{"id":58532,"date":"2025-08-16T12:05:04","date_gmt":"2025-08-16T04:05:04","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/58532.html"},"modified":"2025-08-16T12:05:04","modified_gmt":"2025-08-16T04:05:04","slug":"amcl%ef%bc%88adaptive-monte-carlo-localization%ef%bc%89%e7%ae%97%e6%b3%95%e7%9a%84%e5%8e%9f%e7%90%86%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/58532.html","title":{"rendered":"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3"},"content":{"rendered":"<h3>1. AMCL \u7684\u80cc\u666f\u4e0e\u5b9a\u4f4d\u4efb\u52a1<\/h3>\n<p>\u5728\u79fb\u52a8\u673a\u5668\u4eba\u4e2d&#xff0c;\u6211\u4eec\u5e38\u9047\u5230 \u5b9a\u4f4d\u95ee\u9898&#xff1a; \u5df2\u77e5\u673a\u5668\u4eba\u7684\u5730\u56fe&#xff08;Map&#xff09;\u548c\u4f20\u611f\u5668\u89c2\u6d4b\u6570\u636e&#xff08;\u6fc0\u5149\u96f7\u8fbe\u3001\u91cc\u7a0b\u8ba1\u7b49&#xff09;&#xff0c;\u63a8\u65ad\u673a\u5668\u4eba\u5728\u5730\u56fe\u4e2d\u7684\u4f4d\u7f6e\u4e0e\u59ff\u6001&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>        ,<\/p>\n<p>        y<\/p>\n<p>        ,<\/p>\n<p>        \u03b8<\/p>\n<p>       x, y, \\\\theta<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">x<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/p>\n<p>\u8fd9\u4e2a\u4efb\u52a1\u5c5e\u4e8e \u5168\u5c40\u5b9a\u4f4d\u95ee\u9898 \u6216 \u8ddf\u8e2a\u5b9a\u4f4d\u95ee\u9898&#xff1a;<\/p>\n<ul>\n<li>\u5168\u5c40\u5b9a\u4f4d&#xff08;Global Localization&#xff09;&#xff1a;\u673a\u5668\u4eba\u521d\u59cb\u4f4d\u7f6e\u672a\u77e5<\/li>\n<li>\u8ddf\u8e2a\u5b9a\u4f4d&#xff08;Tracking&#xff09;&#xff1a;\u5df2\u77e5\u521d\u59cb\u4f4d\u7f6e&#xff0c;\u5927\u90e8\u5206\u65f6\u5019\u662f\u4f4d\u7f6e\u8ddf\u8e2a<\/li>\n<\/ul>\n<p>AMCL \u662f \u8499\u7279\u5361\u6d1b\u5b9a\u4f4d&#xff08;MCL&#xff09; \u7684\u6539\u8fdb\u7248&#xff0c;\u672c\u8d28\u662f \u57fa\u4e8e\u7c92\u5b50\u6ee4\u6ce2\u7684\u8d1d\u53f6\u65af\u5b9a\u4f4d\u65b9\u6cd5&#xff0c;\u5e76\u5f15\u5165 KLD-\u91c7\u6837 \u52a8\u6001\u8c03\u6574\u7c92\u5b50\u6570\u91cf&#xff0c;\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002<\/p>\n<hr \/>\n<h3>2. \u7c92\u5b50\u6ee4\u6ce2&#xff08;MCL&#xff09;\u7684\u57fa\u672c\u539f\u7406<\/h3>\n<p>\u7c92\u5b50\u6ee4\u6ce2\u662f\u901a\u8fc7\u4e00\u7ec4\u7c92\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        {<\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>          [<\/p>\n<p>          m<\/p>\n<p>          ]<\/p>\n<p>         }<\/p>\n<p>          m<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>         M<\/p>\n<p>       \\\\{x_t^{[m]}\\\\}_{m&#061;1}^M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2948em;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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">}<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -2.4519em;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\">m<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/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 mathnormal mtight\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2481em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6765\u8fd1\u4f3c\u4f4d\u7f6e\u7684\u6982\u7387\u5206\u5e03 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        p<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         t<\/p>\n<p>        \u2223<\/p>\n<p>         z<\/p>\n<p>          1<\/p>\n<p>          :<\/p>\n<p>          t<\/p>\n<p>        ,<\/p>\n<p>         u<\/p>\n<p>          1<\/p>\n<p>          :<\/p>\n<p>          t<\/p>\n<p>        )<\/p>\n<p>       p(x_t|z_{1:t}, u_{1: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\">p<\/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: 0.2806em\"><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\">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\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/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\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u7c92\u5b50\u6ee4\u6ce2\u6b65\u9aa4&#xff1a;<\/p>\n<li>\n<p>\u521d\u59cb\u5316&#xff08;Initialize&#xff09;&#xff1a;\u5728\u5730\u56fe\u4e0a\u5747\u5300\u91c7\u6837\u7c92\u5b50&#xff0c;\u6216\u56f4\u7ed5\u521d\u59cb\u4f30\u8ba1\u91c7\u6837<\/p>\n<\/li>\n<li>\n<p>\u9884\u6d4b&#xff08;Prediction \/ Motion Update&#xff09;&#xff1a;\u6839\u636e\u8fd0\u52a8\u6a21\u578b\u66f4\u65b0\u7c92\u5b50\u4f4d\u7f6e<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            x<\/p>\n<p>            t<\/p>\n<p>             [<\/p>\n<p>             m<\/p>\n<p>             ]<\/p>\n<p>           \u223c<\/p>\n<p>           p<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            t<\/p>\n<p>           \u2223<\/p>\n<p>            u<\/p>\n<p>            t<\/p>\n<p>           ,<\/p>\n<p>            x<\/p>\n<p>             t<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             [<\/p>\n<p>             m<\/p>\n<p>             ]<\/p>\n<p>           )<\/p>\n<p>           x_t^{[m]} \\\\sim p(x_t | u_t, x_{t-1}^{[m]}) <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2906em;vertical-align: -0.2458em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u223c<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3694em;vertical-align: -0.3246em\"><\/span><span class=\"mord mathnormal\">p<\/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: 0.2806em\"><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\">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\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/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: 