2>\n<h3>1.1 \u5b9a\u4e49\u4e0e\u6838\u5fc3\u601d\u60f3<\/h3>\n<p>Apollo EM Planner \u662f\u767e\u5ea6 Apollo \u81ea\u52a8\u9a7e\u9a76\u7cfb\u7edf\u4e2d\u7684\u4e00\u6b3e \u5b9e\u65f6\u8f68\u8ff9\u89c4\u5212\u5668&#xff08;Motion Planner&#xff09;&#xff0c;\u5176\u547d\u540d\u4e2d\u7684\u201cEM\u201d\u6e90\u81ea Expectation\u2013Maximization&#xff08;\u671f\u671b\u2013\u6700\u5927\u5316&#xff09;\u8fed\u4ee3\u4f18\u5316\u7684\u601d\u60f3\u3002 \u5b83\u7684\u6838\u5fc3\u601d\u8def\u662f \u5c06\u8f68\u8ff9\u89c4\u5212\u95ee\u9898\u62c6\u89e3\u4e3a\u201c\u8def\u5f84\u4f18\u5316\u201d\u548c\u201c\u901f\u5ea6\u4f18\u5316\u201d\u4e24\u4e2a\u5b50\u95ee\u9898&#xff0c;\u5e76\u5728\u4e8c\u8005\u4e4b\u95f4\u53cd\u590d\u4ea4\u66ff\u8fed\u4ee3&#xff0c;\u76f4\u5230\u6536\u655b\u4e3a\u6b62\u3002\u8fd9\u79cd\u65b9\u6cd5\u80fd\u591f\u6709\u6548\u964d\u4f4e\u89c4\u5212\u95ee\u9898\u7684\u7ef4\u5ea6\u4e0e\u8ba1\u7b97\u590d\u6742\u5ea6&#xff0c;\u540c\u65f6\u4fdd\u6301\u8f83\u9ad8\u7684\u8f68\u8ff9\u5e73\u6ed1\u6027\u4e0e\u5b9e\u65f6\u6027\u3002<\/p>\n<p>\u5728\u81ea\u52a8\u9a7e\u9a76\u7cfb\u7edf\u4e2d&#xff0c;EM Planner \u4e3b\u8981\u8d1f\u8d23&#xff1a;<\/p>\n<ul>\n<li>\u6839\u636e\u8f66\u8f86\u5f53\u524d\u4f4d\u7f6e\u3001\u53c2\u8003\u8def\u5f84\u548c\u969c\u788d\u7269\u4fe1\u606f&#xff0c;\u89c4\u5212\u4e00\u6761\u5b89\u5168\u3001\u5e73\u6ed1\u4e14\u8212\u9002\u7684\u8f68\u8ff9&#xff1b;<\/li>\n<li>\u5728\u8def\u5f84\u89c4\u5212\u7684\u57fa\u7840\u4e0a\u5206\u914d\u5408\u7406\u7684\u901f\u5ea6\u66f2\u7ebf&#xff1b;<\/li>\n<li>\u5728\u52a8\u6001\u73af\u5883\u4e2d\u5feb\u901f\u91cd\u89c4\u5212&#xff0c;\u4fdd\u8bc1\u8f66\u8f86\u5b89\u5168\u884c\u9a76\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>1.2 \u4e0e\u5176\u4ed6\u89c4\u5212\u5668&#xff08;\u5982 Lattice\u3001Hybrid A*&#xff09;\u7684\u533a\u522b<\/h3>\n<table>\n<tr>\u7279\u6027Lattice PlannerHybrid A* PlannerEM Planner<\/tr>\n<tbody>\n<tr>\n<td>\u89c4\u5212\u7a7a\u95f4<\/td>\n<td>\u79bb\u6563\u91c7\u6837\u641c\u7d22<\/td>\n<td>\u8fde\u7eed\u66f2\u7ebf\u641c\u7d22<\/td>\n<td>Frenet \u5750\u6807\u4e0b\u8def\u5f84\/\u901f\u5ea6\u89e3\u8026<\/td>\n<\/tr>\n<tr>\n<td>\u6838\u5fc3\u65b9\u6cd5<\/td>\n<td>\u72b6\u6001\u91c7\u6837&#043;\u8f68\u8ff9\u5e93<\/td>\n<td>A* \u641c\u7d22&#043;\u66f2\u7387\u7ea6\u675f<\/td>\n<td>DP&#xff08;\u52a8\u6001\u89c4\u5212&#xff09;&#043;QP&#xff08;\u4e8c\u6b21\u89c4\u5212&#xff09;\u8fed\u4ee3<\/td>\n<\/tr>\n<tr>\n<td>\u8f68\u8ff9\u5e73\u6ed1\u6027<\/td>\n<td>\u4e2d\u7b49<\/td>\n<td>\u8f83\u9ad8<\/td>\n<td>\u9ad8&#xff08;\u6837\u6761\u66f2\u7ebf\u5e73\u6ed1&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u52a8\u6001\u969c\u788d\u7269\u5904\u7406<\/td>\n<td>\u8f83\u5f31<\/td>\n<td>\u8f83\u5f31<\/td>\n<td>\u5f3a&#xff08;ST \u6295\u5f71&#043;\u901f\u5ea6\u4f18\u5316&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u5b9e\u65f6\u6027<\/td>\n<td>\u4e00\u822c<\/td>\n<td>\u8f83\u4f4e<\/td>\n<td>\u9ad8<\/td>\n<\/tr>\n<tr>\n<td>\u9002\u7528\u573a\u666f<\/td>\n<td>\u6709\u9650\u590d\u6742\u5ea6\u73af\u5883<\/td>\n<td>\u5f2f\u66f2\u72ed\u7a84\u7a7a\u95f4<\/td>\n<td>\u57ce\u5e02\u9053\u8def\u3001\u9ad8\u901f\u3001\u52a8\u6001\u573a\u666f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>EM Planner \u6700\u5927\u7684\u4e0d\u540c\u70b9\u5728\u4e8e\u5c06\u89c4\u5212\u95ee\u9898\u5206\u4e3a\u8def\u5f84\u4e0e\u901f\u5ea6\u4e24\u4e2a\u72ec\u7acb\u7684\u4f18\u5316\u5b50\u95ee\u9898&#xff0c;\u5e76\u5728\u4e24\u8005\u4e4b\u95f4\u4ea4\u66ff\u4f18\u5316&#xff0c;\u8fd9\u4e0d\u4ec5\u63d0\u5347\u4e86\u5b9e\u65f6\u6027&#xff0c;\u8fd8\u80fd\u5e94\u5bf9\u52a8\u6001\u969c\u788d\u7269\u3002<\/p>\n<hr \/>\n<h3>1.3 Apollo EM Planner \u7684\u5178\u578b\u5e94\u7528\u573a\u666f<\/h3>\n<p>EM Planner \u5177\u6709\u8f83\u5f3a\u7684\u901a\u7528\u6027\u548c\u52a8\u6001\u73af\u5883\u9002\u5e94\u80fd\u529b&#xff0c;\u4e3b\u8981\u5e94\u7528\u5728\u4ee5\u4e0b\u81ea\u52a8\u9a7e\u9a76\u4efb\u52a1\u4e2d&#xff1a;<\/p>\n<li>\u8f68\u8ff9\u8ddf\u8e2a\u4e0e\u901f\u5ea6\u89c4\u5212&#xff08;Trajectory &amp; Speed Optimization&#xff09; \u5728\u53c2\u8003\u8def\u5f84\u7684\u57fa\u7840\u4e0a&#xff0c;\u89c4\u5212\u7b26\u5408\u5b89\u5168\u3001\u8212\u9002\u6027\u8981\u6c42\u7684\u8f68\u8ff9\u4e0e\u901f\u5ea6\u66f2\u7ebf&#xff0c;\u5b9e\u73b0\u7cbe\u51c6\u8ddf\u8e2a\u3002<\/li>\n<li>\u8f66\u9053\u4fdd\u6301\u4e0e\u6362\u9053\u7b56\u7565&#xff08;Lane Keeping \/ Lane Changing&#xff09; \u5904\u7406\u591a\u8f66\u9053\u573a\u666f\u4e0b\u7684\u8f66\u9053\u4fdd\u6301\u4e0e\u6362\u9053\u51b3\u7b56&#xff0c;\u5e76\u5728\u6362\u9053\u8fc7\u7a0b\u4e2d\u5e73\u6ed1\u8fc7\u6e21\u3002<\/li>\n<li>\u907f\u969c\u4e0e\u4f1a\u8f66\u5904\u7406 \u7ed3\u5408\u969c\u788d\u7269\u52a8\u6001\u9884\u6d4b\u4fe1\u606f&#xff0c;\u5728\u8def\u5f84\u4e0e\u901f\u5ea6\u4f18\u5316\u9636\u6bb5\u5b9e\u73b0\u4e3b\u52a8\u907f\u969c\u4e0e\u5b89\u5168\u4f1a\u8f66\u3002<\/li>\n<li>\u57ce\u5e02\u9053\u8def\u4e0e\u9ad8\u901f\u516c\u8def\u6df7\u5408\u573a\u666f \u80fd\u591f\u5728\u5bc6\u96c6\u4ea4\u901a\u548c\u9ad8\u901f\u884c\u9a76\u573a\u666f\u4e0b\u4fdd\u6301\u7a33\u5b9a\u89c4\u5212\u6027\u80fd&#xff0c;\u9002\u5e94\u5404\u79cd\u901f\u5ea6\u548c\u8f66\u9053\u6761\u4ef6\u3002<\/li>\n<h2>\u4e8c\u3001Apollo EM Planner \u7684\u539f\u7406&#xff08;\u53c2\u8003\u5b98\u65b9\u67b6\u6784\u89e3\u6790&#xff09;<\/h2>\n<p>Apollo EM Planner \u7684\u8bbe\u8ba1\u6838\u5fc3\u662f \u8def\u5f84\u2013\u901f\u5ea6\u89e3\u8026 &#043; EM \u8fed\u4ee3\u4f18\u5316\u3002 \u5b83\u5c06\u8f68\u8ff9\u89c4\u5212\u95ee\u9898\u5206\u89e3\u4e3a\u4e24\u4e2a\u5b50\u95ee\u9898&#xff1a;<\/p>\n<ul>\n<li>E-Step&#xff1a;\u56fa\u5b9a\u901f\u5ea6\u5206\u5e03&#xff0c;\u4f18\u5316\u8def\u5f84\u5f62\u72b6&#xff08;Path Planning&#xff09;\u3002<\/li>\n<li>M-Step&#xff1a;\u56fa\u5b9a\u8def\u5f84\u5f62\u72b6&#xff0c;\u4f18\u5316\u901f\u5ea6\u66f2\u7ebf&#xff08;Speed Planning&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u8fd9\u79cd\u4ea4\u66ff\u4f18\u5316\u65b9\u5f0f\u53ef\u4ee5\u5728\u4fdd\u6301\u8ba1\u7b97\u6548\u7387\u7684\u540c\u65f6&#xff0c;\u517c\u987e\u5b89\u5168\u6027\u3001\u5e73\u6ed1\u6027\u548c\u52a8\u6001\u969c\u788d\u7269\u5904\u7406\u80fd\u529b\u3002<\/p>\n<hr \/>\n<h3>2.1 \u89c4\u5212\u5668\u603b\u4f53\u67b6\u6784&#xff1a;EM \u8fed\u4ee3\u4f18\u5316\u601d\u60f3<\/h3>\n<ul>\n<li>\u8f93\u5165&#xff1a;\u9ad8\u7cbe\u5730\u56fe\u3001\u53c2\u8003\u8def\u7ebf\u3001\u969c\u788d\u7269\u4fe1\u606f&#xff08;\u9759\u6001 &#043; \u52a8\u6001&#xff09;\u3001\u8f66\u8f86\u5f53\u524d\u72b6\u6001\u3002<\/li>\n<li>\u8f93\u51fa&#xff1a;\u65f6\u7a7a\u8f68\u8ff9&#xff08;x(t), y(t), v(t), a(t), \u03b4(t)&#xff09;\u3002<\/li>\n<li>\u6838\u5fc3\u5faa\u73af&#xff1a;\n<li>\u5c06\u73af\u5883\u4e0e\u8f66\u8f86\u72b6\u6001\u6295\u5f71\u5230 Frenet \u5750\u6807\u7cfb&#xff08;S-L \/ S-T \u5e73\u9762&#xff09;\u3002<\/li>\n<li>\u5728 S-L \u5e73\u9762\u8fdb\u884c\u8def\u5f84\u4f18\u5316&#xff08;E-Step&#xff09;\u3002<\/li>\n<li>\u5728 S-T \u5e73\u9762\u8fdb\u884c\u901f\u5ea6\u4f18\u5316&#xff08;M-Step&#xff09;\u3002<\/li>\n<li>\u68c0\u67e5\u6536\u655b\u6761\u4ef6&#xff0c;\u82e5\u672a\u6536\u655b\u5219\u8fd4\u56de E-Step \u7ee7\u7eed\u8fed\u4ee3\u3002<\/li>\n<\/li>\n<\/ul>\n<hr \/>\n<h3>2.2 \u5750\u6807\u7cfb\u9009\u62e9&#xff1a;Frenet \u5750\u6807\u7cfb\u7684\u4f18\u52bf<\/h3>\n<p>Apollo EM Planner \u5728 Frenet \u5750\u6807\u7cfb\u4e2d\u8fdb\u884c\u4f18\u5316&#xff1a;<\/p>\n<ul>\n<li>S&#xff08;Station&#xff09;&#xff1a;\u6cbf\u53c2\u8003\u7ebf\u7684\u5f27\u957f\u4f4d\u7f6e\u3002<\/li>\n<li>L&#xff08;Lateral&#xff09;&#xff1a;\u6a2a\u5411\u504f\u79fb\u3002<\/li>\n<li>T&#xff08;Time&#xff09;&#xff1a;\u65f6\u95f4\u7ef4\u5ea6&#xff08;\u7528\u4e8e\u901f\u5ea6\u4f18\u5316&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u4f18\u52bf&#xff1a;<\/p>\n<li>\u53ef\u4ee5\u5c06\u4e8c\u7ef4\u8f68\u8ff9\u95ee\u9898\u5206\u89e3\u4e3a\u4e00\u7ef4\u7eb5\u5411&#xff08;S&#xff09;\u548c\u4e00\u7ef4\u6a2a\u5411&#xff08;L&#xff09;\u4f18\u5316\u95ee\u9898\u3002<\/li>\n<li>\u969c\u788d\u7269\u7684\u7a7a\u95f4\u4f4d\u7f6e\u548c\u8fd0\u52a8\u9884\u6d4b\u5728 Frenet \u5750\u6807\u4e2d\u66f4\u5bb9\u6613\u8ba1\u7b97\u65f6\u7a7a\u4ea4\u96c6\u3002<\/li>\n<li>\u7ea6\u675f\u8868\u8fbe\u7b80\u5355&#xff08;\u9650\u901f\u3001\u52a0\u901f\u5ea6\u3001\u8f66\u9053\u8fb9\u754c\u7b49\u53ef\u76f4\u63a5\u6620\u5c04\u4e3a\u5750\u6807\u8fb9\u754c&#xff09;\u3002<\/li>\n<hr \/>\n<h3>2.3\u3000E-Step&#xff1a;\u8def\u5f84\u4f18\u5316\u9636\u6bb5<\/h3>\n<h4>2.3.1 \u80cc\u666f\u95ee\u9898<\/h4>\n<p>E-Step \u7684\u76ee\u6807\u662f\u5f97\u5230\u4e00\u6761\u4e0d\u78b0\u969c\u788d\u7269\u4e14\u62d3\u6251\u5408\u7406\u7684\u8def\u5f84\u3002 \u5982\u679c\u76f4\u63a5\u7528\u4e8c\u6b21\u89c4\u5212&#xff08;QP&#xff09;\u8fdb\u884c\u8def\u5f84\u4f18\u5316&#xff0c;\u4f1a\u9047\u5230\u4e24\u4e2a\u95ee\u9898&#xff1a;<\/p>\n<li>QP \u662f\u5c40\u90e8\u4f18\u5316\u5668&#xff0c;\u4e0d\u4f1a\u81ea\u52a8\u9009\u62e9\u6362\u9053\u6216\u7ed5\u969c\u7684\u5168\u5c40\u62d3\u6251\u8def\u5f84&#xff1b;<\/li>\n<li>\u969c\u788d\u7269\u53ef\u80fd\u8ba9\u53ef\u884c\u57df\u4e0d\u8fde\u901a&#xff0c;QP \u53ef\u80fd\u9677\u5165\u5c40\u90e8\u65e0\u89e3\u3002<\/li>\n<p>\u56e0\u6b64 Apollo EM Planner \u5728 QP \u4e4b\u524d\u589e\u52a0\u4e86\u52a8\u6001\u89c4\u5212&#xff08;DP&#xff09;\u641c\u7d22\u7c97\u8def\u5f84&#xff0c;\u5148\u89e3\u51b3\u201c\u8d70\u54ea\u6761\u9053\u201d\u7684\u5168\u5c40\u51b3\u7b56&#xff0c;\u518d\u5728\u5b83\u5468\u56f4\u8fdb\u884c\u5e73\u6ed1\u4f18\u5316\u3002<\/p>\n<hr \/>\n<h4>2.3.2 \u6838\u5fc3\u601d\u60f3<\/h4>\n<ul>\n<li>\u5728 Frenet S\u2013L \u5e73\u9762&#xff08;\u7eb5\u5411\u5f27\u957f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         s<\/p>\n<p>        s<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span><\/span> \u2013 \u6a2a\u5411\u504f\u79fb <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         l<\/p>\n<p>        l<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><\/span><\/span><\/span><\/span>&#xff09;\u4e2d\u79bb\u6563\u5316\u51fa\u683c\u70b9\u56fe&#xff08;Graph&#xff09;\u3002<\/li>\n<li>\u6bcf\u4e2a\u7eb5\u5411\u91c7\u6837\u4f4d\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          s<\/p>\n<p>          k<\/p>\n<p>        s_k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0a&#xff0c;\u53d6\u82e5\u5e72\u6a2a\u5411\u5019\u9009\u70b9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          l<\/p>\n<p>           k<\/p>\n<p>           ,<\/p>\n<p>           j<\/p>\n<p>        l_{k,j}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u8fb9&#xff1a;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         (<\/p>\n<p>          s<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>          l<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>           ,<\/p>\n<p>           i<\/p>\n<p>         )<\/p>\n<p>        (s_{k-1}, l_{k-1,i})<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>          s<\/p>\n<p>          k<\/p>\n<p>         ,<\/p>\n<p>          l<\/p>\n<p>           k<\/p>\n<p>           ,<\/p>\n<p>           j<\/p>\n<p>         )<\/p>\n<p>        (s_k, l_{k,j})<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u4e00\u6761\u53ef\u80fd\u8def\u5f84\u6bb5\u3002<\/li>\n<li>\u4ee3\u4ef7&#xff1a;\u6bcf\u6761\u8fb9\u90fd\u6709\u4e00\u4e2a\u7efc\u5408\u4ee3\u4ef7&#xff0c;\u7ed3\u5408\u5e73\u6ed1\u6027\u3001\u907f\u969c\u3001\u5b89\u5168\u3001\u6362\u9053\u7b49\u6307\u6807\u3002<\/li>\n<li>\u641c\u7d22&#xff1a;\u7528 DP \u5728\u8fd9\u4e2a\u6709\u5411\u65e0\u73af\u56fe&#xff08;DAG&#xff09;\u4e0a\u627e\u5230\u603b\u4ee3\u4ef7\u6700\u5c0f\u7684\u8def\u5f84\u3002<\/li>\n<\/ul>\n<p>\u7ed3\u679c\u662f\u4e00\u6761\u6298\u7ebf\u578b\u7684\u7c97\u8def\u5f84&#xff0c;\u80fd\u591f\u7ed5\u8fc7\u969c\u788d\u7269&#xff0c;\u5e76\u5728\u5168\u5c40\u4e0a\u4ee3\u4ef7\u6700\u4f18\u3002<\/p>\n<hr \/>\n<h4>2.3.3 Step-by-Step \u8fc7\u7a0b<\/h4>\n<h5>Step 1 \u2014 SL \u6295\u5f71\u4e0e\u53ef\u884c\u533a\u57df\u751f\u6210<\/h5>\n<li>\u5c06\u8f66\u9053\u8fb9\u754c\u548c\u969c\u788d\u7269\u5305\u7edc&#xff08;\u81a8\u80c0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          w<\/p>\n<p>          2<\/p>\n<p>         &#043;<\/p>\n<p>         b<\/p>\n<p>        \\\\frac{w}{2} &#043; b<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0404em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6954em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span>&#xff09;\u6295\u5f71\u5230 S\u2013L \u5e73\u9762&#xff1b;<\/li>\n<li>\u5f97\u5230\u6bcf\u4e2a\u7eb5\u5411\u4f4d\u7f6e\u4e0a\u7684\u53ef\u884c\u6a2a\u5411\u533a\u95f4&#xff1a;<\/li>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         L<\/p>\n<p>          f<\/p>\n<p>          r<\/p>\n<p>          e<\/p>\n<p>          e<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        [<\/p>\n<p>         l<\/p>\n<p>         min<\/p>\n<p>         \u2061<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>        ,<\/p>\n<p>         l<\/p>\n<p>         max<\/p>\n<p>         \u2061<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>        ]<\/p>\n<p>        \u2216<\/p>\n<p>         O<\/p>\n<p>         b<\/p>\n<p>         s<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>       \\\\mathcal{L}_{\\\\mathrm{free}}(s) &#061; [l_{\\\\min}(s), l_{\\\\max}(s)] \\\\setminus \\\\mathrm{Obs}(s)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">free<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">i<\/span><span class=\"mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)]<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2216<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">Obs<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<hr \/>\n<h5>Step 2 \u2014 \u52a8\u6001\u89c4\u5212&#xff08;DP&#xff09;\u641c\u7d22\u7c97\u8def\u5f84<\/h5>\n<p>Step 2.1 \u7f51\u683c\u6784\u5efa<\/p>\n<ul>\n<li>\u7eb5\u5411\u91c7\u6837&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         s<\/p>\n<p>         k<\/p>\n<p>        &#061;<\/p>\n<p>         s<\/p>\n<p>         0<\/p>\n<p>        &#043;<\/p>\n<p>        k<\/p>\n<p>        \u22c5<\/p>\n<p>        \u0394<\/p>\n<p>        s<\/p>\n<p>        ,<\/p>\n<p>        k<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>        ,<\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        \u2026<\/p>\n<p>        ,<\/p>\n<p>        K<\/p>\n<p>       s_k &#061; s_0 &#043; k \\\\cdot \\\\Delta s, \\\\quad k &#061; 0, 1, \\\\dots, K<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u901a\u5e38 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0394<\/p>\n<p>        s<\/p>\n<p>        &#061;<\/p>\n<p>        1<br \/>\n       \u2009\u2063<\/p>\n<p>        \u223c<br \/>\n       \u2009\u2063<\/p>\n<p>        2<br \/>\n       \u2009<\/p>\n<p>        m<\/p>\n<p>       \\\\Delta s &#061; 1\\\\! \\\\sim\\\\! 2\\\\,\\\\mathrm{m}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u223c<\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathrm\">m<\/span><\/span><\/span><\/span><\/span>&#xff1b;<\/p>\n<ul>\n<li>\u6a2a\u5411\u91c7\u6837&#xff1a;\u5728\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          s<\/p>\n<p>          k<\/p>\n<p>        s_k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u53ef\u884c\u533a\u95f4\u5185\u53d6\u82e5\u5e72 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          l<\/p>\n<p>           k<\/p>\n<p>           ,<\/p>\n<p>           j<\/p>\n<p>        l_{k,j}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff08;\u7b49\u95f4\u8ddd\u6216\u4e2d\u5fc3\u52a0\u5bc6&#xff09;&#xff1b;<\/li>\n<li>\u53ef\u884c\u6027\u8fc7\u6ee4&#xff1a;\u82e5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         (<\/p>\n<p>          s<\/p>\n<p>          k<\/p>\n<p>         ,<\/p>\n<p>          l<\/p>\n<p>           k<\/p>\n<p>           ,<\/p>\n<p>           j<\/p>\n<p>         )<\/p>\n<p>        (s_k, l_{k,j})<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u843d\u5728\u969c\u788d\u7269\u81a8\u80c0\u533a\u5185&#xff0c;\u5219\u76f4\u63a5\u5254\u9664\u3002<\/li>\n<\/ul>\n<p>Step 2.2 \u5efa\u7acb\u8f6c\u79fb\u89c4\u5219<\/p>\n<ul>\n<li>\u5141\u8bb8\u7684\u8f6c\u79fb\u9700\u6ee1\u8db3&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2223<\/p>\n<p>            l<\/p>\n<p>             k<\/p>\n<p>             ,<\/p>\n<p>             j<\/p>\n<p>           \u2212<\/p>\n<p>            l<\/p>\n<p>             k<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             ,<\/p>\n<p>             i<\/p>\n<p>           \u0394<\/p>\n<p>           s<\/p>\n<p>         \u2223<\/p>\n<p>        \u2264<\/p>\n<p>         \u03c3<\/p>\n<p>         max<\/p>\n<p>         \u2061<\/p>\n<p>       \\\\left|\\\\frac{l_{k,j} &#8211; l_{k-1,i}}{\\\\Delta s}\\\\right| \\\\le \\\\sigma_{\\\\max}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.8em;vertical-align: -0.65em\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.15em\"><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"\" style=\"width: 0.333em;height: 1.8em\"><\/p>\n<p>             <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.65em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9992em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.5131em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.15em\"><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"\" style=\"width: 0.333em;height: 1.8em\"><\/p>\n<p>             <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.65em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2223<\/p>\n<p>            l<\/p>\n<p>             k<\/p>\n<p>             ,<\/p>\n<p>             j<\/p>\n<p>           \u2212<\/p>\n<p>           2<\/p>\n<p>            l<\/p>\n<p>             k<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             ,<\/p>\n<p>             i<\/p>\n<p>           &#043;<\/p>\n<p>            l<\/p>\n<p>             k<\/p>\n<p>             \u2212<\/p>\n<p>             2<\/p>\n<p>             ,<\/p>\n<p>             h<\/p>\n<p>           \u0394<\/p>\n<p>            s<\/p>\n<p>            2<\/p>\n<p>         \u2223<\/p>\n<p>        \u2264<\/p>\n<p>         \u03b1<\/p>\n<p>         max<\/p>\n<p>         \u2061<\/p>\n<p>       \\\\left|\\\\frac{l_{k,j} &#8211; 2l_{k-1,i} &#043; l_{k-2,h}}{\\\\Delta s^2}\\\\right| \\\\le \\\\alpha_{\\\\max}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.8em;vertical-align: -0.65em\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.15em\"><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"\" style=\"width: 0.333em;height: 1.8em\"><\/p>\n<p>             <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.65em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9992em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7463em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.5131em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.15em\"><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"\" style=\"width: 0.333em;height: 1.8em\"><\/p>\n<p>             <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.65em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0037em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5e76\u4e14\u8be5\u7ebf\u6bb5\u4e0d\u4e0e\u969c\u788d\u7269\u76f8\u4ea4&#xff1b;<\/p>\n<ul>\n<li>\u8fdd\u53cd\u6761\u4ef6\u7684\u8fb9\u4e0d\u5efa\u7acb\u3002<\/li>\n<\/ul>\n<p>Step 2.3 \u5b9a\u4e49\u4ee3\u4ef7\u51fd\u6570<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>          e<\/p>\n<p>          d<\/p>\n<p>          g<\/p>\n<p>          e<\/p>\n<p>        &#061;<\/p>\n<p>         w<\/p>\n<p>          d<\/p>\n<p>          e<\/p>\n<p>          v<\/p>\n<p>         C<\/p>\n<p>          d<\/p>\n<p>          e<\/p>\n<p>          v<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>          c<\/p>\n<p>          u<\/p>\n<p>          r<\/p>\n<p>         C<\/p>\n<p>          c<\/p>\n<p>          u<\/p>\n<p>          r<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>          o<\/p>\n<p>          b<\/p>\n<p>          s<\/p>\n<p>         C<\/p>\n<p>          o<\/p>\n<p>          b<\/p>\n<p>          s<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>          l<\/p>\n<p>          c<\/p>\n<p>         C<\/p>\n<p>          l<\/p>\n<p>          c<\/p>\n<p>       C_{\\\\mathrm{edge}} &#061; w_{\\\\mathrm{dev}} C_{\\\\mathrm{dev}} &#043; w_{\\\\mathrm{cur}} C_{\\\\mathrm{cur}} &#043; w_{\\\\mathrm{obs}} C_{\\\\mathrm{obs}} &#043; w_{\\\\mathrm{lc}} C_{\\\\mathrm{lc}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">edge<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\" style=\"margin-right: 0.0139em\">dev<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\" style=\"margin-right: 0.0139em\">dev<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">cur<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">cur<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">lc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">lc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u504f\u79bb\u4ee3\u4ef7&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>          d<\/p>\n<p>          e<\/p>\n<p>          v<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>         l<\/p>\n<p>          k<\/p>\n<p>          ,<\/p>\n<p>          j<\/p>\n<p>        \u2212<\/p>\n<p>         l<\/p>\n<p>          r<\/p>\n<p>          e<\/p>\n<p>          f<\/p>\n<p>        (<\/p>\n<p>         s<\/p>\n<p>         k<\/p>\n<p>        )<\/p>\n<p>         )<\/p>\n<p>         2<\/p>\n<p>       C_{\\\\mathrm{dev}} &#061; (l_{k,j} &#8211; l_{\\\\mathrm{ref}}(s_k))^2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\" style=\"margin-right: 0.0139em\">dev<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\" style=\"margin-right: 0.0778em\">ref<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u5e73\u6ed1\u6027\u4ee3\u4ef7&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>          c<\/p>\n<p>          u<\/p>\n<p>          r<\/p>\n<p>        &#061;<\/p>\n<p>          (<\/p>\n<p>             l<\/p>\n<p>              k<\/p>\n<p>              ,<\/p>\n<p>              j<\/p>\n<p>            \u2212<\/p>\n<p>            2<\/p>\n<p>             l<\/p>\n<p>              k<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>              ,<\/p>\n<p>              i<\/p>\n<p>            &#043;<\/p>\n<p>             l<\/p>\n<p>              k<\/p>\n<p>              \u2212<\/p>\n<p>              2<\/p>\n<p>              ,<\/p>\n<p>              h<\/p>\n<p>            \u0394<\/p>\n<p>             s<\/p>\n<p>             2<\/p>\n<p>          )<\/p>\n<p>         2<\/p>\n<p>       C_{\\\\mathrm{cur}} &#061; \\\\left(\\\\frac{l_{k,j} &#8211; 2l_{k-1,i} &#043; l_{k-2,h}}{\\\\Delta s^2}\\\\right)^2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">cur<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.004em;vertical-align: -0.65em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9992em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7463em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.5131em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.354em\"><span class=\"\" style=\"top: -3.6029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u969c\u788d\u7269\u8ddd\u79bb\u4ee3\u4ef7&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>          o<\/p>\n<p>          b<\/p>\n<p>          s<\/p>\n<p>        &#061;<\/p>\n<p>        \u03d5<\/p>\n<p>        (<\/p>\n<p>         d<\/p>\n<p>         i<\/p>\n<p>         s<\/p>\n<p>         t<\/p>\n<p>        (<\/p>\n<p>         l<\/p>\n<p>          k<\/p>\n<p>          ,<\/p>\n<p>          j<\/p>\n<p>        ,<\/p>\n<p>        B<\/p>\n<p>        (<\/p>\n<p>         s<\/p>\n<p>         k<\/p>\n<p>        )<\/p>\n<p>        )<\/p>\n<p>        )<\/p>\n<p>       C_{\\\\mathrm{obs}} &#061; \\\\phi(\\\\mathrm{dist}(l_{k,j}, B(s_k)))<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">dist<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)))<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u6362\u9053\u60e9\u7f5a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>           l<\/p>\n<p>           c<\/p>\n<p>        C_{\\\\mathrm{lc}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">lc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u8de8\u8d8a\u8f66\u9053\u4e2d\u5fc3\u7ebf\u5219\u52a0\u56fa\u5b9a\u4ee3\u4ef7\u3002<\/li>\n<\/ul>\n<p>Step 2.4 \u52a8\u6001\u89c4\u5212\u6c42\u6700\u4f18\u8def\u5f84<\/p>\n<ul>\n<li>\u521d\u59cb\u5316&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>         o<\/p>\n<p>         s<\/p>\n<p>         t<\/p>\n<p>        (<\/p>\n<p>         s<\/p>\n<p>         0<\/p>\n<p>        ,<\/p>\n<p>         l<\/p>\n<p>         0<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>       \\\\mathrm{Cost}(s_0, l_0) &#061; 0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">Cost<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u9012\u63a8&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>         