{"id":73206,"date":"2026-02-07T09:33:38","date_gmt":"2026-02-07T01:33:38","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/73206.html"},"modified":"2026-02-07T09:33:38","modified_gmt":"2026-02-07T01:33:38","slug":"tdoa%ef%bc%88%e5%88%b0%e8%be%be%e6%97%b6%e9%97%b4%e5%b7%ae%ef%bc%89%e7%9a%84gdop%e5%92%8ccrlb%e8%ae%a1%e7%ae%97%e7%9a%84matlab%e4%be%8b%e7%a8%8b%ef%bc%8c%e8%ae%ba%e6%96%87%e5%a4%8d%e7%8e%b0%ef%bc%8c","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/73206.html","title":{"rendered":"TDOA\uff08\u5230\u8fbe\u65f6\u95f4\u5dee\uff09\u7684GDOP\u548cCRLB\u8ba1\u7b97\u7684MATLAB\u4f8b\u7a0b\uff0c\u8bba\u6587\u590d\u73b0\uff0c\u9644\u53c2\u8003\u6587\u732e\u3002GDOP\uff1a\u51e0\u4f55\u7cbe\u5ea6\u56e0\u5b50&amp;CRLB\uff1a\u514b\u62c9\u7f8e\u7f57\u4e0b\u754c"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260207013337-6986967153415.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u7a0b\u5e8f\u7528\u4e8e\u4e09\u7ef4 TDOA&#xff08;Time Difference of Arrival&#xff09;\u5b9a\u4f4d\u7cfb\u7edf\u4e2d\u51e0\u4f55\u7cbe\u5ea6\u7684\u5b9a\u91cf\u5206\u6790\u3002\u901a\u8fc7\u6784\u5efa\u591a\u57fa\u7ad9 TDOA \u6d4b\u91cf\u6a21\u578b&#xff0c;\u8ba1\u7b97\u76ee\u6807\u5728\u4e0d\u540c\u7a7a\u95f4\u4f4d\u7f6e\u5904\u7684 GDOP&#xff08;Geometric Dilution of Precision&#xff09; \u4ee5\u53ca\u5bf9\u5e94\u7684 CRLB&#xff08;Cram\u00e9r\u2013Rao Lower Bound&#xff09;&#xff0c;\u5e76\u4ee5\u56fa\u5b9a\u9ad8\u5ea6\u5207\u7247\u7684\u5f62\u5f0f&#xff0c;\u5728\u4e8c\u7ef4\u5e73\u9762\u4e0a\u7ed8\u5236 GDOP \u4e0e CRLB \u7684\u4e09\u7ef4\u66f2\u9762\u56fe\u53ca\u7b49\u9ad8\u7ebf\u5730\u5f62\u56fe&#xff0c;\u7528\u4e8e\u8bc4\u4f30\u57fa\u7ad9\u5e03\u5c40\u5bf9\u5b9a\u4f4d\u7cbe\u5ea6\u7684\u5f71\u54cd\u3002<\/p>\n<p>\u4ee3\u7801\u6839\u636e\u53c2\u8003\u6587\u732e\u7f16\u5199&#xff0c;\u975eAI\u751f\u6210&#xff0c;\u4ec5\u4f9b\u5b66\u4e60\u4e0e\u4ea4\u6d41&#xff0c;\u7981\u6b62\u7ffb\u5356<\/p>\n<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u4ee3\u7801\u4ecb\u7ecd<\/li>\n<li>\n<ul>\n<li>\u57fa\u7ad9\u4e0e\u8bef\u5dee\u5efa\u6a21<\/li>\n<li>GDOP \u4e0e CRLB \u8ba1\u7b97\u65b9\u6cd5<\/li>\n<li>\u53ef\u89c6\u5316\u4e0e\u7ed3\u679c\u5206\u6790\u65b9\u5f0f<\/li>\n<\/ul>\n<\/li>\n<li>\u8fd0\u884c\u7ed3\u679c<\/li>\n<li>MATLAB\u6e90\u4ee3\u7801<\/li>\n<\/ul>\n<h2>\u4ee3\u7801\u4ecb\u7ecd<\/h2>\n<h3>\u57fa\u7ad9\u4e0e\u8bef\u5dee\u5efa\u6a21<\/h3>\n<p>\u7a0b\u5e8f\u91c7\u7528 \u4e5d\u57fa\u7ad9\u6b63\u65b9\u5f62\u9635\u5217\u5e03\u5c40&#xff0c;\u57fa\u7ad9\u5206\u5e03\u4e8e\u540c\u4e00\u9ad8\u5ea6\u5e73\u9762&#xff0c;\u5176\u4e2d\u4e00\u4e2a\u4e3a\u4e3b\u57fa\u7ad9&#xff0c;\u5176\u4f59\u4e3a\u53c2\u8003\u57fa\u7ad9\u3002\u8be5\u5e03\u5c40\u5177\u6709\u8f83\u597d\u7684\u5bf9\u79f0\u6027&#xff0c;\u5e38\u7528\u4e8e TDOA \u5b9a\u4f4d\u7cbe\u5ea6\u5206\u6790\u4e0e\u5bf9\u6bd4\u7814\u7a76\u3002<\/p>\n<p>\u5728\u8bef\u5dee\u5efa\u6a21\u65b9\u9762&#xff0c;\u540c\u65f6\u8003\u8651\u4e86\u4e24\u7c7b\u8bef\u5dee\u6765\u6e90&#xff1a;<\/p>\n<li>TDOA \u6d4b\u91cf\u8bef\u5dee&#xff08;\u65f6\u95f4\u5dee\u6d4b\u91cf\u566a\u58f0&#xff09;&#xff0c;\u7528\u6807\u51c6\u5dee \u03b8_r \u63cf\u8ff0&#xff1b;<\/li>\n<li>\u57fa\u7ad9\u4f4d\u7f6e\u8bef\u5dee&#xff0c;\u7528\u6807\u51c6\u5dee \u03b8_s \u63cf\u8ff0&#xff0c;\u5e76\u5728\u534f\u65b9\u5dee\u4e2d\u540c\u65f6\u5305\u542b\u72ec\u7acb\u9879\u4e0e\u76f8\u5173\u9879&#xff0c;\u7528\u4e8e\u523b\u753b\u5b9e\u9645\u90e8\u7f72\u4e2d\u57fa\u7ad9\u5750\u6807\u4e0d\u786e\u5b9a\u6027\u5bf9\u5b9a\u4f4d\u6027\u80fd\u7684\u5f71\u54cd\u3002<\/li>\n<h3>GDOP \u4e0e CRLB \u8ba1\u7b97\u65b9\u6cd5<\/h3>\n<p>\u5bf9\u6bcf\u4e00\u4e2a\u76ee\u6807\u70b9\u4f4d\u7f6e&#xff0c;\u9996\u5148\u6784\u5efa TDOA \u89c2\u6d4b\u65b9\u7a0b\u7684\u51e0\u4f55\u77e9\u9635\u3002\u8be5\u77e9\u9635\u7531\u76ee\u6807\u70b9\u5230\u5404\u57fa\u7ad9\u7684\u89c6\u7ebf\u65b9\u5411\u5411\u91cf\u5dee\u6784\u6210&#xff0c;\u53cd\u6620\u4e86\u7cfb\u7edf\u5728\u8be5\u4f4d\u7f6e\u5904\u7684\u51e0\u4f55\u53ef\u89c2\u6d4b\u6027\u3002<\/p>\n<ul>\n<li>GDOP \u901a\u8fc7\u51e0\u4f55\u77e9\u9635\u7684\u6b63\u89c4\u65b9\u7a0b\u8ba1\u7b97\u5f97\u5230&#xff0c;\u7528\u4e8e\u63cf\u8ff0\u5b9a\u4f4d\u8bef\u5dee\u5bf9\u6d4b\u91cf\u566a\u58f0\u7684\u653e\u5927\u7a0b\u5ea6&#xff0c;GDOP \u8d8a\u5c0f&#xff0c;\u51e0\u4f55\u6784\u578b\u8d8a\u4f18\u3002<\/li>\n<li>CRLB \u5728 GDOP \u7684\u57fa\u7840\u4e0a\u8fdb\u4e00\u6b65\u5f15\u5165\u6d4b\u91cf\u566a\u58f0\u4e0e\u57fa\u7ad9\u8bef\u5dee\u534f\u65b9\u5dee&#xff0c;\u7ed9\u51fa\u4f4d\u7f6e\u4f30\u8ba1\u8bef\u5dee\u7684\u7406\u8bba\u4e0b\u754c&#xff0c;\u80fd\u591f\u66f4\u771f\u5b9e\u5730\u53cd\u6620\u7cfb\u7edf\u7684\u6781\u9650\u5b9a\u4f4d\u7cbe\u5ea6\u3002<\/li>\n<\/ul>\n<h3>\u53ef\u89c6\u5316\u4e0e\u7ed3\u679c\u5206\u6790\u65b9\u5f0f<\/h3>\n<p>\u7a0b\u5e8f\u5728\u7ed9\u5b9a\u9ad8\u5ea6 ( z ) \u6761\u4ef6\u4e0b&#xff0c;\u5bf9\u76ee\u6807\u5728\u4e8c\u7ef4\u5e73\u9762\u5185\u8fdb\u884c\u7f51\u683c\u904d\u5386&#xff0c;\u5206\u522b\u7ed8\u5236&#xff1a;<\/p>\n<ul>\n<li>GDOP \u7684\u4e09\u7ef4\u66f2\u9762\u56fe\u4e0e\u7b49\u9ad8\u7ebf\u5730\u5f62\u56fe&#xff1b;<\/li>\n<li>CRLB \u7684\u4e09\u7ef4\u66f2\u9762\u56fe\u4e0e\u7b49\u9ad8\u7ebf\u5730\u5f62\u56fe\u3002<\/li>\n<\/ul>\n<h2>\u8fd0\u884c\u7ed3\u679c<\/h2>\n<p>\u6839\u636e\u8bba\u6587\u91cc\u9762\u7684\u951a\u70b9\u8bbe\u7f6e&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260207013337-698696716a0cc.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u5f97\u5230\u7684GDOP&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260207013337-698696717aef4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> CRLB&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260207013337-6986967191f9f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u951a\u70b9\u4f4d\u7f6e\u793a\u610f\u56fe&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260207013337-69869671a9dc3.