雷竞技rebat前沿|大量毁灭梯形算法前瞻性单脉冲成像与匀加速运动平台</tgydF4y2B一个itle> <link href="https://209cd62b0febf2a55d40-715eb384bc6027b876e93ad33d5c5ec3.ssl.cf3.rackcdn.com/font-awesome-4.3.0/css/font-awesome.min.css" rel="stylesheet"> <link href="https://9d0dd7a648345f19af83-877d2ecaf11b88d5e17327c758e17ef6.ssl.cf2.rackcdn.com/museo-sans-1.0.1/css/museo-sans.css" rel="stylesheet"> <style type="text/css"> </style> </head> <body class="journal-signal-processing section-radar-signal-processing"> <a href="#main-content" class="bypassBlock-wrapper" id="bypass"><span class="bypassBlock-button">跳转到主要内容</年代p一个n></一个> <noscript> <iframe src="https://www.thespel.com/ns.html?id=GTM-TFKV632>m_auth=NsJH3Ts1-89I8lZURwQYmw>m_preview=env-1>m_cookies_win=x" height="0" width="0" style="display:none;visibility:hidden"></iframe> </noscript>  <noscript> <iframe src="https://www.thespel.com/ns.html?id=GTM-N279F7B>m_auth=jfKETtlWamfZ4l02YiFCQw>m_preview=env-1>m_cookies_win=x" height="0" width="0" style="display:none;visibility:hidden"></iframe> </noscript>  <frontiers-ibar main-domain="frontiersin.org" loop-url="https://loop.frontiersin.org" journal-id="1786"></frontiers-ibar> <div class="page-container sidemenu-collapsed" id="main-content"> <div id="article" class="boxed white no-padding"> <div class="container-fluid main-container-xxl"> <div class="row" id="similar-articles"> <div class="new-wrapper"> <style> .disabled-supplementary-btn { cursor: not-allowed; pointer-events: none; opacity: .65; filter: alpha(opacity=65); -webkit-box-shadow: none; box-shadow: none; } </style> <aside class="right-container"> <div class="side-article-download clearfix"> <ul class="list-unstyled list-inline clearfix"> <li class="dropdown text-center paper"><button data-target="#" class="dropdown-toggle" data-test-id="download-button" data-toggle="dropdown" role="button" aria-expanded="false"><span class="icon-label" data-event="download-button-click">下载文章</年代p一个n></button> <div class="dropdown-menu-wrapper"> <div class="dropdown-menu-mobile-title"> 下载文章</dgydF4y2B一个iv> <ul class="dropdown-menu" role="menu"> <li><a class="download-files-pdf action-link" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/pdf" data-test-id="article-downloadpdf" data-event="downloadpdf-button-click">下载</一个></li> <li><a class="download-files-readcube" href="http://www.readcube.com/articles/10.3389/frsip.2022.1074053" data-test-id="article-viewenhancedpdf" data-event="downloadreadcube-button-click">ReadCube</一个></li> <li><a class="download-files-epub" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/epub" data-test-id="article-epub" data-event="downloadepub-button-click">EPUB</一个></li> <li><a class="download-files-nlm" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/xml/nlm" data-test-id="article-nlm" data-event="downloadnlm-button-click">XML (NLM)</一个></li> </ul> <button class="dropdown-menu-mobile-close-button" aria-label="Close" data-toggle="dropdown"></button> </div></li> <li class="dropdown"><button type="button" class="navbar-toggle navbar-share" data-toggle="dropdown" data-target="#" aria-expanded="false"></button> <div class="dropdown-menu-wrapper"> <div class="dropdown-menu-mobile-title"> 分享</dgydF4y2B一个iv> <ul class="dropdown-menu" role="menu"> <li class="social_block"> <div class="atButton"> <a class="addthis_button_twitter at300b" addthis:title="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:description="Forward-looking imaging for maneuvering platforms has garnered significant interest in many military and civilian