o<\/p>\n<p>         s<\/p>\n<p>         t<\/p>\n<p>        (<\/p>\n<p>         s<\/p>\n<p>         k<\/p>\n<p>        ,<\/p>\n<p>         l<\/p>\n<p>          k<\/p>\n<p>          ,<\/p>\n<p>          j<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>          min<\/p>\n<p>          \u2061<\/p>\n<p>           l<\/p>\n<p>            k<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>            ,<\/p>\n<p>            i<\/p>\n<p>          \u2208<\/p>\n<p>          feasible<\/p>\n<p>         [<\/p>\n<p>          C<\/p>\n<p>          o<\/p>\n<p>          s<\/p>\n<p>          t<\/p>\n<p>         (<\/p>\n<p>          s<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>          l<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>           ,<\/p>\n<p>           i<\/p>\n<p>         )<\/p>\n<p>         &#043;<\/p>\n<p>          C<\/p>\n<p>           e<\/p>\n<p>           d<\/p>\n<p>           g<\/p>\n<p>           e<\/p>\n<p>         ]<\/p>\n<p>       \\\\mathrm{Cost}(s_k, l_{k,j}) &#061; \\\\min_{l_{k-1,i} \\\\in \\\\text{feasible}} \\\\left[ \\\\mathrm{Cost}(s_{k-1}, l_{k-1,i}) &#043; C_{\\\\mathrm{edge}} \\\\right]<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">Cost<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1031em;vertical-align: -0.3531em\"><\/span><span class=\"mop\"><span class=\"mop\">min<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0197em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord text mtight\"><span class=\"mord mtight\">feasible<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3531em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">[<\/span><span class=\"mord\"><span class=\"mord mathrm\">Cost<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">edge<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u8bb0\u5f55\u524d\u9a71\u6307\u9488&#xff0c;\u56de\u6eaf\u5f97\u5230\u7c97\u8def\u5f84&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         l<\/p>\n<p>         ~<\/p>\n<p>        (<\/p>\n<p>         s<\/p>\n<p>         0<\/p>\n<p>        )<\/p>\n<p>        ,<\/p>\n<p>         l<\/p>\n<p>         ~<\/p>\n<p>        (<\/p>\n<p>         s<\/p>\n<p>         1<\/p>\n<p>        )<\/p>\n<p>        ,<\/p>\n<p>        \u2026<\/p>\n<p>        ,<\/p>\n<p>         l<\/p>\n<p>         ~<\/p>\n<p>        (<\/p>\n<p>         s<\/p>\n<p>         K<\/p>\n<p>        )<\/p>\n<p>       \\\\tilde{l}(s_0), \\\\tilde{l}(s_1), \\\\dots, \\\\tilde{l}(s_K)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1813em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><\/span><span class=\"\" style=\"top: -3.6134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><\/span><span class=\"\" style=\"top: -3.6134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><\/span><span class=\"\" style=\"top: -3.6134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<hr \/>\n<h5>Step 3 \u2014 \u751f\u6210\u53ef\u884c\u8d70\u5eca&#xff08;Feasible Tunnel&#xff09;<\/h5>\n<li>\n<p>\u4ee5 DP \u7c97\u8def\u5f84\u4e3a\u4e2d\u5fc3&#xff0c;\u5411\u5de6\u53f3\u6269\u5c55\u56fa\u5b9a\u534a\u5bbd \u03b4\\\\delta\u03b4&#xff1b;<\/p>\n<ul>\n<li>\n<p>\u534a\u5bbd \u03b4\\\\delta\u03b4 \u8ba1\u7b97\u65b9\u6cd5&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             \u03b4<\/p>\n<p>             E<\/p>\n<p>            &#061;<\/p>\n<p>              W<\/p>\n<p>              veh<\/p>\n<p>             2<\/p>\n<p>            &#043;<\/p>\n<p>              W<\/p>\n<p>              obs<\/p>\n<p>             2<\/p>\n<p>            &#043;<\/p>\n<p>             d<\/p>\n<p>             safe<\/p>\n<p>           \\\\delta_{\\\\text{E}} &#061; \\\\frac{W_{\\\\text{veh}}}{2} &#043; \\\\frac{W_{\\\\text{obs}}}{2} &#043; d_{\\\\text{safe}}<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">E<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2392em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8942em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4159em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.1389em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">veh<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2392em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8942em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4159em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.1389em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">safe<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>              W<\/p>\n<p>              veh<\/p>\n<p>            W_{\\\\text{veh}}<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">veh<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u8f66\u8f86\u5bbd\u5ea6<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>              W<\/p>\n<p>              obs<\/p>\n<p>            W_{\\\\text{obs}}<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u969c\u788d\u7269\u5bbd\u5ea6<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>              d<\/p>\n<p>              safe<\/p>\n<p>            d_{\\\\text{safe}}<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">safe<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u989d\u5916\u5b89\u5168\u88d5\u5ea6&#xff08;\u53ef\u6839\u636e\u901f\u5ea6\u52a8\u6001\u8c03\u6574&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>              \u03b4<\/p>\n<p>              E<\/p>\n<p>            \u2009\u2063<\/p>\n<p>             &#043;<\/p>\n<p>             &#061;<\/p>\n<p>              k<\/p>\n<p>              v<\/p>\n<p>             \u22c5<\/p>\n<p>             \u2223<\/p>\n<p>              v<\/p>\n<p>              rel<\/p>\n<p>             \u2223<\/p>\n<p>            \\\\delta_{\\\\text{E}} \\\\!&#043;&#061; k_v \\\\cdot |v_{\\\\text{rel}}|<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">E<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mord\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0315em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">rel<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u8fd9\u6837\u5f97\u5230\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             \u03b4<\/p>\n<p>             E<\/p>\n<p>           \\\\delta_{\\\\text{E}}<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">E<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u969c\u788d\u7269\u6a2a\u5411\u5360\u636e\u533a\u7684\u201c\u5b89\u5168\u534a\u5bbd\u201d&#xff0c;\u786e\u4fdd\u8d70\u5eca\u4e0d\u4f1a\u8fc7\u4e8e\u8d34\u8fd1\u969c\u788d\u7269\u8fb9\u7f18\u3002<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           L<\/p>\n<p>            f<\/p>\n<p>            r<\/p>\n<p>            e<\/p>\n<p>            e<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>         \\\\mathcal{L}_{\\\\mathrm{free}}(s)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">free<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u76f8\u4ea4&#xff0c;\u88c1\u526a\u51fa\u5b89\u5168\u8d70\u5eca&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u8d70\u5eca\u4fdd\u8bc1\u4e0d\u4e0e\u969c\u788d\u7269\u91cd\u53e0&#xff0c;\u6240\u6709\u8f68\u8ff9\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          l<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>         l(s)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5747\u9700\u5728\u8d70\u5eca\u8303\u56f4\u5185\u3002<\/p>\n<\/li>\n<hr \/>\n<h5>Step 4 \u2014 QP &#043; \u6837\u6761\u66f2\u7ebf\u5e73\u6ed1\u4f18\u5316<\/h5>\n<li>\u53c2\u6570\u5316\u8def\u5f84&#xff1a;<\/li>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        l<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>         a<\/p>\n<p>         0<\/p>\n<p>        &#043;<\/p>\n<p>         a<\/p>\n<p>         1<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        \u2212<\/p>\n<p>         S<\/p>\n<p>         i<\/p>\n<p>        )<\/p>\n<p>        &#043;<\/p>\n<p>         a<\/p>\n<p>         2<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        \u2212<\/p>\n<p>         S<\/p>\n<p>         i<\/p>\n<p>         )<\/p>\n<p>         2<\/p>\n<p>        &#043;<\/p>\n<p>         a<\/p>\n<p>         3<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        \u2212<\/p>\n<p>         S<\/p>\n<p>         i<\/p>\n<p>         )<\/p>\n<p>         3<\/p>\n<p>       l(s) &#061; a_0 &#043; a_1(s &#8211; S_i) &#043; a_2(s &#8211; S_i)^2 &#043; a_3(s &#8211; S_i)^3<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u786e\u4fdd\u6bb5\u95f4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>         2<\/p>\n<p>       C^2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8fde\u7eed\u3002<\/p>\n<li>\u4f18\u5316\u76ee\u6807&#xff1a;<\/li>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          min<\/p>\n<p>          \u2061<\/p>\n<p>          l<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>         \u222b<\/p>\n<p>          s<\/p>\n<p>          0<\/p>\n<p>          s<\/p>\n<p>          f<\/p>\n<p>         (<\/p>\n<p>          w<\/p>\n<p>          0<\/p>\n<p>        \u2009<\/p>\n<p>          l<\/p>\n<p>          2<\/p>\n<p>         &#043;<\/p>\n<p>          w<\/p>\n<p>          1<\/p>\n<p>        \u2009<\/p>\n<p>          l<\/p>\n<p>           \u2032<\/p>\n<p>           2<\/p>\n<p>         &#043;<\/p>\n<p>          w<\/p>\n<p>          2<\/p>\n<p>        \u2009<\/p>\n<p>          l<\/p>\n<p>           \u2032<\/p>\n<p>           \u2032<\/p>\n<p>           2<\/p>\n<p>         )<\/p>\n<p>        d<\/p>\n<p>        s<\/p>\n<p>       \\\\min_{l(s)} \\\\int_{s_0}^{s_f} \\\\left( w_0\\\\,l^2 &#043; w_1\\\\,l&#039;^2 &#043; w_2\\\\,l&#039;&#039;^2 \\\\right) ds<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3152em;vertical-align: -0.4559em\"><\/span><span class=\"mop\"><span class=\"mop\">min<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">s<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"margin-right: 0.1945em;position: relative;top: -0.0006em\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8593em\"><span class=\"\" style=\"top: -2.3442em;margin-left: -0.1945em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2579em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4559em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u20322<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032\u20322<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span><\/span><\/p>\n<li>\u7ea6\u675f\u6761\u4ef6&#xff1a;\n<ul>\n<li>\u8d70\u5eca\u8fb9\u754c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            l<\/p>\n<p>             l<\/p>\n<p>             o<\/p>\n<p>             w<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>           \u2264<\/p>\n<p>           l<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>           \u2264<\/p>\n<p>            l<\/p>\n<p>             u<\/p>\n<p>             p<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>          l_{\\\\mathrm{low}}(s) \\\\le l(s) \\\\le l_{\\\\mathrm{up}}(s)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\" style=\"margin-right: 0.0139em\">low<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">up<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u66f2\u7387\u9650\u5236<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           \u2223<\/p>\n<p>           \u03ba<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>           \u2223<\/p>\n<p>           \u2264<\/p>\n<p>            \u03ba<\/p>\n<p>            max<\/p>\n<p>            \u2061<\/p>\n<p>          |\\\\kappa(s)| \\\\le \\\\kappa_{\\\\max}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">\u03ba<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03ba<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1b;<\/li>\n<li>\u8d77\u7ec8\u70b9\u8fb9\u754c\u6761\u4ef6\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>2.3.4 \u6570\u5b66\u5efa\u6a21<\/h4>\n<p>E-Step \u4f18\u5316\u95ee\u9898\u53ef\u5f62\u5f0f\u5316\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>              min<\/p>\n<p>              \u2061<\/p>\n<p>              l<\/p>\n<p>              (<\/p>\n<p>              s<\/p>\n<p>              )<\/p>\n<p>             \u222b<\/p>\n<p>              s<\/p>\n<p>              0<\/p>\n<p>              s<\/p>\n<p>              f<\/p>\n<p>            (<\/p>\n<p>             w<\/p>\n<p>             0<\/p>\n<p>           \u2009<\/p>\n<p>             l<\/p>\n<p>             2<\/p>\n<p>            &#043;<\/p>\n<p>             w<\/p>\n<p>             1<\/p>\n<p>           \u2009<\/p>\n<p>             l<\/p>\n<p>              \u2032<\/p>\n<p>              2<\/p>\n<p>            &#043;<\/p>\n<p>             w<\/p>\n<p>             2<\/p>\n<p>           \u2009<\/p>\n<p>             l<\/p>\n<p>              \u2032<\/p>\n<p>              \u2032<\/p>\n<p>              2<\/p>\n<p>            )<br \/>\n           \u2009<\/p>\n<p>            d<\/p>\n<p>            s<\/p>\n<p>            s.t.