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u57fa\u7ad9\u4fee\u6539\u4e3a\u975e\u5171\u9762\u4ee5\u540e&#xff0c;\u7ed3\u679c\u5982\u4e0b&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260207013337-69869671bec26.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>MATLAB\u6e90\u4ee3\u7801<\/h2>\n<p>\u90e8\u5206\u4ee3\u7801\u5982\u4e0b&#xff1a;<\/p>\n<p><span class=\"token comment\">%% \u4e09\u7ef4TDOA\u5b9a\u4f4d\u7684GDOP\u8ba1\u7b97\u3001\u7ed8\u5236\u3010\u4e0d\u540c\u9ad8\u5ea6\u3011\u4e0b\u7684GDOP\u5207\u7247&#xff0c;\u5730\u5f62\u56fe\u5f62\u5f0f<\/span><br \/>\n<span class=\"token comment\">% \u53c2\u8003\u6587\u732e&#xff1a;\u5f20\u667a\u8d85,\u674e\u65b0\u5a25,\u5f20\u745c.\u5e03\u5c40\u65b9\u5f0f\u5bf9TDOA\u5ba4\u5185\u5b9a\u4f4d\u7cbe\u5ea6\u5f71\u54cd\u5206\u6790[J].\u4f20\u611f\u5668\u4e0e\u5fae\u7cfb\u7edf,2023,42(09):61-64<\/span><br \/>\n<span class=\"token comment\">% \u4f5c\u8005&#xff1a;matlabfilter<\/span><br \/>\n<span class=\"token comment\">% 2026-01-28\/Ver1<\/span><\/p>\n<p>clear<span class=\"token punctuation\">;<\/span> close all<span class=\"token punctuation\">;<\/span> clc<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token function\">rng<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>theta_r <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">5e-9<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">%\u6d4b\u91cf\u65f6\u5dee\u8bef\u5dee\u7684\u6807\u51c6\u5dee<\/span><br \/>\ntheta_s <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.005<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">%\u5404\u57fa\u7ad9\u4f4d\u7f6e\u8bef\u5dee\u7684\u6807\u51c6\u5dee<\/span><br \/>\n<span class=\"token comment\">% \u4e5d\u7ad9\u6b63\u65b9\u5f62\u9635\u5217\u914d\u7f6e<\/span><br \/>\nstations <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><br \/>\n    <span class=\"token number\">0<\/span>    <span class=\"token number\">0<\/span>    <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u4e3b\u57fa\u7ad9 (\u4e2d\u5fc3\u4f4d\u7f6e)<\/span><br \/>\n    <span class=\"token number\">0<\/span>    <span class=\"token number\">200<\/span>  <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad91<\/span><br \/>\n    <span class=\"token number\">0<\/span>   <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">200<\/span>  <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad92<\/span><br \/>\n    <span class=\"token number\">200<\/span>  <span class=\"token number\">0<\/span>    <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad93<\/span><br \/>\n   <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">200<\/span>  <span class=\"token number\">0<\/span>    <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad94<\/span><br \/>\n    <span class=\"token number\">200<\/span>  <span class=\"token number\">200<\/span>  <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad95<\/span><br \/>\n   <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">200<\/span>  <span class=\"token number\">200<\/span>  <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad96<\/span><br \/>\n   <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">200<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">200<\/span>  <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad97<\/span><br \/>\n    <span class=\"token number\">200<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">200<\/span>  <span class=\"token number\">3<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">% \u53c2\u8003\u57fa\u7ad98<\/span><br \/>\n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">% \u57fa\u7ad9\u4f4d\u7f6e&#xff0c;\u6bcf\u884c\u4e00\u4e2a\u57fa\u7ad9&#xff0c;XYZ\u4e09\u8f74\u5750\u6807<\/span><\/p>\n<p><span class=\"token comment\">%% \u5728\u904d\u5386\u76ee\u6807\u70b9&#xff08;\u53ef\u4f7f\u7528for\u5faa\u73af&#xff09;&#xff0c;\u7ed8\u5236\u4e0d\u540c\u76ee\u6807\u70b9\u7684GPOD<\/span><br \/>\n<span class=\"token keyword\">for<\/span> z <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><br \/>\nX <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">400<\/span><span class=\"token operator\">:<\/span><span class=\"token number\">1<\/span><span class=\"token operator\">:<\/span><span class=\"token number\">400<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">% m    <\/span><br \/>\nY <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">400<\/span><span class=\"token operator\">:<\/span><span class=\"token number\">1<\/span><span class=\"token operator\">:<\/span><span class=\"token number\">400<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">% m   <\/span><br \/>\nG<span class=\"token operator\">&#061;<\/span><span class=\"token function\">zeros<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">length<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><span class=\"token function\">length<\/span><span class=\"token punctuation\">(<\/span>Y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><span class=\"token string\">&#039;double&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\nCRLB <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">zeros<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">length<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><span class=\"token function\">length<\/span><span class=\"token punctuation\">(<\/span>Y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><span class=\"token string\">&#039;double&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token number\">i<\/span> <span 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