fields. As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" data-event-param="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" title="" target="_blank" href="#"><span class="at-icon-wrapper"></span></a> </div></li> <li class="social_block"> <div class="atButton"> <a class="addthis_button_linkedin at300b" addthis:title="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:description="Forward-looking imaging for maneuvering platforms has garnered significant interest in many military and civilian fields. As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" data-event-param="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" title="" target="_blank" href="#"><span class="at-icon-wrapper"></span></a> </div></li> <li class="social_block"> <div class="atButton"> <a class="addthis_button_facebook at300b" addthis:title="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:description="Forward-looking imaging for maneuvering platforms has garnered significant interest in many military and civilian fields. As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" data-event-param="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" title="" target="_blank" href="#"><span class="at-icon-wrapper"></span></a> </div></li> </ul> <button class="dropdown-menu-mobile-close-button" aria-label="Close" data-toggle="dropdown"></button> </div></li> <li class="dropdown"><button type="button" class="navbar-toggle navbar-citations" data-event="citation-button-click" data-toggle="dropdown" data-target="#" aria-expanded="false"></button> <div class="dropdown-menu-wrapper"> <div class="dropdown-menu-mobile-title"> 出口的引用</dgydF4y2B一个iv> <ul class="dropdown-menu" role="menu"> <li><a data-test-id="article-endnote" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/endNote" data-event="endnotedownload-button-click">尾注</一个></li> <li><a data-test-id="article-referencemanager" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/reference" data-event="referencemanagerdownload-button-click">引用管理器</一个></li> <li><a data-test-id="article-simpletextfile" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/text" data-event="simpletextfiledownload-button-click">简单的文本文件</一个></li> <li><a data-test-id="article-bibtex" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/bibTex" data-event="bibtexdownload-button-click">助理</一个></li> </ul> <button class="dropdown-menu-mobile-close-button" aria-label="Close" data-toggle="dropdown"></button> </div></li> </ul> </div> <div class="side-article-impact"> <ul class="nav"> <li class="impact-data" title="View numbers are not up-to-date. 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As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" title=""><span class="at-icon-wrapper" style=" background-color: rgb(29, 161, 242); line-height: 16px; height: 16px; width: 16px; "></span></a> </div><a><span class="facebook_count"></span></a></li> <li class="social_block"> <div class="atButton"> <a class="addthis_button_twitter at300b" data-event="shareicon-button-click" data-event-param="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:title="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:description="Forward-looking imaging for maneuvering platforms has garnered significant interest in many military and civilian fields. As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" title=""><span class="at-icon-wrapper" style=" background-color: rgb(29, 161, 242); line-height: 16px; height: 16px; width: 16px; "></span></a> </div><a><span class="twitter_count"></span></a></li> <li