[2410.05883] Improved PCRLB for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control

<!DOCTYPE html> <html lang="en"> <head> <title>[2410.05883] Improved PCRLB for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control</title> <meta name="viewport" content="width=device-width, initial-scale=1"> <link rel="apple-touch-icon" sizes="180x180" href="/static/browse/0.3.4/images/icons/apple-touch-icon.png"> <link rel="icon" type="image/png" sizes="32x32" href="/static/browse/0.3.4/images/icons/favicon-32x32.png"> <link rel="icon" type="image/png" sizes="16x16" href="/static/browse/0.3.4/images/icons/favicon-16x16.png"> <link rel="manifest" href="/static/browse/0.3.4/images/icons/site.webmanifest"> <link rel="mask-icon" href="/static/browse/0.3.4/images/icons/safari-pinned-tab.svg" color="#5bbad5"> <meta name="msapplication-TileColor" content="#da532c"> <meta name="theme-color" content="#ffffff"> <link rel="stylesheet" type="text/css" media="screen" href="/static/browse/0.3.4/css/arXiv.css?v=20241206" /> <link rel="stylesheet" type="text/css" media="print" href="/static/browse/0.3.4/css/arXiv-print.css?v=20200611" /> <link rel="stylesheet" type="text/css" media="screen" href="/static/browse/0.3.4/css/browse_search.css" /> <script language="javascript" src="/static/browse/0.3.4/js/accordion.js" /></script> <link rel="canonical" href="https://arxiv.org/abs/2410.05883"/> <meta name="description" content="Abstract page for arXiv paper 2410.05883: Improved PCRLB for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control"><meta property="og:type" content="website" /> <meta property="og:site_name" content="arXiv.org" /> <meta property="og:title" content="Improved PCRLB for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control" /> <meta property="og:url" content="https://arxiv.org/abs/2410.05883v1" /> <meta property="og:image" content="/static/browse/0.3.4/images/arxiv-logo-fb.png" /> <meta property="og:image:secure_url" content="/static/browse/0.3.4/images/arxiv-logo-fb.png" /> <meta property="og:image:width" content="1200" /> <meta property="og:image:height" content="700" /> <meta property="og:image:alt" content="arXiv logo"/> <meta property="og:description" content="In realistic radar tracking, target measurement uncertainty (TMU) in terms of both detection probability and measurement error covariance is significantly affected by the target-to-radar (T2R) geometry. However, existing posterior Cramer-Rao Lower Bounds (PCRLBs) rarely investigate the fundamental impact of T2R geometry on target measurement uncertainty and eventually on mean square error (MSE) of state estimate, inevitably resulting in over-conservative lower bound. To address this issue, this paper firstly derives the generalized model of target measurement error covariance for bistatic radar with moving receiver and transmitter illuminating any type of signal, along with its approximated solution to specify the impact of T2R geometry on error covariance. Based upon formulated TMU model, an improved PCRLB (IPCRLB) fully accounting for both measurement origin uncertainty and geometry-dependent TMU is then re-derived, both detection probability and measurement error covariance are treated as state-dependent parameters when differentiating log-likelihood with respect to target state. Compared to existing PCRLBs that partially or completely ignore the dependence of target measurement uncertainty on T2R geometry, proposed IPCRLB provides a much accurate (less-conservative) lower bound for radar tracking in clutter with geometry-dependent TMU. The new bound is then applied to radar trajectory control to effectively optimize T2R geometry and exhibits least uncertainty of acquired target measurement and more accurate state estimate for bistatic radar tracking in clutter, compared to state-of-the-art trajectory control methods."/> <meta name="twitter:site" content="@arxiv"/> <meta name="twitter:card" content="summary"/> <meta name="twitter:title" content="Improved PCRLB for radar tracking in clutter with..."/> <meta name="twitter:description" content="In realistic radar tracking, target measurement uncertainty (TMU) in terms of both detection probability and measurement error covariance is significantly affected by the target-to-radar (T2R)..."