<\/p>\n<p>             l<\/p>\n<p>              l<\/p>\n<p>              o<\/p>\n<p>              w<\/p>\n<p>            (<\/p>\n<p>            s<\/p>\n<p>            )<\/p>\n<p>            \u2264<\/p>\n<p>            l<\/p>\n<p>            (<\/p>\n<p>            s<\/p>\n<p>            )<\/p>\n<p>            \u2264<\/p>\n<p>             l<\/p>\n<p>              u<\/p>\n<p>              p<\/p>\n<p>            (<\/p>\n<p>            s<\/p>\n<p>            )<\/p>\n<p>            ,<\/p>\n<p>            \u2223<\/p>\n<p>            \u03ba<\/p>\n<p>            (<\/p>\n<p>            s<\/p>\n<p>            )<\/p>\n<p>            \u2223<\/p>\n<p>            \u2264<\/p>\n<p>             \u03ba<\/p>\n<p>             max<\/p>\n<p>             \u2061<\/p>\n<p>            ,<\/p>\n<p>            l<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             0<\/p>\n<p>            )<\/p>\n<p>            &#061;<\/p>\n<p>             l<\/p>\n<p>             0<\/p>\n<p>            ,<\/p>\n<p>             l<\/p>\n<p>             \u2032<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             0<\/p>\n<p>            )<\/p>\n<p>            &#061;<\/p>\n<p>            tan<\/p>\n<p>            \u2061<\/p>\n<p>             \u03c8<\/p>\n<p>             0<\/p>\n<p>       \\\\begin{aligned} \\\\min_{l(s)}\\\\quad &amp; \\\\int_{s_0}^{s_f} \\\\big( w_0\\\\,l^2 &#043; w_1\\\\,l&#039;^2 &#043; w_2\\\\,l&#039;&#039;^2 \\\\big)\\\\,ds \\\\\\\\ \\\\text{s.t.}\\\\quad &amp; l_{\\\\mathrm{low}}(s) \\\\le l(s) \\\\le l_{\\\\mathrm{up}}(s), \\\\\\\\ &amp; |\\\\kappa(s)| \\\\le \\\\kappa_{\\\\max}, \\\\\\\\ &amp; l(s_0)&#061;l_0,\\\\quad l&#039;(s_0)&#061;\\\\tan\\\\psi_0 \\\\end{aligned}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 7.2263em;vertical-align: -3.3632em\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 3.8632em\"><span class=\"\" style=\"top: -5.8632em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.309em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">s<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.966em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -3.7111em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">s.t.<\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -2.2111em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: -0.7111em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 3.3632em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 3.8632em\"><span class=\"\" style=\"top: -5.8632em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right: 0.4445em;position: relative;top: -0.0011em\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4143em\"><span class=\"\" style=\"top: -1.7881em;margin-left: -0.4445em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.8129em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.012em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u20322<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032\u20322<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"delimsizing size1\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3.7111em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\" style=\"margin-right: 0.0139em\">low<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">up<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.2111em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">\u03ba<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03ba<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -0.7111em\"><span class=\"pstrut\" style=\"height: 3.4143em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mop\">tan<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 3.3632em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<hr \/>\n<h4>2.3.5 \u53ef\u89c6\u5316\u793a\u610f<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815182003-689f7a5392745.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe\u4f8b&#xff1a;<\/p>\n<ul>\n<li>\u7070\u8272\u70b9&#xff1a;S\u2013L \u5e73\u9762\u91c7\u6837\u7f51\u683c<\/li>\n<li>\u7ea2\u8272\u77e9\u5f62&#xff1a;\u969c\u788d\u7269\u6295\u5f71&#xff08;\u4e0d\u53ef\u884c\u533a&#xff09;<\/li>\n<li>\u7eff\u8272\u6298\u7ebf&#xff1a;DP \u7c97\u8def\u5f84&#xff08;\u4e25\u683c\u907f\u969c&#xff09;<\/li>\n<li>\u6d45\u84dd\u5e26&#xff1a;\u53ef\u884c\u8d70\u5eca&#xff08;\u88c1\u526a\u540e&#xff09;<\/li>\n<li>\u84dd\u8272\u66f2\u7ebf&#xff1a;QP \u5e73\u6ed1\u8def\u5f84<\/li>\n<li>\u6ce8\u91ca\u6846&#xff08;Dev \/ Curv \/ Obs \/ LC&#xff09;&#xff1a;DP \u8fb9\u4ee3\u4ef7\u9879\u8bf4\u660e<\/li>\n<\/ul>\n<p>&#xff08;\u8fd9\u91cc\u53ef\u63d2\u5165\u6211\u4eec\u7ed8\u5236\u7684\u4e25\u683c\u907f\u969c\u56fe&#xff09;<\/p>\n<hr \/>\n<h4>2.3.6 \u7ed3\u679c\u610f\u4e49<\/h4>\n<ul>\n<li>DP \u7c97\u8def\u5f84&#xff1a;\u89e3\u51b3\u5168\u5c40\u62d3\u6251\u9009\u62e9&#xff08;\u7ed5\u969c\u3001\u6362\u9053&#xff09;&#xff0c;\u4fdd\u8bc1\u65e0\u78b0\u649e&#xff1b;<\/li>\n<li>\u53ef\u884c\u8d70\u5eca&#xff1a;\u5c06 QP \u4f18\u5316\u9650\u5236\u5728\u5b89\u5168\u8303\u56f4\u5185&#xff0c;\u63d0\u9ad8\u6548\u7387\u4e0e\u7a33\u5b9a\u6027&#xff1b;<\/li>\n<li>QP \u5e73\u6ed1\u8def\u5f84&#xff1a;\u63d0\u5347\u8212\u9002\u6027\u548c\u53ef\u63a7\u6027&#xff0c;\u5e76\u4e3a\u901f\u5ea6\u4f18\u5316\u63d0\u4f9b\u66f2\u7387\u4e0a\u754c\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>2.4 M-Step&#xff1a;\u901f\u5ea6\u4f18\u5316\u9636\u6bb5<\/h3>\n<h4>2.4.1 \u80cc\u666f\u95ee\u9898<\/h4>\n<p>E-Step \u5df2\u7ecf\u5728 S\u2013L \u5e73\u9762\u751f\u6210\u4e86\u4e00\u6761 \u5e73\u6ed1\u3001\u907f\u969c\u3001\u5b89\u5168 \u7684\u8def\u5f84\u5f62\u72b6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        l<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>       l(s)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002 M-Step \u7684\u4efb\u52a1\u662f\u5728\u8be5\u8def\u5f84\u4e0a\u5206\u914d\u4e00\u4e2a\u5408\u7406\u7684\u901f\u5ea6\u66f2\u7ebf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        v<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>       v(s)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        v<\/p>\n<p>        (<\/p>\n<p>        t<\/p>\n<p>        )<\/p>\n<p>       v(t)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f7f\u8f66\u8f86\u5728\u52a8\u6001\u73af\u5883\u4e2d\u65e2\u80fd\u9ad8\u6548\u884c\u9a76&#xff0c;\u53c8\u80fd\u6ee1\u8db3 \u5b89\u5168\u3001\u8212\u9002\u548c\u52a8\u529b\u5b66\u7ea6\u675f\u3002<\/p>\n<p>\u5982\u679c\u4e0d\u8fdb\u884c\u901f\u5ea6\u4f18\u5316&#xff0c;\u5e38\u89c1\u95ee\u9898\u5305\u62ec&#xff1a;<\/p>\n<ul>\n<li>\u65e0\u6cd5\u6b63\u786e\u5904\u7406\u52a8\u6001\u969c\u788d\u7269\u7684\u4ea4\u4e92&#xff08;\u8ba9\u884c\u3001\u8d85\u8f66\u3001\u8ddf\u968f\u7b49&#xff09;&#xff1b;<\/li>\n<li>\u901f\u5ea6\u53d8\u5316\u4e0d\u5e73\u6ed1&#xff0c;\u4e58\u5750\u4f53\u9a8c\u5dee&#xff1b;<\/li>\n<li>\u8d85\u8fc7\u8f66\u8f86\u52a8\u529b\u5b66\u6781\u9650&#xff08;\u52a0\u901f\u5ea6\u3001\u52a0\u52a0\u901f\u5ea6\u8d85\u6807&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u56e0\u6b64&#xff0c;M-Step \u4f1a\u5c06\u969c\u788d\u7269\u4e0e\u8def\u5f84\u7ed3\u5408\u6295\u5f71\u5230 S\u2013T \u5e73\u9762&#xff0c;\u5148\u7528 \u52a8\u6001\u89c4\u5212&#xff08;DP&#xff09; \u5728\u65f6\u7a7a\u57df\u9009\u62e9\u4e00\u6761\u5b89\u5168\u7684\u901f\u5ea6\u66f2\u7ebf&#xff0c;\u518d\u7528 \u4e8c\u6b21\u89c4\u5212&#xff08;QP&#xff09; \u8fdb\u884c\u5e73\u6ed1\u4f18\u5316\u3002<\/p>\n<hr \/>\n<h4>2.4.2 \u6838\u5fc3\u601d\u60f3<\/h4>\n<li>\u6295\u5f71\n<ul>\n<li>\u5c06\u8def\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           l<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>          l(s)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0e\u52a8\u6001\u969c\u788d\u7269\u7684\u9884\u6d4b\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>            y<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          (x_{obs}(t), y_{obs}(t))<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span> \u6295\u5f71\u5230 S\u2013T \u5e73\u9762&#xff08;Station\u2013Time&#xff09;\u3002<\/li>\n<li>\u969c\u788d\u7269\u9884\u6d4b\u8f68\u8ff9\u901a\u8fc7 Frenet \u8f6c\u6362\u5f97\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            s<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          s_{obs}(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            l<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          l_{obs}(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u7ed3\u5408\u6a2a\u5411\u91cd\u53e0\u6761\u4ef6\u751f\u6210\u969c\u788d\u7269\u7981\u5165\u533a\u3002<\/li>\n<\/ul>\n<\/li>\n<li>DP \u641c\u7d22\n<ul>\n<li>\u5728 S\u2013T \u5e73\u9762\u641c\u7d22\u4e00\u6761\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           (<\/p>\n<p>            s<\/p>\n<p>            0<\/p>\n<p>           ,<\/p>\n<p>            t<\/p>\n<p>            0<\/p>\n<p>           )<\/p>\n<p>          (s_0, t_0)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           (<\/p>\n<p>            s<\/p>\n<p>            f<\/p>\n<p>           ,<\/p>\n<p>            t<\/p>\n<p>            f<\/p>\n<p>           )<\/p>\n<p>          (s_f, t_f)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u7c97\u7565\u66f2\u7ebf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          s(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u907f\u5f00\u969c\u788d\u7269\u65f6\u7a7a\u5360\u636e\u533a&#xff0c;\u5904\u7406\u907f\u969c\u4e0e\u4ea4\u4e92\u7b56\u7565\u3002<\/li>\n<\/ul>\n<\/li>\n<li>QP \u4f18\u5316\n<ul>\n<li>\u5728 DP \u7ed3\u679c\u7684\u5b89\u5168\u8d70\u5eca\u5185\u4f18\u5316\u901f\u5ea6\u66f2\u7ebf&#xff0c;\u786e\u4fdd\u5e73\u6ed1\u6027\u4e0e\u52a8\u529b\u5b66\u53ef\u884c\u6027\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u8f93\u51fa\n<ul>\n<li>\u751f\u6210\u6700\u7ec8\u901f\u5ea6\u2013\u65f6\u95f4\u66f2\u7ebf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           v<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          v(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e0e E-Step \u8def\u5f84\u5408\u6210\u5b8c\u6574\u7684\u65f6\u7a7a\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>           y<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          (x(t), y(t))<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>2.4.3 Step-by-Step \u8fc7\u7a0b<\/h4>\n<h5>Step 1 \u2014 ST \u6295\u5f71\u4e0e\u5b89\u5168\u533a\u57df\u751f\u6210<\/h5>\n<ul>\n<li>\n<p>\u8def\u5f84\u6620\u5c04&#xff1a;\u5c06 E-Step \u8def\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          l<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>         l(s)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8f6c\u6362\u4e3a Frenet \u5750\u6807\u7cfb\u4e0b\u7684\u7eb5\u5411\u4f4d\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          s<\/p>\n<p>         s<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<\/li>\n<li>\n<p>\u969c\u788d\u7269\u9884\u6d4b&#xff1a;\u83b7\u53d6\u611f\u77e5\u4e0e\u9884\u6d4b\u6a21\u5757\u63d0\u4f9b\u7684\u969c\u788d\u7269\u672a\u6765\u8f68\u8ff9&#xff0c;\u5e76\u8f6c\u6362\u5230 Frenet \u5750\u6807\u5f97\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           s<\/p>\n<p>            o<\/p>\n<p>            b<\/p>\n<p>            s<\/p>\n<p>          (<\/p>\n<p>          t<\/p>\n<p>          )<\/p>\n<p>         s_{obs}(t)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u533a\u95f4\u3002<\/p>\n<\/li>\n<li>\n<p>\u65f6\u95f4\u5f15\u5165&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u521d\u59cb\u53c2\u8003\u8def\u5f84\u5047\u8bbe\u8f66\u8f86\u4ee5\u671f\u671b\u901f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             v<\/p>\n<p>              r<\/p>\n<p>              e<\/p>\n<p>              f<\/p>\n<p>           