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\">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: 0.1667em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4337em;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\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.3246em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u66f4\u65b0&#xff08;Update \/ Measurement Update&#xff09;&#xff1a;\u6839\u636e\u4f20\u611f\u5668\u89c2\u6d4b\u66f4\u65b0\u7c92\u5b50\u6743\u91cd<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            w<\/p>\n<p>            t<\/p>\n<p>             [<\/p>\n<p>             m<\/p>\n<p>             ]<\/p>\n<p>           \u221d<\/p>\n<p>           p<\/p>\n<p>           (<\/p>\n<p>            z<\/p>\n<p>            t<\/p>\n<p>           \u2223<\/p>\n<p>            x<\/p>\n<p>            t<\/p>\n<p>             [<\/p>\n<p>             m<\/p>\n<p>             ]<\/p>\n<p>           ,<\/p>\n<p>           m<\/p>\n<p>           )<\/p>\n<p>           w_t^{[m]} \\\\propto p(z_t | x_t^{[m]}, m) <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2906em;vertical-align: -0.2458em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u221d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2948em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">\u2223<\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><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\">m<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u91cd\u91c7\u6837&#xff08;Resampling&#xff09;&#xff1a;\u6839\u636e\u6743\u91cd\u91c7\u6837\u65b0\u7c92\u5b50&#xff0c;\u907f\u514d\u6743\u91cd\u9000\u5316<\/p>\n<\/li>\n<hr \/>\n<h3>3. AMCL \u7684\u6838\u5fc3\u6539\u8fdb&#xff1a;KLD-Sampling<\/h3>\n<p>\u6807\u51c6 MCL \u7f3a\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u7c92\u5b50\u6570\u56fa\u5b9a&#xff0c;\u8ba1\u7b97\u91cf\u5927<\/li>\n<li>\u5982\u679c\u7c92\u5b50\u6570\u592a\u5c11 \u2192 \u5b9a\u4f4d\u7cbe\u5ea6\u5dee<\/li>\n<li>\u5982\u679c\u7c92\u5b50\u6570\u592a\u591a \u2192 \u6d6a\u8d39\u8ba1\u7b97\u8d44\u6e90<\/li>\n<\/ul>\n<p>AMCL \u5f15\u5165\u81ea\u9002\u5e94\u91c7\u6837&#xff08;KLD-sampling&#xff09;&#xff1a; \u6839\u636e\u5f53\u524d\u4f30\u8ba1\u7684 \u4f4d\u7f6e\u5206\u5e03\u590d\u6742\u5ea6 \u52a8\u6001\u8c03\u6574\u7c92\u5b50\u6570\u3002<\/p>\n<h4>3.1 KLD-Sampling \u539f\u7406<\/h4>\n<p>\u4f7f\u7528 Kullback\u2013Leibler Divergence&#xff08;KL\u6563\u5ea6&#xff09;\u6765\u7ea6\u675f\u8fd1\u4f3c\u5206\u5e03\u548c\u771f\u5b9e\u5206\u5e03\u7684\u5dee\u8ddd\u3002<\/p>\n<p>KL \u6563\u5ea6\u5b9a\u4e49&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          D<\/p>\n<p>           K<\/p>\n<p>           L<\/p>\n<p>         (<\/p>\n<p>         p<\/p>\n<p>         \u2223<\/p>\n<p>         \u2223<\/p>\n<p>         q<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u2211<\/p>\n<p>          x<\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         )<\/p>\n<p>         log<\/p>\n<p>         \u2061<\/p>\n<p>           p<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           )<\/p>\n<p>           q<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           )<\/p>\n<p>         D_{KL}(p||q) &#061; \\\\sum_{x} p(x) \\\\log \\\\frac{p(x)}{q(x)} <\/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: 0.0278em\">D<\/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: -0.0278em;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: 0.0715em\">K<\/span><span class=\"mord mathnormal mtight\">L<\/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\">p<\/span><span class=\"mord\">\u2223\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/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: 2.677em;vertical-align: -1.25em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.9em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.25em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/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: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/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: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>AMCL \u8981\u6c42&#xff1a;<\/p>\n<ul>\n<li>\u5728\u7f6e\u4fe1\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         1<\/p>\n<p>         \u2212<\/p>\n<p>         \u03b4<\/p>\n<p>        1 &#8211; \\\\delta<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/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: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><\/span><\/span><\/span><\/span> \u4e0b<\/li>\n<li>\u8fd1\u4f3c\u8bef\u5dee\u4e0d\u8d85\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u03f5<\/p>\n<p>        \\\\epsilon<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">\u03f5<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p>\u63a8\u5bfc\u540e\u5f97\u5230\u7c92\u5b50\u6570\u4e0a\u754c\u516c\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         M<\/p>\n<p>         &#061;<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>           2<\/p>\n<p>           \u03f5<\/p>\n<p>           [<\/p>\n<p>           1<\/p>\n<p>           \u2212<\/p>\n<p>            2<\/p>\n<p>             9<\/p>\n<p>             (<\/p>\n<p>             k<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             )<\/p>\n<p>           &#043;<\/p>\n<p>             2<\/p>\n<p>              9<\/p>\n<p>              (<\/p>\n<p>              k<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>              )<\/p>\n<p>            z<\/p>\n<p>             1<\/p>\n<p>             \u2212<\/p>\n<p>             \u03b4<\/p>\n<p>           ]<\/p>\n<p>          3<\/p>\n<p>         M &#061; \\\\frac{k-1}{2\\\\epsilon} \\\\left[1 &#8211; \\\\frac{2}{9(k-1)} &#043; \\\\sqrt{\\\\frac{2}{9(k-1)}} z_{1-\\\\delta} \\\\right]^3 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/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: 3.2806em;vertical-align: -1.25em\"><\/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: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">\u03f5<\/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: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/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\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">[<\/span><\/span><span class=\"mord\">1<\/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=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">9<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/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\">1<\/span><span class=\"mclose\">)<\/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: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><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 class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8266em\"><span class=\"svg-align\" style=\"top: -5em\"><span class=\"pstrut\" style=\"height: 5em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><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: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">9<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/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\">1<\/span><span class=\"mclose\">)<\/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: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.7866em\"><span class=\"pstrut\" style=\"height: 5em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 3.08em\"><\/p>\n<p>              <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2134em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">1<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0379em\">\u03b4<\/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=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.0306em\"><span class=\"\" style=\"top: -4.2795em;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><\/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>         k<\/p>\n<p>        k<\/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: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u662f\u79bb\u6563\u4f4d\u7f6e\u683c\u5b50\u7684\u6570\u91cf&#xff08;\u5df2\u88ab\u7c92\u5b50\u8986\u76d6\u7684 bins&#xff09;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          z<\/p>\n<p>           1<\/p>\n<p>           \u2212<\/p>\n<p>           \u03b4<\/p>\n<p>        z_{1-\\\\delta}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">1<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0379em\">\u03b4<\/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><\/span><\/span><\/span> \u662f\u6807\u51c6\u6b63\u6001\u5206\u5e03\u5206\u4f4d\u6570<\/li>\n<\/ul>\n<p>\u7c92\u5b50\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        M<\/p>\n<p>       M<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u4f1a\u6839\u636e\u89c2\u6d4b\u548c\u5206\u5e03\u7a00\u758f\u7a0b\u5ea6\u52a8\u6001\u8c03\u6574\u3002<\/p>\n<hr \/>\n<h3>4. AMCL \u6570\u5b66\u63a8\u5bfc\u6d41\u7a0b<\/h3>\n<h4>4.1 \u8d1d\u53f6\u65af\u5b9a\u4f4d\u516c\u5f0f<\/h4>\n<p>\u673a\u5668\u4eba\u5b9a\u4f4d\u95ee\u9898\u53ef\u7528\u9012\u5f52\u8d1d\u53f6\u65af\u6ee4\u6ce2\u8868\u793a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         \u2223<\/p>\n<p>          z<\/p>\n<p>           1<\/p>\n<p>           :<\/p>\n<p>           t<\/p>\n<p>         ,<\/p>\n<p>          u<\/p>\n<p>           1<\/p>\n<p>           :<\/p>\n<p>           t<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         \u03b7<br \/>\n        \u2009<\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>          z<\/p>\n<p>          t<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         ,<\/p>\n<p>         m<\/p>\n<p>         )<\/p>\n<p>         \u222b<\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         \u2223<\/p>\n<p>          u<\/p>\n<p>          t<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         )<br \/>\n        \u2009<\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         \u2223<\/p>\n<p>          z<\/p>\n<p>           1<\/p>\n<p>           :<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>          u<\/p>\n<p>           1<\/p>\n<p>           :<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         )<br \/>\n        \u2009<\/p>\n<p>         d<\/p>\n<p>          x<\/p>\n<p>           t<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         p(x_t|z_{1:t}, u_{1:t}) &#061; \\\\eta \\\\, p(z_t|x_t, m) \\\\int p(x_t|u_t, x_{t-1}) \\\\, p(x_{t-1}|z_{1:t-1}, u_{1:t-1}) \\\\, dx_{t-1} <\/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\">p<\/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: 0.2806em\"><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\">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\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/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\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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><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: 