class="social_block"> <div class="atButton"> <a class="addthis_button_google at300b" data-event="shareicon-button-click" data-event-param="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:title="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:description="Forward-looking imaging for maneuvering platforms has garnered significant interest in many military and civilian fields. As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" title=""><span class="at-icon-wrapper" style=" background-color: rgb(29, 161, 242); line-height: 16px; height: 16px; width: 16px; "></span></a> </div><a><span class="twitter_count"></span></a></li> <li class="social_block"> <div class="atButton"> <a class="addthis_button_linkedin at300b" data-event="shareicon-button-click" data-event-param="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:title="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:description="Forward-looking imaging for maneuvering platforms has garnered significant interest in many military and civilian fields. As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" title=""><span class="at-icon-wrapper" style=" background-color: rgb(29, 161, 242); line-height: 16px; height: 16px; width: 16px; "></span></a> </div><a><span class="linkedin_count"></span></a></li> <li class="social_block"> <div class="atButton"> <a class="addthis_button_more at300b" data-event="shareicon-button-click" data-event-param="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:title="Decimation keystone algorithm for forward-looking monopulse imaging on platforms with uniformly accelerated motion" addthis:description="Forward-looking imaging for maneuvering platforms has garnered significant interest in many military and civilian fields. As the maneuvering trajectory in the scanning period can be simplified as the constant acceleration maneuver, monopulse imaging is applied to enhance the azimuthal resolution of the forward-looking image. However, the maneuver causes severe range migration and Doppler shift; this often results in range location error due to the space-varying Doppler shifts and the failure of angle estimation. We propose a decimation keystone algorithm based on the chirp-Z transform (CZT). First, the pulse repetition frequency (PRF) is decimated with an integer; thus, the azimuthal sampling sequence is decimated into many sub-sequences. Then, the linear range walk correction (LRWC) is performed on each sub-sequence using the keystone transform, significantly reducing the influence of the change of Doppler-ambiguity-number on range location. Further, the sub-sequences are regrouped as one sequence, and the range curvature due to the acceleration is compensated in the frequency domain. Finally, the varying Doppler centroid in each coherent processing interval (CPI) is analyzed and compensated for the sum-difference angular measurements. Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction." addthis:url="//www.thespel.com/articles/10.3389/frsip.2022.1074053" title=""><span class="at-icon-wrapper" style=" background-color: rgb(29, 161, 242); line-height: 16px; height: 16px; width: 16px; "></span></a> </div><a><span class="total_count"></span></a></li> </ul> </div> <aside id="anchors" class="pull-left table-of-contents side-article"> <div class="side-people hidden-sm hidden-xs"> <section class="side-article-editors"> <header> <h5 class="like-h4">编辑</h5></he一个der><一个class="authors" href="//www.thespel.com/loop/people/1856822/overview" target="_blank"><img alt="" class="pr5 pull-left" onerror="this.src = '/Areas/Articles/Images/Frontiers/Common/Profile/default-loop-profile.jpg'" src="https://loop.frontiersin.org/images/profile/1856822/24"><h6 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data-event="simpletextfiledownload-button-click">简单的文本文件</一个></li> <li><a data-test-id="article-bibtex" href="//www.thespel.com/articles/10.3389/frsip.2022.1074053/bibTex" data-event="bibtexdownload-button-click">助理</一个></li> </ul></li> </ul> </div> <div class="side-crossmark"> <a data-target="crossmark" class="crossmark"> <figure> <img id="crossmark-icon" style="border: 0; width:64px; height:64px;" src="https://crossmark-cdn.crossref.org/widget/v2.0/logos/CROSSMARK_BW_square_no_text.svg" title="" alt=""> </figure> <div id="crossmark-icon"> 检查更新</dgydF4y2B一个iv></a> </div> <article class="widget-listing people-also-looked-at side-article-related hidden"> <h5 class="like-h4" data-event="peoplelookedat-link-click">人也看了</h5></一个rticle> </aside> <main class=""> <div class="article-section"> <div class="article-container" data-html="True"> <div class="abstract-container"> <div class="article-header-container">   <div class="header-bar-one"> <h2>原始研究的文章</h2></dgydF4y2B一个iv> <div class="header-bar-three-container"> <div class="header-bar-three"> 前面。信号的过程。,05January 2023<br>秒。雷达信号处理<gydF4y2B一个br> <span class="volumeInfo">卷2 - 2022 |</年代p一个n><一个href="https://doi.org/10.3389/frsip.2022.1074053">https://doi.org/10.3389/frsip.2022.1074053</一个></div> </div> </div> <div class="JournalAbstract"> <a id="h1" name="h1"></a> <h1>大量毁灭梯形算法前瞻性单脉冲成像与匀加速运动平台</h1><dgydF4y2B一个iv class="authors"> <a href="//www.thespel.com/people/u/1911724" class="user-id-1911724"><img class="pr5" src="https://loop.frontiersin.org/images/profile/1911724/24" onerror="this.src='https://f96a1a95aaa960e01625-a34624e694c43cdf8b40aa048a644ca4.ssl.cf2.rackcdn.com/Design/Images/newprofile_default_profileimage_new.jpg'" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个">Ze-Sen李</一个>和<一个href="//www.thespel.com/people/u/2129075" class="user-id-2129075"><img class="pr5" src="https://loop.frontiersin.org/images/profile/2129075/24" onerror="this.src='https://f96a1a95aaa960e01625-a34624e694c43cdf8b40aa048a644ca4.ssl.cf2.rackcdn.com/Design/Images/newprofile_default_profileimage_new.jpg'" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个">Yue-Li李</一个>*</dgydF4y2B一个iv> <ul class="notes"> <li>电子科学与技术学院,国防科技大学、长沙,中国</gydF4y2B一个li> </ul> <p class="mb15">前瞻性的成像为机动平台得到了显著的许多军用和民用领域的兴趣。的机动轨迹扫描周期可以简化为恒定加速度机动,单脉冲成像应用于提高方位分辨率的前瞻性形象。然而,操作会导致严重的移民和多普勒频移;这往往导致定位误差范围由于space-varying多普勒频移和角估计的失败。我们提出一个大批杀害梯形算法基于chirp-Z变换(CZT)。首先,脉冲重复频率(脉冲)摧毁一个整数;因此,方位采样序列是摧毁成许多子。然后,线性范围走校正(LRWC)上执行的每个子使用梯形变换,大大减少Doppler-ambiguity-number的变化的影响范围的位置。此外,子重新集结为一个序列,由于曲率加速度补偿范围在频域。最后,不同的多普勒质心在每个相干处理间隔(CPI)分析和补偿和差角测量。 Simulation results demonstrate the effectiveness of the proposed algorithm for forward-looking imaging under constant acceleration maneuvers and the feasibility of range location error correction.</p><div class="clear"></div> </div> <div class="JournalFullText"> <a id="h2" name="h2"></a> <h2>1介绍</h2><pcgydF4y2B一个lass="mb15">高分辨率微波成像的飞机领域引发了近年来大量研究人员的兴趣。多普勒波束锐化(DBS)和单脉冲成像技术是两种广泛使用的技术来提高横向距离/角分辨率机载扫描雷达传感器。多普勒波束锐化不能解决多个散射大斜视情况下因为严重下降的多普勒质心差异,导致“盲区”的前瞻性的方向。前瞻性单脉冲成像是指二维微波成像的前视图基于单脉冲技术的飞机。通常,雷达天线扫描前的场景,和单脉冲技术是利用来提高方位分辨率的图像(<一个href="#B1">格里菲思1998</一个>;<gydF4y2B一个一个href="#B9">镍,2006</一个>;<gydF4y2B一个一个href="#B19">Zhang et al ., 2016</一个>)。该方法的特点是系统复杂性低,良好的适应性的飞行路线,重要的分辨率增强。但是,单脉冲技术无法解决目标多重性的范围和方位分辨率本一个普通的单脉冲雷达。引起的角闪烁目标多重性可能会导致成像模糊的前瞻性的图像,尤其是对扩展目标由大量的散射。