v_{ref}<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">re<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u884c\u9a76&#xff0c;\u901a\u8fc7<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            t<\/p>\n<p>            (<\/p>\n<p>            s<\/p>\n<p>            )<\/p>\n<p>            &#061;<\/p>\n<p>             \u222b<\/p>\n<p>              s<\/p>\n<p>              0<\/p>\n<p>             s<\/p>\n<p>             1<\/p>\n<p>              v<\/p>\n<p>              (<\/p>\n<p>               s<\/p>\n<p>               \u2032<\/p>\n<p>              )<\/p>\n<p>           \u2009<\/p>\n<p>            d<\/p>\n<p>             s<\/p>\n<p>             \u2032<\/p>\n<p>           t(s) &#061; \\\\int_{s_0}^{s} \\\\frac{1}{v(s&#039;)} \\\\, ds&#039;<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3793em;vertical-align: -0.52em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"margin-right: 0.1945em;position: relative;top: -0.0006em\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8593em\"><span class=\"\" style=\"top: -2.3442em;margin-left: -0.1945em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2579em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4559em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6828em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5173\u8054\u7eb5\u5411\u4f4d\u7f6e\u4e0e\u65f6\u95f4\u3002<\/p>\n<\/li>\n<li>\n<p>\u5728\u8fed\u4ee3\u4e2d&#xff0c;\u6bcf\u6b21 M-Step \u90fd\u57fa\u4e8e E-Step \u66f4\u65b0\u7684\u8def\u5f84\u91cd\u65b0\u8ba1\u7b97\u8be5\u6620\u5c04\u3002<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u5b89\u5168\u533a\u57df&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           T<\/p>\n<p>           free<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>          &#061;<\/p>\n<p>           R<\/p>\n<p>           &#043;<\/p>\n<p>          \u2216<\/p>\n<p>          O<\/p>\n<p>          b<\/p>\n<p>           s<\/p>\n<p>            S<\/p>\n<p>            T<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>         T_{\\\\text{free}}(s) &#061; R^&#043; \\\\setminus Obs_{ST}(s)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">free<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0213em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7713em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">&#043;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2216<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">ST<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          O<\/p>\n<p>          b<\/p>\n<p>           s<\/p>\n<p>            S<\/p>\n<p>            T<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>         Obs_{ST}(s)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">ST<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u969c\u788d\u7269\u5360\u636e\u7684\u65f6\u95f4\u533a\u95f4\u96c6\u5408\u3002<\/p>\n<\/li>\n<\/ul>\n<hr \/>\n<h5>Step 2 \u2014 \u52a8\u6001\u89c4\u5212&#xff08;DP&#xff09;\u641c\u7d22\u901f\u5ea6\u66f2\u7ebf<\/h5>\n<p>2.1 \u7f51\u683c\u6784\u5efa<\/p>\n<ul>\n<li>\u7eb5\u5411\u91c7\u6837&#xff1a;\u6cbf\u8def\u5f84\u5747\u5300\u91c7\u6837 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          s<\/p>\n<p>          k<\/p>\n<p>        s_k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1b;<\/li>\n<li>\u65f6\u95f4\u91c7\u6837&#xff1a;\u6bcf\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          s<\/p>\n<p>          k<\/p>\n<p>        s_k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5bf9\u5e94\u82e5\u5e72\u53ef\u80fd\u5230\u8fbe\u65f6\u95f4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          t<\/p>\n<p>           k<\/p>\n<p>           ,<\/p>\n<p>           j<\/p>\n<p>        t_{k,j}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9012em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1b;<\/li>\n<li>\u53ef\u884c\u6027\u8fc7\u6ee4&#xff1a;\u5254\u9664\u843d\u5728\u969c\u788d\u7269 ST \u533a\u57df\u5185\u7684\u70b9\u3002<\/li>\n<\/ul>\n<p>2.2 \u8f6c\u79fb\u89c4\u5219<\/p>\n<ul>\n<li>\n<p>\u5e73\u5747\u901f\u5ea6\u9650\u5236&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          0<\/p>\n<p>          &lt;<\/p>\n<p>            \u0394<\/p>\n<p>            s<\/p>\n<p>            \u0394<\/p>\n<p>            t<\/p>\n<p>          \u2264<\/p>\n<p>           v<\/p>\n<p>           max<\/p>\n<p>           \u2061<\/p>\n<p>          (<\/p>\n<p>           s<\/p>\n<p>           k<\/p>\n<p>          )<\/p>\n<p>         0 &lt; \\\\frac{\\\\Delta s}{\\\\Delta t} \\\\le v_{\\\\max}(s_k)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6835em;vertical-align: -0.0391em\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2173em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8723em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u52a0\u901f\u5ea6\u9650\u5236&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          \u2061<\/p>\n<p>           a<\/p>\n<p>           min<\/p>\n<p>           \u2061<\/p>\n<p>          \u2264<\/p>\n<p>            \u0394<\/p>\n<p>            v<\/p>\n<p>            \u0394<\/p>\n<p>            t<\/p>\n<p>          \u2264<\/p>\n<p>           a<\/p>\n<p>           max<\/p>\n<p>           \u2061<\/p>\n<p>         \u2061a_{\\\\min} \\\\le \\\\frac{\\\\Delta v}{\\\\Delta t} \\\\le a_{\\\\max}<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.786em;vertical-align: -0.15em\"><\/span><span class=\"mord\">\u2061<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">i<\/span><span class=\"mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2173em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8723em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>jerk \u9650\u5236\u53ef\u4f5c\u4e3a\u8f6f\u7ea6\u675f\u6216\u4ee3\u4ef7\u9879\u3002<\/p>\n<\/li>\n<\/ul>\n<p>2.3 \u4ee3\u4ef7\u51fd\u6570<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>         edge<\/p>\n<p>        &#061;<\/p>\n<p>         w<\/p>\n<p>         time<\/p>\n<p>         C<\/p>\n<p>         time<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         acc<\/p>\n<p>         C<\/p>\n<p>         acc<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         jerk<\/p>\n<p>         C<\/p>\n<p>         jerk<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         eff<\/p>\n<p>         C<\/p>\n<p>         eff<\/p>\n<p>       C_{\\\\text{edge}} &#061; w_{\\\\text{time}}C_{\\\\text{time}} &#043; w_{\\\\text{acc}}C_{\\\\text{acc}} &#043; w_{\\\\text{jerk}}C_{\\\\text{jerk}} &#043; w_{\\\\text{eff}}C_{\\\\text{eff}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">edge<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">time<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">time<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">acc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">acc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">jerk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">jerk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">eff<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">eff<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          time<\/p>\n<p>        C_{\\\\text{time}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">time<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u603b\u884c\u9a76\u65f6\u95f4<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          acc<\/p>\n<p>        C_{\\\\text{acc}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">acc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u52a0\u901f\u5ea6\u5e73\u65b9\u548c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          jerk<\/p>\n<p>        C_{\\\\text{jerk}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">jerk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;jerk \u5e73\u65b9\u548c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          eff<\/p>\n<p>        C_{\\\\text{eff}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">eff<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u6548\u7387\u60e9\u7f5a&#xff08;\u4e0e\u671f\u671b\u901f\u5ea6\u504f\u5dee&#xff09;<\/li>\n<\/ul>\n<p>2.4 \u6c42\u89e3\u4e0e\u56de\u6eaf<\/p>\n<ul>\n<li>\n<p>\u521d\u59cb\u5316&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          C<\/p>\n<p>          o<\/p>\n<p>          s<\/p>\n<p>          t<\/p>\n<p>          (<\/p>\n<p>           s<\/p>\n<p>           0<\/p>\n<p>          ,<\/p>\n<p>           t<\/p>\n<p>           0<\/p>\n<p>          )<\/p>\n<p>          &#061;<\/p>\n<p>          0<\/p>\n<p>         Cost(s_0, t_0) &#061; 0<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u9012\u63a8&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          C<\/p>\n<p>          o<\/p>\n<p>          s<\/p>\n<p>          t<\/p>\n<p>          (<\/p>\n<p>           s<\/p>\n<p>           k<\/p>\n<p>          ,<\/p>\n<p>           t<\/p>\n<p>            k<\/p>\n<p>            ,<\/p>\n<p>            j<\/p>\n<p>          )<\/p>\n<p>          &#061;<\/p>\n<p>            min<\/p>\n<p>            \u2061<\/p>\n<p>             t<\/p>\n<p>              k<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>              ,<\/p>\n<p>              i<\/p>\n<p>            \u2208<\/p>\n<p>            f<\/p>\n<p>            e<\/p>\n<p>            a<\/p>\n<p>            s<\/p>\n<p>            i<\/p>\n<p>            b<\/p>\n<p>            l<\/p>\n<p>            e<\/p>\n<p>           [<\/p>\n<p>           C<\/p>\n<p>           o<\/p>\n<p>           s<\/p>\n<p>           t<\/p>\n<p>           (<\/p>\n<p>            s<\/p>\n<p>             k<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>           ,<\/p>\n<p>            t<\/p>\n<p>             k<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             ,<\/p>\n<p>             i<\/p>\n<p>           )<\/p>\n<p>           &#043;<\/p>\n<p>            C<\/p>\n<p>            edge<\/p>\n<p>           ]<\/p>\n<p>         Cost(s_k, t_{k,j}) &#061; \\\\min_{t_{k-1,i} \\\\in feasible} \\\\left[ Cost(s_{k-1}, t_{k-1,i}) &#043; C_{\\\\text{edge}} \\\\right]<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1031em;vertical-align: -0.3531em\"><\/span><span class=\"mop\"><span class=\"mop\">min<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2901em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mord mathnormal mtight\">s<\/span><span class=\"mord mathnormal mtight\">ib<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal mtight\">e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3531em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">os<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">edge<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u56de\u6eaf\u5f97\u5230\u7c97\u65f6\u95f4\u2013\u4f4d\u7f6e\u66f2\u7ebf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           t<\/p>\n<p>           ~<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>         \\\\tilde{t}(s)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1019em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8519em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><span class=\"\" style=\"top: -3.5341em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<\/li>\n<\/ul>\n<hr \/>\n<h5>Step 3 \u2014 \u751f\u6210\u901f\u5ea6\u8d70\u5eca&#xff08;Feasible ST Tunnel&#xff09;<\/h5>\n<ul>\n<li>\n<p>\u4ee5 DP \u7c97\u66f2\u7ebf\u4e3a\u4e2d\u5fc3&#xff0c;\u7ed9\u6bcf\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           s<\/p>\n<p>           k<\/p>\n<p>         s_k<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5206\u914d\u65f6\u95f4\u533a\u95f4\u4e0a\u4e0b\u754c&#xff0c;\u907f\u5f00\u969c\u788d\u7269 ST \u5360\u636e\u533a&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u65f6\u95f4\u533a\u95f4\u4e0a\u4e0b\u754c\u786e\u5b9a\u65b9\u6cd5&#xff1a;<\/p>\n<li>\n<p>\u521d\u59cb\u533a\u95f4&#xff1a;\u6839\u636e DP \u7c97\u66f2\u7ebf\u7684\u65f6\u95f4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             t<\/p>\n<p>             ~<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             k<\/p>\n<p>            )<\/p>\n<p>           \\\\tilde{t}(s_k)<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1019em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8519em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><span class=\"\" style=\"top: -3.5341em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5728\u5176\u4e0a\u4e0b\u6269\u5c55\u56fa\u5b9a\u65f6\u95f4\u88d5\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             \u03b4<\/p>\n<p>             t<\/p>\n<p>           \\\\delta_t<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             t<\/p>\n<p>             low<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             k<\/p>\n<p>            )<\/p>\n<p>            &#061;<\/p>\n<p>             t<\/p>\n<p>             ~<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             k<\/p>\n<p>            )<\/p>\n<p>            \u2212<\/p>\n<p>             \u03b4<\/p>\n<p>             t<\/p>\n<p>            ,<\/p>\n<p>             t<\/p>\n<p>             up<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             k<\/p>\n<p>            )<\/p>\n<p>            &#061;<\/p>\n<p>             t<\/p>\n<p>             ~<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             k<\/p>\n<p>            )<\/p>\n<p>            &#043;<\/p>\n<p>             \u03b4<\/p>\n<p>             t<\/p>\n<p>           t_{\\\\text{low}}(s_k) &#061; \\\\tilde{t}(s_k) &#8211; \\\\delta_t,\\\\quad t_{\\\\text{up}}(s_k) &#061; \\\\tilde{t}(s_k) &#043; \\\\delta_t<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">low<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1019em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8519em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><span class=\"\" style=\"top: -3.5341em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">up<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1019em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8519em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><span class=\"\" style=\"top: -3.5341em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             \u03b4<\/p>\n<p>             t<\/p>\n<p>           \\\\delta_t<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ef\u6839\u636e\u901f\u5ea6\u3001\u52a0\u901f\u5ea6\u7ea6\u675f\u52a8\u6001\u8c03\u6574&#xff0c;\u4f8b\u5982&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             \u03b4<\/p>\n<p>             t<\/p>\n<p>            &#061;<\/p>\n<p>             t<\/p>\n<p>             base<\/p>\n<p>            &#043;<\/p>\n<p>             k<\/p>\n<p>             a<\/p>\n<p>            \u22c5<\/p>\n<p>            \u2223<\/p>\n<p>             a<\/p>\n<p>             max<\/p>\n<p>            \u2223<\/p>\n<p>           \\\\delta_t &#061; t_{\\\\text{base}} &#043; k_a \\\\cdot |a_{\\\\text{max}}|<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0379em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7651em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">base<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0315em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">max<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<\/li>\n<li>\n<p>\u5b89\u5168\u88c1\u526a&#xff1a;\u4e0e\u969c\u788d\u7269 ST \u5360\u636e\u533a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            O<\/p>\n<p>            b<\/p>\n<p>             s<\/p>\n<p>              S<\/p>\n<p>              T<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             k<\/p>\n<p>            )<\/p>\n<p>           Obs_{ST}(s_k)<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">ST<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u505a\u5dee\u96c6\u8fd0\u7b97&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            [<\/p>\n<p>             t<\/p>\n<p>             low<\/p>\n<p>            ,<\/p>\n<p>            \u00a0<\/p>\n<p>             t<\/p>\n<p>             up<\/p>\n<p>            ]<\/p>\n<p>            \u2190<\/p>\n<p>            [<\/p>\n<p>             t<\/p>\n<p>             low<\/p>\n<p>            ,<\/p>\n<p>            \u00a0<\/p>\n<p>             t<\/p>\n<p>             up<\/p>\n<p>            ]<\/p>\n<p>            \u2216<\/p>\n<p>            O<\/p>\n<p>            b<\/p>\n<p>             s<\/p>\n<p>              S<\/p>\n<p>              T<\/p>\n<p>            (<\/p>\n<p>             s<\/p>\n<p>             k<\/p>\n<p>            )<\/p>\n<p>           [t_{\\\\text{low}},\\\\ t_{\\\\text{up}}] \\\\gets [t_{\\\\text{low}},\\\\ t_{\\\\text{up}}] \\\\setminus Obs_{ST}(s_k)<\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">low<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">up<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">low<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">up<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2216<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">ST<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u786e\u4fdd\u65f6\u95f4\u8d70\u5eca\u4e0d\u4e0e\u969c\u788d\u7269\u91cd\u53e0\u3002<\/p>\n<\/li>\n<li>\n<p>\u53ef\u884c\u6027\u68c0\u67e5&#xff1a;\u5982\u679c\u88c1\u526a\u540e\u533a\u95f4\u4e3a\u7a7a&#xff0c;\u5219\u9700\u56de\u9000\u5230 E-Step \u91cd\u65b0\u89c4\u5212\u8def\u5f84\u3002<\/p>\n<\/li>\n<\/li>\n<li>\n<p>\u6700\u7ec8\u5f97\u5230\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          {<\/p>\n<p>          [<\/p>\n<p>           t<\/p>\n<p>           low<\/p>\n<p>          (<\/p>\n<p>           s<\/p>\n<p>           k<\/p>\n<p>          )<\/p>\n<p>          ,<\/p>\n<p>          \u00a0<\/p>\n<p>           t<\/p>\n<p>           up<\/p>\n<p>          (<\/p>\n<p>           s<\/p>\n<p>           k<\/p>\n<p>          )<\/p>\n<p>          ]<\/p>\n<p>          }<\/p>\n<p>         \\\\{[t_{\\\\text{low}}(s_k),\\\\ t_{\\\\text{up}}(s_k)]\\\\}<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mopen\">{[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">low<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">up<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)]}<\/span><\/span><\/span><\/span><\/span> \u7ec4\u6210 Feasible ST Tunnel&#xff0c;\u4f9b QP \u4f18\u5316\u9636\u6bb5\u4f7f\u7528\u3002<\/p>\n<\/li>\n<\/ul>\n<hr \/>\n<h5>Step 4 \u2014 QP \u5e73\u6ed1\u901f\u5ea6\u66f2\u7ebf<\/h5>\n<ul>\n<li>\n<p>\u4f18\u5316\u53d8\u91cf&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          s<\/p>\n<p>          (<\/p>\n<p>          t<\/p>\n<p>          )<\/p>\n<p>         s(t)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          v<\/p>\n<p>          (<\/p>\n<p>          t<\/p>\n<p>          )<\/p>\n<p>         v(t)<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u76ee\u6807\u51fd\u6570&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          min<\/p>\n<p>          \u2061<\/p>\n<p>           \u2211<\/p>\n<p>           i<\/p>\n<p>           [<\/p>\n<p>            w<\/p>\n<p>            a<\/p>\n<p>            a<\/p>\n<p>            i<\/p>\n<p>            2<\/p>\n<p>           &#043;<\/p>\n<p>            w<\/p>\n<p>            j<\/p>\n<p>            j<\/p>\n<p>            i<\/p>\n<p>            2<\/p>\n<p>           &#043;<\/p>\n<p>            w<\/p>\n<p>            v<\/p>\n<p>           (<\/p>\n<p>            v<\/p>\n<p>            i<\/p>\n<p>           \u2212<\/p>\n<p>            v<\/p>\n<p>            des<\/p>\n<p>            )<\/p>\n<p>            2<\/p>\n<p>           ]<\/p>\n<p>         \\\\min \\\\sum_i \\\\left[ w_a a_i^2 &#043; w_j j_i^2 &#043; w_v (v_i &#8211; v_{\\\\text{des}})^2 \\\\right]<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2em;vertical-align: -0.35em\"><\/span><span class=\"mop\">min<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.162em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">[<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.0572em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">des<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u7ea6\u675f\u6761\u4ef6&#xff1a;<\/p>\n<ul>\n<li>ST \u8d70\u5eca\u7ea6\u675f<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           0<\/p>\n<p>           \u2264<\/p>\n<p>            v<\/p>\n<p>            i<\/p>\n<p>           \u2264<\/p>\n<p>            v<\/p>\n<p>            max<\/p>\n<p>            \u2061<\/p>\n<p>           (<\/p>\n<p>            s<\/p>\n<p>            i<\/p>\n<p>           )<\/p>\n<p>          0 \\\\le v_i \\\\le v_{\\\\max}(s_i)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7804em;vertical-align: -0.136em\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            a<\/p>\n<p>            min<\/p>\n<p>            \u2061<\/p>\n<p>           \u2264<\/p>\n<p>            a<\/p>\n<p>            i<\/p>\n<p>           \u2264<\/p>\n<p>            a<\/p>\n<p>            max<\/p>\n<p>            \u2061<\/p>\n<p>          a_{\\\\min} \\\\le a_i \\\\le a_{\\\\max}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">i<\/span><span class=\"mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>jerk \u9650\u5236<\/li>\n<li>\u8d77\u70b9\/\u7ec8\u70b9\u901f\u5ea6\u6761\u4ef6<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815182005-689f7a558cae4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<hr \/>\n<h4>2.4.4 E\u2013M \u4ea4\u4e92\u673a\u5236<\/h4>\n<ul>\n<li>M-Step \u68c0\u67e5\u5f53\u524d\u8def\u5f84\u4e0e\u969c\u788d\u7269\u7684\u65f6\u7a7a\u51b2\u7a81&#xff1a;\n<ul>\n<li>\u65e0\u51b2\u7a81 \u2192 \u76f4\u63a5\u4f18\u5316\u901f\u5ea6\u66f2\u7ebf&#xff1b;<\/li>\n<li>\u6709\u51b2\u7a81 \u2192 \u8fd4\u56de E-Step \u91cd\u65b0\u4f18\u5316\u8def\u5f84&#xff08;\u53ef\u80fd\u6362\u9053\u6216\u6a2a\u5411\u8c03\u6574&#xff09;\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u6bcf\u6b21\u8fed\u4ee3\u90fd\u4f1a\u57fa\u4e8e\u6700\u65b0\u7684\u8def\u5f84\u91cd\u65b0\u8ba1\u7b97 ST \u6295\u5f71\u548c\u901f\u5ea6\u66f2\u7ebf&#xff0c;\u4ece\u800c\u9010\u6b65\u903c\u8fd1\u540c\u65f6\u6ee1\u8db3\u7a7a\u95f4\u4e0e\u65f6\u95f4\u53ef\u884c\u6027\u7684\u89e3\u3002<\/li>\n<\/ul>\n<hr \/>\n<h4>2.4.5 \u7ed3\u679c\u610f\u4e49<\/h4>\n<ul>\n<li>DP \u66f2\u7ebf&#xff1a;\u63d0\u4f9b\u5168\u5c40\u65f6\u5e8f\u7b56\u7565&#xff08;\u8ba9\u884c\u3001\u8ddf\u968f\u3001\u8d85\u8f66&#xff09;\u3002<\/li>\n<li>\u901f\u5ea6\u8d70\u5eca&#xff1a;\u9650\u5236 QP \u4f18\u5316\u5728\u5b89\u5168\u8303\u56f4\u5185&#xff0c;\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002<\/li>\n<li>QP \u66f2\u7ebf&#xff1a;\u4fdd\u8bc1\u5e73\u6ed1\u3001\u8212\u9002\u548c\u52a8\u529b\u5b66\u53ef\u884c\u6027\u3002<\/li>\n<li>\u5408\u6210\u65f6\u7a7a\u8f68\u8ff9&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         ,<\/p>\n<p>         v<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         ,<\/p>\n<p>         a<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         )<\/p>\n<p>        (x(t), y(t), v(t), a(t))<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span> \u4ea4\u7ed9\u63a7\u5236\u5668\u6267\u884c\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>2.5 E-Step \u4e0e M-Step \u7684\u4ea4\u4e92\u673a\u5236<\/h3>\n<h4>2.5.1 \u6982\u8ff0<\/h4>\n<p>\u5728 Apollo EM Planner \u4e2d&#xff0c;E-Step&#xff08;S\u2013L \u7a7a\u95f4\u7684\u8def\u5f84\u89c4\u5212&#xff09;\u4e0e M-Step&#xff08;S\u2013T \u7a7a\u95f4\u7684\u901f\u5ea6\u89c4\u5212&#xff09;\u901a\u8fc7 \u7d27\u5bc6\u8fed\u4ee3\u5faa\u73af \u534f\u4f5c&#xff0c;\u786e\u4fdd\u6700\u7ec8\u751f\u6210\u7684\u8f68\u8ff9\u65e2 \u4e0d\u78b0\u649e \u53c8 \u52a8\u529b\u5b66\u53ef\u884c\u3002 \u4ea4\u4e92\u7684\u5fc5\u8981\u6027\u5728\u4e8e&#xff1a;<\/p>\n<ul>\n<li>E-Step \u89e3\u51b3 \u7a7a\u95f4\u53ef\u884c\u6027\u4e0e\u62d3\u6251\u9009\u62e9&#xff08;\u4fdd\u6301\u8f66\u9053\u3001\u6362\u9053\u3001\u907f\u9759\u6001\u969c\u788d\u7269&#xff09;\u3002<\/li>\n<li>M-Step \u89e3\u51b3 \u65f6\u95f4\u53ef\u884c\u6027&#xff08;\u907f\u52a8\u6001\u969c\u788d\u7269\u3001\u4fdd\u8bc1\u52a0\u51cf\u901f\u8212\u9002&#xff09;\u3002<\/li>\n<li>\u4e00\u6761\u7a7a\u95f4\u4e0a\u53ef\u884c\u7684\u8def\u5f84&#xff0c;\u5728\u65f6\u95f4\u57df\u4e0a\u53ef\u80fd\u4f9d\u7136\u4e0d\u53ef\u884c&#xff08;\u4f8b\u5982\u524d\u65b9\u6709\u79fb\u52a8\u969c\u788d\u7269\u963b\u6321&#xff09;\u3002<\/li>\n<\/ul>\n<hr \/>\n<h4>2.5.2 \u8fed\u4ee3\u6d41\u7a0b<\/h4>\n<li>\u521d\u59cb\u8def\u5f84\u751f\u6210&#xff08;E-Step&#xff09;\n<ul>\n<li>\u57fa\u4e8e\u8def\u7531\u548c\u5730\u56fe\u6a21\u5757\u63d0\u4f9b\u7684 \u53c2\u8003\u7ebf\u3002<\/li>\n<li>\u5728 S\u2013L \u5e73\u9762\u6267\u884c \u52a8\u6001\u89c4\u5212&#xff08;DP&#xff09;\u7c97\u641c\u7d22 &#043; \u4e8c\u6b21\u89c4\u5212&#xff08;QP&#xff09;\u5e73\u6ed1&#xff0c;\u5f97\u5230\u4e00\u6761\u65e0\u9759\u6001\u969c\u788d\u7269\u78b0\u649e\u4e14\u66f2\u7387\u5e73\u6ed1\u7684\u6a2a\u5411\u8f68\u8ff9 