2.2222em;vertical-align: -0.8622em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">\u2223<\/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: 0.2806em\"><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\">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: 0.1667em\"><\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-symbol large-op\" style=\"margin-right: 0.4445em;position: relative;top: -0.0011em\">\u222b<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/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: 0.2806em\"><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\">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\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/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: 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\">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: 0.1667em\"><\/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: 0.3011em\"><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\"><span class=\"mord mathnormal mtight\">t<\/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=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/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: 0.3011em\"><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\"><span class=\"mord mathnormal mtight\">t<\/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=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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\">u<\/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\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">d<\/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: 0.3011em\"><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\"><span class=\"mord mathnormal mtight\">t<\/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><\/span><\/span><\/span><\/span><\/p>\n<h4>4.2 \u7c92\u5b50\u6ee4\u6ce2\u8fd1\u4f3c<\/h4>\n<p>\u7528\u7c92\u5b50\u96c6\u5408\u8fd1\u4f3c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         p<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         \u2223<\/p>\n<p>          z<\/p>\n<p>           1<\/p>\n<p>           :<\/p>\n<p>           t<\/p>\n<p>         ,<\/p>\n<p>          u<\/p>\n<p>           1<\/p>\n<p>           :<\/p>\n<p>           t<\/p>\n<p>         )<\/p>\n<p>         \u2248<\/p>\n<p>          \u2211<\/p>\n<p>           m<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          M<\/p>\n<p>          w<\/p>\n<p>          t<\/p>\n<p>           [<\/p>\n<p>           m<\/p>\n<p>           ]<\/p>\n<p>         \u03b4<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>         \u2212<\/p>\n<p>          x<\/p>\n<p>          t<\/p>\n<p>           [<\/p>\n<p>           m<\/p>\n<p>           ]<\/p>\n<p>         )<\/p>\n<p>         p(x_t|z_{1:t}, u_{1:t}) \\\\approx \\\\sum_{m&#061;1}^M w_t^{[m]} \\\\delta(x_t &#8211; x_t^{[m]}) <\/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\">p<\/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: 0.2806em\"><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\">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\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/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: -0.044em;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\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/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\"><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">:<\/span><span class=\"mord mathnormal mtight\">t<\/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><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.0954em;vertical-align: -1.2671em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8829em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">m<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2671em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/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: 0.2806em\"><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\">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: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2948em;vertical-align: -0.25em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>4.3 \u6743\u91cd\u66f4\u65b0\u516c\u5f0f<\/h4>\n<p>\u6fc0\u5149\u96f7\u8fbe\u6d4b\u91cf\u6a21\u578b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          w<\/p>\n<p>          t<\/p>\n<p>           [<\/p>\n<p>           m<\/p>\n<p>           ]<\/p>\n<p>         \u221d<\/p>\n<p>         exp<\/p>\n<p>         \u2061<\/p>\n<p>          (<\/p>\n<p>          \u2212<\/p>\n<p>           1<\/p>\n<p>            2<\/p>\n<p>             \u03c3<\/p>\n<p>             2<\/p>\n<p>           \u2211<\/p>\n<p>            i<\/p>\n<p>            &#061;<\/p>\n<p>            1<\/p>\n<p>           K<\/p>\n<p>            [<\/p>\n<p>             z<\/p>\n<p>             t<\/p>\n<p>             i<\/p>\n<p>            \u2212<\/p>\n<p>             z<\/p>\n<p>             ^<\/p>\n<p>            (<\/p>\n<p>             x<\/p>\n<p>             t<\/p>\n<p>              [<\/p>\n<p>              m<\/p>\n<p>              ]<\/p>\n<p>            ,<\/p>\n<p>            m<\/p>\n<p>            )<\/p>\n<p>            ]<\/p>\n<p>           2<\/p>\n<p>          )<\/p>\n<p>         w_t^{[m]} \\\\propto \\\\exp\\\\left(-\\\\frac{1}{2\\\\sigma^2} \\\\sum_{i&#061;1}^K \\\\left[ z_t^i &#8211; \\\\hat{z}(x_t^{[m]}, m) \\\\right]^2 \\\\right) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2906em;vertical-align: -0.2458em\"><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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 class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u221d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.106em;vertical-align: -1.2777em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">(<\/span><\/span><span class=\"mord\">\u2212<\/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: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;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 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: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/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: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.044em;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 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><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 accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/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: 1.0448em\"><span class=\"\" style=\"top: -2.4542em;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\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;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=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">m<\/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: 0.2458em\"><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\">m<\/span><span class=\"mclose\">)<\/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 class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">)<\/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>          z<\/p>\n<p>          t<\/p>\n<p>          i<\/p>\n<p>        z_t^i<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0717em;vertical-align: -0.247em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8247em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.044em;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 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5b9e\u9645\u6fc0\u5149\u6d4b\u8ddd\u503c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          z<\/p>\n<p>          ^<\/p>\n<p>         (<\/p>\n<p>         \u22c5<\/p>\n<p>         )<\/p>\n<p>        \\\\hat{z}(\\\\cdot)<\/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 accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u22c5<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u5730\u56fe\u9884\u6d4b\u6d4b\u8ddd<\/li>\n<\/ul>\n<h4>4.4 \u81ea\u9002\u5e94\u91c7\u6837\u6761\u4ef6<\/h4>\n<p>\u5f53\u7c92\u5b50\u6570\u91cf\u6ee1\u8db3 KLD-sampling \u516c\u5f0f\u65f6\u505c\u6b62\u91c7\u6837&#xff0c;\u5426\u5219\u7ee7\u7eed\u91c7\u6837\u66f4\u591a\u7c92\u5b50\u3002<\/p>\n<hr \/>\n<h3>5. AMCL \u7b97\u6cd5\u6d41\u7a0b\u56fe<\/h3>\n<p>         \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n         \u2502 \u521d\u59cb\u5316\u7c92\u5b50\u96c6 \u2502<br \/>\n         \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n                \u2193<br \/>\n        \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n        \u2502 \u8fd0\u52a8\u66f4\u65b0(Pred)\u2502 \u2190 \u91cc\u7a0b\u8ba1\u6570\u636e<br \/>\n        \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n               \u2193<br \/>\n        \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n        \u2502 \u6d4b\u91cf\u66f4\u65b0(Upd) \u2502 \u2190 \u6fc0\u5149\u96f7\u8fbe\u6570\u636e<br \/>\n        \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n               \u2193<br \/>\n        \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n        \u2502 \u6743\u91cd\u5f52\u4e00\u5316   \u2502<br \/>\n        \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n               \u2193<br \/>\n        \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n        \u2502 KLD\u91c7\u6837\u8ba1\u7b97  \u2502<br \/>\n        \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n               \u2193<br \/>\n        \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n        \u2502 \u91cd\u91c7\u6837        \u2502<br \/>\n        \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<br \/>\n               \u2193<br \/>\n        \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n        \u2502 \u8f93\u51fa\u4f4d\u59ff\u4f30\u8ba1 \u2502<br \/>\n        \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<\/p>\n<hr \/>\n<h3>6. AMCL \u7684\u4f18\u7f3a\u70b9<\/h3>\n<p>\u4f18\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u7c92\u5b50\u6570\u81ea\u9002\u5e94&#xff0c;\u8282\u7701\u8ba1\u7b97<\/li>\n<li>\u80fd\u5904\u7406\u5168\u5c40\u5b9a\u4f4d\u4e0e\u8ddf\u8e2a<\/li>\n<li>\u5bf9\u4f20\u611f\u5668\u566a\u58f0\u6709\u9c81\u68d2\u6027<\/li>\n<\/ul>\n<p>\u7f3a\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u521d\u59cb\u5168\u5c40\u5b9a\u4f4d\u4ecd\u7136\u8017\u65f6<\/li>\n<li>\u5bf9\u8fd0\u52a8\u6a21\u578b\u548c\u6d4b\u91cf\u6a21\u578b\u4f9d\u8d56\u5927<\/li>\n<li>\u5730\u56fe\u4e0d\u51c6\u786e\u65f6\u4f1a\u6f02\u79fb<\/li>\n<\/ul>\n<hr \/>\n<h3>7. Python \u7b80\u6613 AMCL \u793a\u4f8b<\/h3>\n<p><span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">SimpleAMCL<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">def<\/span> <span class=\"token function\">__init__<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> num_particles<span class=\"token punctuation\">,<\/span> map_size<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>num_particles <span class=\"token operator\">&#061;<\/span> num_particles<br \/>\n        self<span class=\"token punctuation\">.