/> <meta name="twitter:image" content="https://static.arxiv.org/icons/twitter/arxiv-logo-twitter-square.png"/> <meta name="twitter:image:alt" content="arXiv logo"/> <link rel="stylesheet" media="screen" type="text/css" href="/static/browse/0.3.4/css/tooltip.css"/><link rel="stylesheet" media="screen" type="text/css" href="https://static.arxiv.org/js/bibex-dev/bibex.css?20200709"/> <script src="/static/browse/0.3.4/js/mathjaxToggle.min.js" type="text/javascript"></script> <script src="//code.jquery.com/jquery-latest.min.js" type="text/javascript"></script> <script src="//cdn.jsdelivr.net/npm/js-cookie@2/src/js.cookie.min.js" type="text/javascript"></script> <script src="//cdn.jsdelivr.net/npm/dompurify@2.3.5/dist/purify.min.js"></script> <script src="/static/browse/0.3.4/js/toggle-labs.js?20241022" type="text/javascript"></script> <script src="/static/browse/0.3.4/js/cite.js" type="text/javascript"></script><meta name="citation_title" content="Improved PCRLB for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control" /><meta name="citation_author" content="Shi, Yifang" /><meta name="citation_author" content="Zhang, Yu" /><meta name="citation_author" content="Fu, Linjiao" /><meta name="citation_author" content="Peng, Dongliang" /><meta name="citation_author" content="Lu, Qiang" /><meta name="citation_author" content="Choi, Jee Woong" /><meta name="citation_author" content="Farina, Alfonso" /><meta name="citation_date" content="2024/10/08" /><meta name="citation_online_date" content="2024/10/08" /><meta name="citation_pdf_url" content="http://arxiv.org/pdf/2410.05883" /><meta name="citation_arxiv_id" content="2410.05883" /><meta name="citation_abstract" content="In realistic radar tracking, target measurement uncertainty (TMU) in terms of both detection probability and measurement error covariance is significantly affected by the target-to-radar (T2R) geometry. However, existing posterior Cramer-Rao Lower Bounds (PCRLBs) rarely investigate the fundamental impact of T2R geometry on target measurement uncertainty and eventually on mean square error (MSE) of state estimate, inevitably resulting in over-conservative lower bound. To address this issue, this paper firstly derives the generalized model of target measurement error covariance for bistatic radar with moving receiver and transmitter illuminating any type of signal, along with its approximated solution to specify the impact of T2R geometry on error covariance. Based upon formulated TMU model, an improved PCRLB (IPCRLB) fully accounting for both measurement origin uncertainty and geometry-dependent TMU is then re-derived, both detection probability and measurement error covariance are treated as state-dependent parameters when differentiating log-likelihood with respect to target state. Compared to existing PCRLBs that partially or completely ignore the dependence of target measurement uncertainty on T2R geometry, proposed IPCRLB provides a much accurate (less-conservative) lower bound for radar tracking in clutter with geometry-dependent TMU. The new bound is then applied to radar trajectory control to effectively optimize T2R geometry and exhibits least uncertainty of acquired target measurement and more accurate state estimate for bistatic radar tracking in clutter, compared to state-of-the-art trajectory control methods." /> </head> <body class="with-cu-identity"> <div class="flex-wrap-footer"> <header> <a href="#content" class="is-sr-only">Skip to main content</a>  <div class="columns is-vcentered is-hidden-mobile" id="cu-identity"> <div class="column" id="cu-logo"> <a href="https://www.cornell.edu/"><img src="/static/browse/0.3.4/images/icons/cu/cornell-reduced-white-SMALL.svg" alt="Cornell University" /></a> </div><div class="column" id="support-ack"> <span id="support-ack-url">We gratefully acknowledge support from the Simons Foundation, <a href="https://info.arxiv.org/about/ourmembers.html">member institutions</a>, and all contributors.