l(s)l(s)l(s)\u3002<\/li>\n<li>\u8f93\u51fa\u8def\u5f84\u89e3\u51b3\u4e86 \u201c\u8d70\u54ea\u6761\u9053\u3001\u7ed5\u54ea\u8fb9\u969c\u201d \u7684\u5168\u5c40\u7a7a\u95f4\u51b3\u7b56\u95ee\u9898\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u6295\u5f71\u5230\u65f6\u95f4\u57df&#xff08;M-Step \u8f93\u5165&#xff09;\n<ul>\n<li>\u5c06 E-Step \u8f68\u8ff9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           l<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>          l(s)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8f6c\u6362\u4e3a\u7b1b\u5361\u5c14\u5750\u6807 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>           y<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          (x(s), y(s))<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u5c06\u52a8\u6001\u969c\u788d\u7269\u7684\u9884\u6d4b\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           (<\/p>\n<p>            x<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>            y<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          (x_{obs}(t), y_{obs}(t))<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span> \u8f6c\u6362\u5230 Frenet \u5750\u6807\u7cfb <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           (<\/p>\n<p>            s<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>            l<\/p>\n<p>             o<\/p>\n<p>             b<\/p>\n<p>             s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          (s_{obs}(t), l_{obs}(t))<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u5f97\u5230 S\u2013T \u5e73\u9762\u7684 \u969c\u788d\u7269\u7981\u5165\u533a&#xff08;Obstacle Forbidden Zone&#xff09;\u3002<\/li>\n<\/ul>\n<\/li>\n<li>S\u2013T \u78b0\u649e\u68c0\u6d4b\n<ul>\n<li>\u68c0\u67e5\u8f66\u8f86\u6cbf\u8def\u5f84\u7684\u7eb5\u5411\u4f4d\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          s(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u4e0e\u969c\u788d\u7269\u7981\u5165\u533a\u91cd\u53e0&#xff1a; <\/p>\n<ul>\n<li>\u53d1\u751f\u91cd\u53e0 \u2192 \u53cd\u9988\u56de E-Step \u91cd\u65b0\u89c4\u5212\u7a7a\u95f4\u8def\u5f84&#xff08;\u5982\u63d0\u524d\u6362\u9053\u6216\u8c03\u6574\u6a2a\u5411\u504f\u79fb&#xff09;\u3002<\/li>\n<li>\u672a\u91cd\u53e0 \u2192 \u8fdb\u5165\u901f\u5ea6\u4f18\u5316\u9636\u6bb5\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\u901f\u5ea6\u4f18\u5316&#xff08;M-Step&#xff09;\n<ul>\n<li>\u5728\u53ef\u884c\u7684\u65f6\u7a7a\u8d70\u5eca\u5185\u5148\u7528 DP \u7c97\u89c4\u5212 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          s(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u518d\u7528 QP \u5e73\u6ed1\u5f97\u5230\u52a8\u529b\u5b66\u53ef\u884c\u7684\u901f\u5ea6\u66f2\u7ebf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           v<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          v(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u751f\u6210\u6700\u7ec8\u8f68\u8ff9\n<ul>\n<li>\u5c06 E-Step \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           l<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>          l(s)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0e M-Step \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           s<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          s(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5408\u6210\u5f97\u5230\u6700\u7ec8\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>           y<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          (x(t), y(t))<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u53d1\u9001\u7ed9\u63a7\u5236\u6a21\u5757\u6267\u884c\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>2.5.3 \u6267\u884c\u9891\u7387<\/h4>\n<ul>\n<li>\u6574\u4e2a E\u2013M \u5faa\u73af \u4ee5 \u6eda\u52a8\u89c4\u5212&#xff08;rolling planning&#xff09; \u65b9\u5f0f\u8fd0\u884c&#xff0c;\u901a\u5e38\u6bcf 100 ms \u6267\u884c\u4e00\u6b21\u3002<\/li>\n<li>\u6bcf\u4e00\u8f6e\u90fd\u4f1a\u66f4\u65b0&#xff1a;\n<ul>\n<li>\u5f53\u524d\u8f66\u8f86\u72b6\u6001\u4f5c\u4e3a\u65b0\u7684\u8d77\u70b9\u3002<\/li>\n<li>\u6700\u65b0\u7684\u5730\u56fe\u4e0e\u969c\u788d\u7269\u4fe1\u606f\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u5373\u4f7f HD Map \u63d0\u4f9b\u7684\u53c2\u8003\u7ebf\u4e0d\u53d8&#xff0c;E-Step \u8f93\u51fa\u7684\u8def\u5f84\u4e5f\u53ef\u80fd\u56e0\u4ea4\u901a\u72b6\u51b5\u548c\u969c\u788d\u7269\u53d8\u5316\u800c\u5fae\u8c03\u3002<\/li>\n<\/ul>\n<hr \/>\n<h4>2.5.4 \u4ea4\u4e92\u673a\u5236\u7684\u4f18\u52bf<\/h4>\n<ul>\n<li>\u5168\u5c40\u2013\u5c40\u90e8\u534f\u540c&#xff1a;E-Step \u51b3\u5b9a\u53ef\u884c\u8d70\u5eca\u7684\u62d3\u6251&#xff0c;M-Step \u5728\u8be5\u8d70\u5eca\u5185\u4f18\u5316\u884c\u9a76\u65f6\u5e8f\u3002<\/li>\n<li>\u52a8\u6001\u907f\u969c\u80fd\u529b\u5f3a&#xff1a;\u82e5\u65f6\u95f4\u57df\u4e0d\u53ef\u884c&#xff0c;\u53ef\u63d0\u524d\u89e6\u53d1\u7a7a\u95f4\u91cd\u89c4\u5212\u3002<\/li>\n<li>\u9c81\u68d2\u6027\u9ad8&#xff1a;\u6bcf\u5468\u671f\u6301\u7eed\u8bc4\u4f30\u73af\u5883\u53d8\u5316&#xff0c;\u5feb\u901f\u9002\u5e94\u52a8\u6001\u573a\u666f\u3002<\/li>\n<\/ul>\n<h3>\u4e09\u3001Apollo EM Planner \u7684\u5173\u952e\u6280\u672f\u7ec6\u8282<\/h3>\n<h4>3.1 \u89c4\u5212\u95ee\u9898\u5efa\u6a21<\/h4>\n<p>Apollo \u7684 EM Planner \u5c06\u8f68\u8ff9\u89c4\u5212\u95ee\u9898\u5206\u89e3\u4e3a\u8def\u5f84\u4e0e\u901f\u5ea6\u4e24\u4e2a\u5b50\u95ee\u9898&#xff0c;\u901a\u8fc7\u4ea4\u66ff\u4f18\u5316\u6c42\u89e3\u3002<\/p>\n<ul>\n<li>\u8def\u5f84\u4f18\u5316&#xff08;E-Step&#xff09;&#xff1a;\u5728 S\u2013L \u5e73\u9762\u751f\u6210\u5b89\u5168\u3001\u5e73\u6ed1\u3001\u53ef\u884c\u7684\u6a2a\u5411\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         l<\/p>\n<p>         (<\/p>\n<p>         s<\/p>\n<p>         )<\/p>\n<p>        l(s)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u901f\u5ea6\u4f18\u5316&#xff08;M-Step&#xff09;&#xff1a;\u5728\u56fa\u5b9a\u8def\u5f84\u4e0a&#xff0c;\u4e8e S\u2013T \u5e73\u9762\u751f\u6210\u6ee1\u8db3\u907f\u969c\u3001\u52a8\u529b\u5b66\u4e0e\u8212\u9002\u6027\u8981\u6c42\u7684\u901f\u5ea6\u66f2\u7ebf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         v<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>        v(t)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n<p>\u6574\u4f53\u4f18\u5316\u76ee\u6807\u53ef\u62bd\u8c61\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          min<\/p>\n<p>          \u2061<\/p>\n<p>          X<\/p>\n<p>          (<\/p>\n<p>          t<\/p>\n<p>          )<\/p>\n<p>       \u2005\u200a<\/p>\n<p>         w<\/p>\n<p>         l<\/p>\n<p>         C<\/p>\n<p>         lat<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         s<\/p>\n<p>         C<\/p>\n<p>         smooth<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         t<\/p>\n<p>         C<\/p>\n<p>         time<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         a<\/p>\n<p>         C<\/p>\n<p>         acc<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         j<\/p>\n<p>         C<\/p>\n<p>         jerk<\/p>\n<p>        X<\/p>\n<p>        (<\/p>\n<p>        t<\/p>\n<p>        )<\/p>\n<p>       \\\\min_{\\\\mathcal{X}(t)} \\\\; w_l C_{\\\\text{lat}} &#043; w_s C_{\\\\text{smooth}} &#043; w_t C_{\\\\text{time}} &#043; w_a C_{\\\\text{acc}} &#043; w_j C_{\\\\text{jerk}}X(t)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0385em;vertical-align: -0.3552em\"><\/span><span class=\"mop\"><span class=\"mop\">min<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathcal mtight\" style=\"margin-right: 0.1464em\">X<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">lat<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">smooth<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">time<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">acc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">jerk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          lat<\/p>\n<p>        C_{\\\\text{lat}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">lat<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u6a2a\u5411\u5b89\u5168\u4e0e\u78b0\u649e\u60e9\u7f5a<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          smooth<\/p>\n<p>        C_{\\\\text{smooth}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">smooth<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u8def\u5f84\u66f2\u7387\u4e0e\u8fde\u7eed\u6027\u60e9\u7f5a<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          time<\/p>\n<p>        C_{\\\\text{time}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">time<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u603b\u884c\u9a76\u65f6\u95f4<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          acc<\/p>\n<p>        C_{\\\\text{acc}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">acc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u52a0\u901f\u5ea6\u5e73\u6ed1\u6027<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          C<\/p>\n<p>          jerk<\/p>\n<p>        C_{\\\\text{jerk}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">jerk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u52a0\u52a0\u901f\u5ea6\u5e73\u6ed1\u6027<\/li>\n<\/ul>\n<hr \/>\n<h4>3.2 E-Step \u6838\u5fc3\u6280\u672f&#xff08;S\u2013L \u5e73\u9762&#xff09;<\/h4>\n<h5>3.2.1 \u969c\u788d\u7269\u6295\u5f71\u4e0e\u5360\u636e\u533a\u751f\u6210<\/h5>\n<li>\u5c06\u969c\u788d\u7269\u7684\u7b1b\u5361\u5c14\u5750\u6807\u9884\u6d4b\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          obs<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         ,<\/p>\n<p>          y<\/p>\n<p>          obs<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         )<\/p>\n<p>        (x_{\\\\text{obs}}(t),y_{\\\\text{obs}}(t))<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span> \u8f6c\u6362\u4e3a Frenet \u5750\u6807 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>          s<\/p>\n<p>          obs<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         ,<\/p>\n<p>          l<\/p>\n<p>          obs<\/p>\n<p>         (<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         )<\/p>\n<p>        (s_{\\\\text{obs}}(t),l_{\\\\text{obs}}(t))<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u5728 S\u2013L \u5e73\u9762\u4e0a\u751f\u6210\u969c\u788d\u7269\u5360\u636e\u591a\u8fb9\u5f62\u533a\u57df&#xff0c;\u5e76\u8003\u8651\u5b89\u5168\u88d5\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u0394<\/p>\n<p>          l<\/p>\n<p>          safe<\/p>\n<p>        \\\\Delta l_{\\\\text{safe}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">safe<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<h5>3.2.2 \u52a8\u6001\u89c4\u5212\u7c97\u641c\u7d22<\/h5>\n<ul>\n<li>\u7f51\u683c\u5316 S\u2013L \u7a7a\u95f4&#xff0c;\u91c7\u6837\u8def\u5f84\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         (<\/p>\n<p>          s<\/p>\n<p>          k<\/p>\n<p>         ,<\/p>\n<p>          l<\/p>\n<p>          k<\/p>\n<p>         )<\/p>\n<p>        (s_k,l_k)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u5254\u9664\u843d\u5728\u969c\u788d\u7269\u5360\u636e\u533a\u7684\u7f51\u683c\u70b9\u3002<\/li>\n<li>\u4f7f\u7528 DP \u641c\u7d22\u8fde\u63a5\u8d77\u70b9\u5230\u7ec8\u70b9\u7684\u6700\u5c0f\u4ee3\u4ef7\u8def\u5f84&#xff08;\u4ee3\u4ef7\u5305\u542b\u6a2a\u5411\u504f\u79fb\u3001\u66f2\u7387\u53d8\u5316\u7b49&#xff09;\u3002<\/li>\n<\/ul>\n<h5>3.2.3 \u4e8c\u6b21\u89c4\u5212\u5e73\u6ed1<\/h5>\n<ul>\n<li>\u5728 DP \u7c97\u8def\u5f84\u7684\u201c\u53ef\u884c\u5e26\u201d\u5185&#xff0c;\u7528\u4e8c\u6b21\u89c4\u5212\u4f18\u5316&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          min<\/p>\n<p>          \u2061<\/p>\n<p>          l<\/p>\n<p>          (<\/p>\n<p>          s<\/p>\n<p>          )<\/p>\n<p>        \u222b<\/p>\n<p>         (<\/p>\n<p>          w<\/p>\n<p>          \u03ba<\/p>\n<p>         \u03ba<\/p>\n<p>         (<\/p>\n<p>         s<\/p>\n<p>          )<\/p>\n<p>          2<\/p>\n<p>         &#043;<\/p>\n<p>          w<\/p>\n<p>          l<\/p>\n<p>         (<\/p>\n<p>         l<\/p>\n<p>         (<\/p>\n<p>         s<\/p>\n<p>         )<\/p>\n<p>         \u2212<\/p>\n<p>          l<\/p>\n<p>          ref<\/p>\n<p>          )<\/p>\n<p>          2<\/p>\n<p>         )<\/p>\n<p>        