<\/span>particles <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>rand<span class=\"token punctuation\">(<\/span>num_particles<span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> map_size  <span class=\"token comment\"># x, y, theta<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>weights <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>ones<span class=\"token punctuation\">(<\/span>num_particles<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> num_particles<\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">motion_update<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">,<\/span> noise_std<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>particles<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;&#061;<\/span> u<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>num_particles<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> noise_std<br \/>\n        self<span class=\"token punctuation\">.<\/span>particles<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;&#061;<\/span> u<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>num_particles<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> noise_std<br \/>\n        self<span class=\"token punctuation\">.<\/span>particles<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;&#061;<\/span> u<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>num_particles<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> noise_std<\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">measurement_update<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> z<span class=\"token punctuation\">,<\/span> z_pred<span class=\"token punctuation\">,<\/span> sigma<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        error <span class=\"token operator\">&#061;<\/span> z <span class=\"token operator\">&#8211;<\/span> z_pred<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>particles<span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>weights <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>exp<span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">0.5<\/span> <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>error <span class=\"token operator\">\/<\/span> sigma<span class=\"token punctuation\">)<\/span><span class=\"token operator\">**<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>weights <span class=\"token operator\">\/&#061;<\/span> np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>weights<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">resample<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        indices <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>choice<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>num_particles<span class=\"token punctuation\">,<\/span> self<span class=\"token punctuation\">.<\/span>num_particles<span class=\"token punctuation\">,<\/span> p<span class=\"token operator\">&#061;<\/span>self<span class=\"token punctuation\">.<\/span>weights<span class=\"token punctuation\">)<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>particles <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>particles<span class=\"token punctuation\">[<\/span>indices<span class=\"token punctuation\">]<\/span><br \/>\n        self<span class=\"token punctuation\">.<\/span>weights<span class=\"token punctuation\">.<\/span>fill<span class=\"token punctuation\">(<\/span><span class=\"token number\">1.0<\/span> <span class=\"token operator\">\/<\/span> self<span class=\"token punctuation\">.<\/span>num_particles<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">def<\/span> <span class=\"token function\">estimate<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> np<span class=\"token punctuation\">.<\/span>average<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>particles<span class=\"token punctuation\">,<\/span> axis<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> weights<span class=\"token operator\">&#061;<\/span>self<span class=\"token punctuation\">.<\/span>weights<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u4f7f\u7528\u793a\u4f8b<\/span><br \/>\n<span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    amcl <span class=\"token operator\">&#061;<\/span> SimpleAMCL<span class=\"token punctuation\">(<\/span><span class=\"token number\">500<\/span><span class=\"token punctuation\">,<\/span> map_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    amcl<span class=\"token punctuation\">.<\/span>motion_update<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    amcl<span class=\"token punctuation\">.<\/span>measurement_update<span class=\"token punctuation\">(<\/span>z<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5.0<\/span><span class=\"token punctuation\">,<\/span> z_pred<span class=\"token operator\">&#061;<\/span><span class=\"token keyword\">lambda<\/span> p<span class=\"token punctuation\">:<\/span> p<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    amcl<span class=\"token punctuation\">.