</span> <a href="https://info.arxiv.org/about/donate.html" 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for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control</h1> <div class="authors"><span class="descriptor">Authors:</span><a href="https://arxiv.org/search/eess?searchtype=author&query=Shi,+Y" rel="nofollow">Yifang Shi</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Zhang,+Y" rel="nofollow">Yu Zhang</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Fu,+L" rel="nofollow">Linjiao Fu</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Peng,+D" rel="nofollow">Dongliang Peng</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Lu,+Q" rel="nofollow">Qiang Lu</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Choi,+J+W" rel="nofollow">Jee Woong Choi</a>, <a href="https://arxiv.org/search/eess?searchtype=author&query=Farina,+A" rel="nofollow">Alfonso Farina</a></div> <div id="download-button-info" hidden>View a PDF of the paper titled Improved PCRLB for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control, by Yifang Shi and 5 other authors</div> <a class="mobile-submission-download" href="/pdf/2410.05883">View PDF</a> <a class="mobile-submission-download" href="https://arxiv.org/html/2410.05883v1">HTML (experimental)</a> <blockquote class="abstract mathjax"> <span class="descriptor">Abstract:</span>In realistic radar tracking, target measurement uncertainty (TMU) in terms of both detection probability and measurement error covariance is significantly affected by the target-to-radar (T2R) geometry. However, existing posterior Cramer-Rao Lower Bounds (PCRLBs) rarely investigate the fundamental impact of T2R geometry on target measurement uncertainty and eventually on mean square error (MSE) of state estimate, inevitably resulting in over-conservative lower bound. To address this issue, this paper firstly derives the generalized model of target measurement error covariance for bistatic radar with moving receiver and transmitter illuminating any type of signal, along with its approximated solution to specify the impact of T2R geometry on error covariance. Based upon formulated TMU model, an improved PCRLB (IPCRLB) fully accounting for both measurement origin uncertainty and geometry-dependent TMU is then re-derived, both detection probability and measurement error covariance are treated as state-dependent parameters when differentiating log-likelihood with respect to target state. Compared to existing PCRLBs that partially or completely ignore the dependence of target measurement uncertainty on T2R geometry, proposed IPCRLB provides a much accurate (less-conservative) lower bound for radar tracking in clutter with geometry-dependent TMU. The new bound is then applied to radar trajectory control to effectively optimize T2R geometry and exhibits least uncertainty of acquired target measurement and more accurate state estimate for bistatic radar tracking in clutter, compared to state-of-the-art trajectory control methods. </blockquote>  <div class="metatable"> <table summary="Additional metadata"> <tr> <td class="tablecell label">Comments:</td> <td class="tablecell comments mathjax">15 pages,12 figures</td> </tr> <tr> <td class="tablecell label">Subjects:</td> <td class="tablecell subjects"> <span class="primary-subject">Signal Processing (eess.SP)</span>; Optimization and Control (math.OC)</td> </tr> <tr> <td class="tablecell label"><abbr title="Association of Computing Machinery Classification">ACM</abbr> classes:</td> <td class="tablecell acm-classes">F.2.1</td> </tr> <tr> <td class="tablecell label">Cite as:</td> <td class="tablecell arxivid"><span class="arxivid"><a href="https://arxiv.org/abs/2410.05883">arXiv:2410.05883</a> [eess.SP]</span></td> </tr> <tr> <td class="tablecell label"> </td> <td class="tablecell arxividv">(or <span class="arxivid"> <a href="https://arxiv.org/abs/2410.05883v1">arXiv:2410.05883v1</a> [eess.SP]</span> for this version) </td> </tr> <tr> <td class="tablecell label"> </td> <td class="tablecell arxivdoi"> <a href="https://doi.org/10.48550/arXiv.2410.05883" id="arxiv-doi-link">https://doi.org/10.48550/arXiv.2410.05883</a><div class="button-and-tooltip"> <button class="more-info" aria-describedby="more-info-desc-1"> <svg height="15" role="presentation" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 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[2410.05883] Improved PCRLB for radar tracking in clutter with geometry-dependent target measurement uncertainty and application to radar trajectory control