d<\/p>\n<p>        s<\/p>\n<p>       \\\\min_{l(s)} \\\\int \\\\left( w_\\\\kappa \\\\kappa(s)^2 &#043; w_l (l(s)-l_{\\\\text{ref}})^2 \\\\right) ds<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2052em;vertical-align: -0.3552em\"><\/span><span class=\"mop\"><span class=\"mop\">min<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">s<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-symbol small-op\" style=\"margin-right: 0.1945em;position: relative;top: -0.0006em\">\u222b<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">\u03ba<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">\u03ba<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0197em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">ref<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u7ea6\u675f\u6761\u4ef6&#xff1a;\n<ul>\n<li>\u6a2a\u5411\u504f\u79fb\u9650\u5236<\/li>\n<li>\u6700\u5927\u66f2\u7387\u9650\u5236<\/li>\n<li>\u8d77\u70b9\/\u7ec8\u70b9\u59ff\u6001\u7ea6\u675f<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h4>3.3 M-Step \u6838\u5fc3\u6280\u672f&#xff08;S\u2013T \u5e73\u9762&#xff09;<\/h4>\n<h5>3.3.1 S\u2013T \u6295\u5f71\u4e0e\u5b89\u5168\u533a\u6784\u5efa<\/h5>\n<li>\u5c06\u8def\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         l<\/p>\n<p>         (<\/p>\n<p>         s<\/p>\n<p>         )<\/p>\n<p>        l(s)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u6620\u5c04\u56de <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         (<\/p>\n<p>         s<\/p>\n<p>         )<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         (<\/p>\n<p>         s<\/p>\n<p>         )<\/p>\n<p>         )<\/p>\n<p>        (x(s),y(s))<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span> \u7b1b\u5361\u5c14\u8f68\u8ff9\u3002<\/li>\n<li>\u5c06\u969c\u788d\u7269\u9884\u6d4b\u8f68\u8ff9\u6295\u5f71\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         (<\/p>\n<p>         s<\/p>\n<p>         ,<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>        (s,t)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7a7a\u95f4&#xff0c;\u5f97\u5230\u969c\u788d\u7269\u7981\u5165\u533a&#xff08;Obstacle Forbidden Zone&#xff09;\u3002<\/li>\n<li>\u5b89\u5168\u533a\u5b9a\u4e49&#xff1a;<\/li>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         T<\/p>\n<p>         free<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>         R<\/p>\n<p>         &#043;<\/p>\n<p>        \u2216<\/p>\n<p>        O<\/p>\n<p>        b<\/p>\n<p>         s<\/p>\n<p>         ST<\/p>\n<p>        (<\/p>\n<p>        s<\/p>\n<p>        )<\/p>\n<p>       T_{\\\\text{free}}(s) &#061; \\\\mathbb{R}^&#043; \\\\setminus Obs_{\\\\text{ST}}(s)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">free<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0213em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7713em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">&#043;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2216<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">ST<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h5>3.3.2 DP \u7c97\u901f\u5ea6\u66f2\u7ebf\u641c\u7d22<\/h5>\n<ul>\n<li>\u6784\u5efa S\u2013T \u7f51\u683c&#xff1a;\u7eb5\u5411\u91c7\u6837 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          s<\/p>\n<p>          k<\/p>\n<p>        s_k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u65f6\u95f4\u91c7\u6837 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          t<\/p>\n<p>           k<\/p>\n<p>           ,<\/p>\n<p>           j<\/p>\n<p>        t_{k,j}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9012em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1b;<\/li>\n<li>\u8fc7\u6ee4\u6389\u969c\u788d\u7269\u7981\u5165\u533a\u7f51\u683c\u70b9&#xff1b;<\/li>\n<li>\u4ee3\u4ef7\u51fd\u6570&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         C<\/p>\n<p>         edge<\/p>\n<p>        &#061;<\/p>\n<p>         w<\/p>\n<p>         time<\/p>\n<p>         C<\/p>\n<p>         time<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         acc<\/p>\n<p>         C<\/p>\n<p>         acc<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         jerk<\/p>\n<p>         C<\/p>\n<p>         jerk<\/p>\n<p>        &#043;<\/p>\n<p>         w<\/p>\n<p>         eff<\/p>\n<p>         C<\/p>\n<p>         eff<\/p>\n<p>       C_{\\\\text{edge}} &#061; w_{\\\\text{time}} C_{\\\\text{time}} &#043; w_{\\\\text{acc}} C_{\\\\text{acc}} &#043; w_{\\\\text{jerk}} C_{\\\\text{jerk}} &#043; w_{\\\\text{eff}} C_{\\\\text{eff}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">edge<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">time<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">time<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">acc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">acc<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">jerk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">jerk<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">eff<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0715em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">eff<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u56de\u6eaf\u5f97\u5230\u7c97\u65f6\u95f4\u2013\u4f4d\u7f6e\u66f2\u7ebf t<sub>(s)\\\\tilde{t}(s)t<\/sub>(s)\u3002<\/li>\n<\/ul>\n<h5>3.3.3 \u5b89\u5168\u8d70\u5eca&#xff08;ST Tunnel&#xff09;\u751f\u6210<\/h5>\n<ul>\n<li>\u4ee5\u7c97\u89e3\u4e3a\u4e2d\u5fc3&#xff0c;\u7ed9\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          s<\/p>\n<p>          k<\/p>\n<p>        s_k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5206\u914d\u53ef\u884c\u7684\u65f6\u95f4\u533a\u95f4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         [<\/p>\n<p>         t<\/p>\n<p>         l<\/p>\n<p>         o<\/p>\n<p>         w<\/p>\n<p>         ,<\/p>\n<p>         t<\/p>\n<p>         u<\/p>\n<p>         p<\/p>\n<p>         ]<\/p>\n<p>        [tlow,tup]<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">tl<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u4fdd\u8bc1\u8fd9\u4e9b\u65f6\u95f4\u6bb5\u4e0d\u4e0e\u969c\u788d\u7269\u7981\u5165\u533a\u91cd\u53e0\u3002<\/li>\n<\/ul>\n<h5>3.3.4 QP \u5e73\u6ed1\u901f\u5ea6\u66f2\u7ebf<\/h5>\n<ul>\n<li>\u4f18\u5316\u53d8\u91cf&#xff1a;\u901f\u5ea6\u5411\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         v<\/p>\n<p>         &#061;<\/p>\n<p>         [<\/p>\n<p>          v<\/p>\n<p>          1<\/p>\n<p>         ,<\/p>\n<p>          v<\/p>\n<p>          2<\/p>\n<p>         ,<\/p>\n<p>         \u2026<\/p>\n<p>         ,<\/p>\n<p>          v<\/p>\n<p>          N<\/p>\n<p>         ]<\/p>\n<p>        \\\\mathbf{v} &#061; [v_1, v_2, \\\\dots, v_N]<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4444em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u76ee\u6807&#xff1a;<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        min<\/p>\n<p>        \u2061<\/p>\n<p>         \u2211<\/p>\n<p>         i<\/p>\n<p>         (<\/p>\n<p>          w<\/p>\n<p>          a<\/p>\n<p>          a<\/p>\n<p>          i<\/p>\n<p>          2<\/p>\n<p>         &#043;<\/p>\n<p>          w<\/p>\n<p>          j<\/p>\n<p>          j<\/p>\n<p>          i<\/p>\n<p>          2<\/p>\n<p>         &#043;<\/p>\n<p>          w<\/p>\n<p>          v<\/p>\n<p>         (<\/p>\n<p>          v<\/p>\n<p>          i<\/p>\n<p>         \u2212<\/p>\n<p>          v<\/p>\n<p>          des<\/p>\n<p>          )<\/p>\n<p>          2<\/p>\n<p>         )<\/p>\n<p>       \\\\min \\\\sum_i \\\\left( w_a a_i^2 &#043; w_j j_i^2 &#043; w_v (v_i &#8211; v_{\\\\text{des}})^2 \\\\right)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2em;vertical-align: -0.35em\"><\/span><span class=\"mop\">min<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.162em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4413em;margin-left: -0.0572em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">des<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u7ea6\u675f&#xff1a;\n<ul>\n<li>\u8d70\u5eca\u7ea6\u675f&#xff1a;\u5728\u5141\u8bb8\u7684\u65f6\u95f4\u533a\u95f4\u901a\u8fc7\u5bf9\u5e94\u7684 sks_ksk&#xff1b;<\/li>\n<li>\u901f\u5ea6\u3001\u52a0\u901f\u5ea6\u3001jerk \u8fb9\u754c\u7ea6\u675f&#xff1b;<\/li>\n<li>\u8d77\u70b9\/\u7ec8\u70b9\u901f\u5ea6\u6761\u4ef6\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h4>3.4 E\u2013M \u8fed\u4ee3\u673a\u5236<\/h4>\n<h5>3.4.1 \u4ea4\u4e92\u6d41\u7a0b<\/h5>\n<li>E-Step \u2192 M-Step&#xff1a;\n<ul>\n<li>E-Step \u751f\u6210\u7684\u65b0\u8def\u5f84\u4f5c\u4e3a M-Step \u7684\u57fa\u7840&#xff0c;M-Step \u5728\u8be5\u8def\u5f84\u4e0a\u8fdb\u884c\u901f\u5ea6\u4f18\u5316\u3002<\/li>\n<\/ul>\n<\/li>\n<li>M-Step \u2192 E-Step&#xff1a;\n<ul>\n<li>\u82e5 M-Step \u5f97\u5230\u7684\u901f\u5ea6\u66f2\u7ebf\u5728\u56de\u6295\u5f71\u540e\u4e0e\u969c\u788d\u7269\u53d1\u751f\u51b2\u7a81&#xff0c;\u5219\u53cd\u9988\u7ed9 E-Step \u91cd\u65b0\u4f18\u5316\u8def\u5f84\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u7ec8\u6b62\u6761\u4ef6&#xff1a;\n<ul>\n<li>\u8fbe\u5230\u6700\u5927\u8fed\u4ee3\u6b21\u6570&#xff1b;<\/li>\n<li>\u8def\u5f84\u548c\u901f\u5ea6\u53d8\u5316\u91cf\u5747\u4f4e\u4e8e\u9608\u503c\u3002<\/li>\n<\/ul>\n<\/li>\n<h5>3.4.2 \u4f18\u52bf<\/h5>\n<ul>\n<li>\u5206\u6cbb\u4f18\u5316&#xff1a;\u51cf\u5c11\u8054\u5408\u4f18\u5316\u7684\u8ba1\u7b97\u590d\u6742\u5ea6&#xff1b;<\/li>\n<li>\u53ef\u5e76\u884c\u6269\u5c55&#xff1a;\u8def\u5f84\u4e0e\u901f\u5ea6\u53ef\u7531\u4e0d\u540c\u7ebf\u7a0b\u5904\u7406&#xff0c;\u63d0\u9ad8\u5b9e\u65f6\u6027&#xff1b;<\/li>\n<li>\u52a8\u6001\u9002\u5e94&#xff1a;\u53ef\u5feb\u901f\u54cd\u5e94\u7a81\u53d1\u969c\u788d\u7269\u6216\u4ea4\u4e92\u7b56\u7565\u53d8\u5316\u3002<\/li>\n<\/ul>\n<hr \/>\n<h4>3.5 \u6a21\u5757\u95f4\u6570\u636e\u4ea4\u4e92<\/h4>\n<table>\n<tr>\u6a21\u5757\u8f93\u5165\u6570\u636e\u8f93\u51fa\u6570\u636e\u8bf4\u660e<\/tr>\n<tbody>\n<tr>\n<td>E-Step<\/td>\n<td>\u53c2\u8003\u7ebf\u3001\u969c\u788d\u7269\u9884\u6d4b\u3001\u4e0a\u5468\u671f\u8def\u5f84<\/td>\n<td>S\u2013L \u8def\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           l<\/p>\n<p>           (<\/p>\n<p>           s<\/p>\n<p>           )<\/p>\n<p>          l(s)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u4fdd\u8bc1\u6a2a\u5411\u5b89\u5168\u4e0e\u5e73\u6ed1<\/td>\n<\/tr>\n<tr>\n<td>M-Step<\/td>\n<td>S\u2013L \u8def\u5f84\u3001\u969c\u788d\u7269\u9884\u6d4b\u3001\u521d\u59cb\u901f\u5ea6<\/td>\n<td>S\u2013T \u901f\u5ea6\u66f2\u7ebf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           v<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>          v(t)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u4fdd\u8bc1\u7eb5\u5411\u5b89\u5168\u4e0e\u5e73\u6ed1<\/td>\n<\/tr>\n<tr>\n<td>\u63a7\u5236\u6a21\u5757<\/td>\n<td>\u65f6\u7a7a\u8f68\u8ff9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>           y<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>           v<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           ,<\/p>\n<p>           a<\/p>\n<p>           (<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           )<\/p>\n<p>          (x(t),y(t),v(t),a(t))<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u63a7\u5236\u6307\u4ee4<\/td>\n<td>\u6267\u884c\u8f66\u8f86\u52a0\u901f\u3001\u5236\u52a8\u3001\u8f6c\u5411<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb973\u6b21\uff0c\u70b9\u8d5e36\u6b21\uff0c\u6536\u85cf9\u6b21\u3002Apollo EM Planner \u662f\u767e\u5ea6\u81ea\u52a8\u9a7e\u9a76\u7cfb\u7edf\u4e2d\u7684\u8f68\u8ff9\u89c4\u5212\u7b97\u6cd5\uff0c\u91c7\u7528\u671f\u671b-\u6700\u5927\u5316\uff08EM\uff09\u8fed\u4ee3\u4f18\u5316\u601d\u60f3\u3002\u5176\u6838\u5fc3\u662f\u5c06\u8f68\u8ff9\u89c4\u5212\u5206\u89e3\u4e3a\u8def\u5f84\u4f18\u5316\uff08E-Step\uff09\u548c\u901f\u5ea6\u4f18\u5316\uff08M-Step\uff09\u4e24\u4e2a\u5b50\u95ee\u9898\uff0c\u5728Frenet\u5750\u6807\u7cfb\u4e0b\u4ea4\u66ff\u6c42\u89e3\u3002\u7b97\u6cd5\u5148\u901a\u8fc7\u52a8\u6001\u89c4\u5212\uff08DP\uff09\u641c\u7d22\u7c97\u8def\u5f84\uff0c\u518d\u4f7f\u7528\u4e8c\u6b21\u89c4\u5212\uff08QP\uff09\u8fdb\u884c\u5e73\u6ed1\u4f18\u5316\uff0c\u5e76\u7ed3\u5408\u969c\u788d\u7269\u4fe1\u606f\u751f\u6210\u5b89\u5168\u8d70\u5eca\u3002\u76f8\u8f83Lattice\u3001Hybrid A*\u7b49\u89c4\u5212\u5668\uff0cEM 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