<\/span>resample<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u4f30\u8ba1\u4f4d\u7f6e&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span> amcl<span class=\"token punctuation\">.<\/span>estimate<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<hr \/>\n<h3>8.\u53c2\u8003\u6587\u732e<\/h3>\n<hr \/>\n<h4>1. \u539f\u59cb\u8bba\u6587\u4e0e\u5f00\u521b\u6027\u5de5\u4f5c<\/h4>\n<li>\n<p>Fox, D. (2001). KLD-sampling: Adaptive particle filters. In Advances in Neural Information Processing Systems (NeurIPS), 14, pp. 713\u2013720.<\/p>\n<ul>\n<li>\u8fd9\u662f AMCL \u6838\u5fc3\u601d\u60f3\u7684\u5960\u57fa\u8bba\u6587&#xff0c;\u5f15\u5165\u4e86\u57fa\u4e8e Kullback\u2013Leibler Divergence \u7684\u81ea\u9002\u5e94\u7c92\u5b50\u6570\u8c03\u6574\u65b9\u6cd5\u3002<\/li>\n<li>PDF \u4e0b\u8f7d&#xff08;CMU&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>Fox, D., Burgard, W., Dellaert, F., &amp; Thrun, S. (1999). Monte Carlo Localization: Efficient position estimation for mobile robots. In Proceedings of AAAI.<\/p>\n<ul>\n<li>\u65e9\u671f MCL \u65b9\u6cd5\u7684\u63d0\u51fa&#xff0c;AMCL \u662f\u5b83\u7684\u6539\u8fdb\u7248\u672c\u3002<\/li>\n<li>PDF \u4e0b\u8f7d&#xff08;AAAI&#xff09;<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>2. \u673a\u5668\u4eba\u5b66\u4e0e\u6982\u7387\u673a\u5668\u4eba\u5b66\u7ecf\u5178\u6559\u6750<\/h4>\n<li>\n<p>Thrun, S., Burgard, W., &amp; Fox, D. (2005). Probabilistic Robotics. MIT Press.<\/p>\n<ul>\n<li>\u7b2c 8 \u7ae0\u8be6\u7ec6\u4ecb\u7ecd\u4e86 MCL \u548c AMCL&#xff0c;\u5305\u62ec\u6570\u5b66\u63a8\u5bfc\u3001\u7b97\u6cd5\u6d41\u7a0b\u548c\u6539\u8fdb\u65b9\u6cd5\u3002<\/li>\n<li>\u5b98\u65b9\u7f51\u7ad9&#xff08;\u542b\u90e8\u5206\u4ee3\u7801&#xff09;&#xff1a;http:\/\/probabilistic-robotics.org\/<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>Siegwart, R., Nourbakhsh, I. R., &amp; Scaramuzza, D. (2011). Introduction to Autonomous Mobile Robots. MIT Press.<\/p>\n<ul>\n<li>\u7b2c 6 \u7ae0\u5bf9\u7c92\u5b50\u6ee4\u6ce2\u5b9a\u4f4d\u6709\u8f83\u597d\u7684\u76f4\u89c2\u89e3\u91ca\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>3. ROS \u4e0e\u5de5\u7a0b\u5b9e\u73b0\u76f8\u5173\u8d44\u6599<\/h4>\n<li>\n<p>ROS Wiki &#8211; AMCL: http:\/\/wiki.ros.org\/amcl<\/p>\n<ul>\n<li>\u5305\u542b ROS \u4e2d amcl \u8282\u70b9\u7684\u914d\u7f6e\u53c2\u6570\u3001\u6e90\u7801\u94fe\u63a5\u3001\u8fd0\u884c\u65b9\u6cd5\u3002<\/li>\n<li>ROS \u7248\u672c\u5b9e\u73b0\u57fa\u4e8e Fox \u7684 KLD-sampling AMCL\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>ROS Navigation Stack \u6e90\u7801&#xff1a;<\/p>\n<ul>\n<li>GitHub: https:\/\/github.com\/ros-planning\/navigation\/tree\/noetic-devel\/amcl<\/li>\n<li>\u53ef\u76f4\u63a5\u67e5\u770b amcl \u7684 C&#043;&#043; \u5b9e\u73b0\u7ec6\u8282&#xff0c;\u5305\u62ec\u8fd0\u52a8\u6a21\u578b\u3001\u4f20\u611f\u5668\u6a21\u578b\u3001\u7c92\u5b50\u6ee4\u6ce2\u66f4\u65b0\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>4. \u6269\u5c55\u4e0e\u6539\u8fdb\u6027\u8bba\u6587<\/h4>\n<li>\n<p>Zhang, J., &amp; Singh, S. (2014). LOAM: Lidar Odometry and Mapping in Real-time. In Robotics: Science and Systems (RSS).<\/p>\n<ul>\n<li>\u867d\u7136\u4e0d\u662f AMCL&#xff0c;\u4f46\u5176\u5730\u56fe\u914d\u51c6\u601d\u60f3\u53ef\u4e0e AMCL \u878d\u5408\u505a\u591a\u4f20\u611f\u5668\u5b9a\u4f4d\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>Pfaff, P., Triebel, R., &amp; Burgard, W. (2006). An Efficient Extension to Monte Carlo Localization for Robust Localization in Dynamic Environments. In Robotics and Autonomous Systems, 54(2), 131\u2013143.<\/p>\n<ul>\n<li>\u9488\u5bf9\u52a8\u6001\u73af\u5883\u7684\u6539\u8fdb\u7248\u672c AMCL\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>Koide, K., Yokozuka, M., Oishi, S., &amp; Menegatti, E. (2019). Portable 3D LiDAR-based System for Long-term and Wide-area People Behavior Measurement. In IEEE RA-L, 4(2), 820\u2013827.<\/p>\n<ul>\n<li>\u4f7f\u7528 AMCL \u601d\u60f3\u7684\u4e09\u7ef4\u5b9a\u4f4d\u53d8\u4f53\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb577\u6b21\uff0c\u70b9\u8d5e14\u6b21\uff0c\u6536\u85cf8\u6b21\u3002\u5df2\u77e5\u673a\u5668\u4eba\u7684\u5730\u56fe\uff08Map\uff09\u548c\u4f20\u611f\u5668\u89c2\u6d4b\u6570\u636e\uff08\u6fc0\u5149\u96f7\u8fbe\u3001\u91cc\u7a0b\u8ba1\u7b49\uff09\uff0c\u63a8\u65ad\u673a\u5668\u4eba\u5728\u5730\u56fe\u4e2d\u7684\u4f4d\u7f6e\u4e0e\u59ff\u6001\uff08\u5f53\u7c92\u5b50\u6570\u91cf\u6ee1\u8db3 KLD-sampling \u516c\u5f0f\u65f6\u505c\u6b62\u91c7\u6837\uff0c\u5426\u5219\u7ee7\u7eed\u91c7\u6837\u66f4\u591a\u7c92\u5b50\u3002\uff08KL\u6563\u5ea6\uff09\u6765\u7ea6\u675f\u8fd1\u4f3c\u5206\u5e03\u548c\u771f\u5b9e\u5206\u5e03\u7684\u5dee\u8ddd\u3002\uff1a\u5728\u5730\u56fe\u4e0a\u5747\u5300\u91c7\u6837\u7c92\u5b50\uff0c\u6216\u56f4\u7ed5\u521d\u59cb\u4f30\u8ba1\u91c7\u6837\u3002\u4f1a\u6839\u636e\u89c2\u6d4b\u548c\u5206\u5e03\u7a00\u758f\u7a0b\u5ea6\u52a8\u6001\u8c03\u6574\u3002\uff1a\u6839\u636e\u6743\u91cd\u91c7\u6837\u65b0\u7c92\u5b50\uff0c\u907f\u514d\u6743\u91cd\u9000\u5316\u3002\u52a8\u6001\u8c03\u6574\u7c92\u5b50\u6570\u91cf\uff0c\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002\u5728\u79fb\u52a8\u673a\u5668\u4eba\u4e2d\uff0c\u6211\u4eec\u5e38\u9047\u5230\u3002\uff1a\u6839\u636e\u4f20\u611f\u5668\u89c2\u6d4b\u66f4\u65b0\u7c92\u5b50\u6743\u91cd\u3002\uff1a\u6839\u636e\u8fd0\u52a8\u6a21\u578b\u66f4\u65b0\u7c92\u5b50\u4f4d\u7f6e\u3002\u7c92\u5b50\u6ee4\u6ce2\u662f\u901a\u8fc7\u4e00\u7ec4\u7c92\u5b50\u3002\u6765\u8fd1\u4f3c\u4f4d\u7f6e\u7684\u6982\u7387\u5206\u5e03\u3002<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[6167,6168,5986,5985,427,6169,5987],"topic":[],"class_list":["post-58532","post","type-post","status-publish","format-standard","hentry","category-server","tag-amcl","tag-kld-","tag-slam","tag-5985","tag-427","tag-6169","tag-5987"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/58532.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb577\u6b21\uff0c\u70b9\u8d5e14\u6b21\uff0c\u6536\u85cf8\u6b21\u3002\u5df2\u77e5\u673a\u5668\u4eba\u7684\u5730\u56fe\uff08Map\uff09\u548c\u4f20\u611f\u5668\u89c2\u6d4b\u6570\u636e\uff08\u6fc0\u5149\u96f7\u8fbe\u3001\u91cc\u7a0b\u8ba1\u7b49\uff09\uff0c\u63a8\u65ad\u673a\u5668\u4eba\u5728\u5730\u56fe\u4e2d\u7684\u4f4d\u7f6e\u4e0e\u59ff\u6001\uff08\u5f53\u7c92\u5b50\u6570\u91cf\u6ee1\u8db3 KLD-sampling \u516c\u5f0f\u65f6\u505c\u6b62\u91c7\u6837\uff0c\u5426\u5219\u7ee7\u7eed\u91c7\u6837\u66f4\u591a\u7c92\u5b50\u3002\uff08KL\u6563\u5ea6\uff09\u6765\u7ea6\u675f\u8fd1\u4f3c\u5206\u5e03\u548c\u771f\u5b9e\u5206\u5e03\u7684\u5dee\u8ddd\u3002\uff1a\u5728\u5730\u56fe\u4e0a\u5747\u5300\u91c7\u6837\u7c92\u5b50\uff0c\u6216\u56f4\u7ed5\u521d\u59cb\u4f30\u8ba1\u91c7\u6837\u3002\u4f1a\u6839\u636e\u89c2\u6d4b\u548c\u5206\u5e03\u7a00\u758f\u7a0b\u5ea6\u52a8\u6001\u8c03\u6574\u3002\uff1a\u6839\u636e\u6743\u91cd\u91c7\u6837\u65b0\u7c92\u5b50\uff0c\u907f\u514d\u6743\u91cd\u9000\u5316\u3002\u52a8\u6001\u8c03\u6574\u7c92\u5b50\u6570\u91cf\uff0c\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002\u5728\u79fb\u52a8\u673a\u5668\u4eba\u4e2d\uff0c\u6211\u4eec\u5e38\u9047\u5230\u3002\uff1a\u6839\u636e\u4f20\u611f\u5668\u89c2\u6d4b\u66f4\u65b0\u7c92\u5b50\u6743\u91cd\u3002\uff1a\u6839\u636e\u8fd0\u52a8\u6a21\u578b\u66f4\u65b0\u7c92\u5b50\u4f4d\u7f6e\u3002\u7c92\u5b50\u6ee4\u6ce2\u662f\u901a\u8fc7\u4e00\u7ec4\u7c92\u5b50\u3002\u6765\u8fd1\u4f3c\u4f4d\u7f6e\u7684\u6982\u7387\u5206\u5e03\u3002\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/58532.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2025-08-16T04:05:04+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/58532.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/58532.html\",\"name\":\"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2025-08-16T04:05:04+00:00\",\"dateModified\":\"2025-08-16T04:05:04+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/58532.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/58532.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/58532.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/58532.html","og_locale":"zh_CN","og_type":"article","og_title":"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb577\u6b21\uff0c\u70b9\u8d5e14\u6b21\uff0c\u6536\u85cf8\u6b21\u3002\u5df2\u77e5\u673a\u5668\u4eba\u7684\u5730\u56fe\uff08Map\uff09\u548c\u4f20\u611f\u5668\u89c2\u6d4b\u6570\u636e\uff08\u6fc0\u5149\u96f7\u8fbe\u3001\u91cc\u7a0b\u8ba1\u7b49\uff09\uff0c\u63a8\u65ad\u673a\u5668\u4eba\u5728\u5730\u56fe\u4e2d\u7684\u4f4d\u7f6e\u4e0e\u59ff\u6001\uff08\u5f53\u7c92\u5b50\u6570\u91cf\u6ee1\u8db3 KLD-sampling \u516c\u5f0f\u65f6\u505c\u6b62\u91c7\u6837\uff0c\u5426\u5219\u7ee7\u7eed\u91c7\u6837\u66f4\u591a\u7c92\u5b50\u3002\uff08KL\u6563\u5ea6\uff09\u6765\u7ea6\u675f\u8fd1\u4f3c\u5206\u5e03\u548c\u771f\u5b9e\u5206\u5e03\u7684\u5dee\u8ddd\u3002\uff1a\u5728\u5730\u56fe\u4e0a\u5747\u5300\u91c7\u6837\u7c92\u5b50\uff0c\u6216\u56f4\u7ed5\u521d\u59cb\u4f30\u8ba1\u91c7\u6837\u3002\u4f1a\u6839\u636e\u89c2\u6d4b\u548c\u5206\u5e03\u7a00\u758f\u7a0b\u5ea6\u52a8\u6001\u8c03\u6574\u3002\uff1a\u6839\u636e\u6743\u91cd\u91c7\u6837\u65b0\u7c92\u5b50\uff0c\u907f\u514d\u6743\u91cd\u9000\u5316\u3002\u52a8\u6001\u8c03\u6574\u7c92\u5b50\u6570\u91cf\uff0c\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002\u5728\u79fb\u52a8\u673a\u5668\u4eba\u4e2d\uff0c\u6211\u4eec\u5e38\u9047\u5230\u3002\uff1a\u6839\u636e\u4f20\u611f\u5668\u89c2\u6d4b\u66f4\u65b0\u7c92\u5b50\u6743\u91cd\u3002\uff1a\u6839\u636e\u8fd0\u52a8\u6a21\u578b\u66f4\u65b0\u7c92\u5b50\u4f4d\u7f6e\u3002\u7c92\u5b50\u6ee4\u6ce2\u662f\u901a\u8fc7\u4e00\u7ec4\u7c92\u5b50\u3002\u6765\u8fd1\u4f3c\u4f4d\u7f6e\u7684\u6982\u7387\u5206\u5e03\u3002","og_url":"https:\/\/www.wsisp.com\/helps\/58532.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2025-08-16T04:05:04+00:00","author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"4 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/58532.html","url":"https:\/\/www.wsisp.com\/helps\/58532.html","name":"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2025-08-16T04:05:04+00:00","dateModified":"2025-08-16T04:05:04+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/58532.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/58532.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/58532.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"AMCL\uff08Adaptive Monte Carlo Localization\uff09\u7b97\u6cd5\u7684\u539f\u7406\u8be6\u89e3"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/58532","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=58532"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/58532\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=58532"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=58532"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=58532"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=58532"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}