摘要单脉冲技术结合多普勒波束锐化(DBS)技术,散射的多普勒频差在主瓣用于分离成不同的多普勒单元(<一个href="#B8">陆et al ., 2011</一个>)。然后,和差多普勒估计重建和用于估计散射的角度。方法可以显著减少造成的图像模糊限制自由角尺寸(<一个href="#B5">李et al ., 2021</一个>)。</p><pcgydF4y2B一个lass="mb15">通常,均匀运动在相干处理间隔(CPI)往往导致严重的space-varying范围迁移(<一个href="#B3">李et al ., 2012</一个>),因此影响聚焦性能和定位精度。因此,线性范围走校正(LRWC)实现基于前瞻性的梯形变换成像(<一个href="#B3">李et al ., 2012</一个>)。然而,Doppler-ambiguity-number的变化由于不同多普勒频移的目标在不同的方向也应该解决。</p><pcgydF4y2B一个lass="mb15">机动轨迹可以简化为恒定加速度运动在单脉冲估计的CPI。和扫描过程中的速度变化的平台迁移和space-varying多普勒频移引起非线性范围。所以,曲率范围和多普勒频移需要解决。特别是当采用扫描模式,改变的Doppler-ambiguity-number散射位于大斜视角度可能引起严重的位置误差范围(<一个href="#B7">李et al ., 2022</一个>)。此外,角度测量基于多普勒估计可能遭受不同多普勒变化由于加速度。</p><pcgydF4y2B一个lass="mb15">前瞻性的雷达成像的目标是积累散射的反射能量前后一致地。这就像使用固定雷达系统探测一个移动的目标。两个应用程序之间的相关运动必须克服雷达的天线相位中心(APC)和目标。范围迁移和多普勒的历史回声是相似的。因此,提出了探测目标的方法与匀加速运动可能可行的补偿运动误差前瞻性成像。</p><pcgydF4y2Balass="mb15">积累目标的能源的恒定加速度运动,步行范围通常是与梯形变换,纠正和加速度引起的二阶相位误差补偿使用距离(<一个href="#B15">吴et al ., 2009</一个>)。李x et al。(<一个href="#B4">李et al ., 2015</一个>)提出了一种相干累积算法基于梯形变换和分数傅里叶变换(FrFT)。LRWC之后,FrFT的信号中提取完整的能量积累。然而,由于只有走路是补偿范围,范围曲率加速度时导致贫困积累性能不容忽视。谢里夫r等人提出了一个基于梯形变换方法和Wigner-Hough (<一个href="#B12">谢里夫和Abeysekera, 2007</一个>)。二阶曲率梯形变换消除了范围(<一个href="#B2">柯克兰,2011</一个>)(<gydF4y2B一个一个href="#B17">杨et al ., 2011</一个>)。第一,二次耦合的频率范围和缓慢的时间是通过二阶解耦的梯形变换。第二,重建一个匹配滤波器补偿多普勒质心偏移量和估计加速度。最后,第二阶段的二阶梯形变换用于正确的曲率和积累目标能量范围。然而,在上述研究中,多普勒模糊数的变化并不认为,因为只有在主瓣担心移动目标检测情况。此外,二阶梯形变换的意思是一个广泛的计算负载。</p><pcgydF4y2Balass="mb15">在成像情况下,运动参数通常是衡量使用GPS / INS安装在平台。相反,迁移和多普勒频移范围由于目标或散射从现场不同的方向。所以,space-varying运动补偿前瞻性成像起着至关重要的作用。解决问题,一大批杀害梯形算法。首先,走路范围是纠正使用大量毁灭梯形变换,这解决了多普勒模糊数的变化通过减少空间采样率。然后,在频域内偿还的因素消除构造曲率范围。最后,对多普勒质心加速度的影响被认为是在角度测量和删除。仿真实验验证了该方法的有效性。</p><一个id="h3" name="h3"></a> <h2>2分析信号模型的前瞻性的匀加速平台上的成像</h2><h3cgydF4y2Balass="pt0">2.1为前瞻性的匀加速平台上的成像几何模型</h3><pcgydF4y2B一个lass="mb0">前瞻性单脉冲成像扫描模式提高方位分辨率的基础上的实孔径图像前现场通过单脉冲技术(<一个href="#B14">吴et al ., 2010</一个>)。</p><pcgydF4y2B一个lass="mb0">假设雷达平台苍蝇<在line-formula id="inf1"> <math id="m1"> <mrow> <mi> 一个</米i> </mrow> </math> </inline-formula>来<在line-formula id="inf2"> <math id="m2"> <mrow> <mi> B</米i> </mrow> </math> </inline-formula>与最初的前进速度<在line-formula id="inf3"> <math id="m3"> <mrow> <mi> v</米i> </mrow> </math> </inline-formula>。<在line-formula id="inf4"> <math id="m4"> <mrow> <msub> <mi> 一个</米i> <mi> x</米i> </msub> </mrow> </math> </inline-formula>横向加速度,<在line-formula id="inf5"> <math id="m5"> <mrow> <msub> <mi> 一个</米i> <mi> y</米i> </msub> </mrow> </math> </inline-formula>是向前加速,<在line-formula id="inf6"> <math id="m6"> <mrow> <msub> <mi> 一个</米i> <mi> z</米i> </msub> </mrow> </math> </inline-formula>是纵向加速度。雷达天线波束扫描前区域一致,和当前的方位角,对飞行路径,是<在line-formula id="inf7"> <math id="m7"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>。在成像过程中,目标的倾斜范围变化由于平台运动,如所示<一个href="#F1">图1</一个>。的坐标<e米>B</egydF4y2B一个米>和<e米>P</egydF4y2B一个米>是<在line-formula id="inf8"> <math id="m8"> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> /</米o> <mn> 2</米n></米row> </mfenced> </mrow> <msub> <mi> 一个</米i> <mi> x</米i> </msub> <msubsup> <mi> t</米i> <mi> 米</米i> <mn> 2</米n></米年代ubsup> <mo> ,</米o> <mi> v</米i> <msub> <mi> t</米i> <mi> 米</米i> </msub> <mo> +</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> /</米o> <mn> 2</米n></米row> </mfenced> </mrow> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msubsup> <mi> t</米i> <mi> 米</米i> <mn> 2</米n></米年代ubsup> <mo> ,</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 罪</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> +</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> /</米o> <mn> 2</米n></米row> </mfenced> </mrow> <msub> <mi> 一个</米i> <mi> z</米i> </msub> <msubsup> <mi> t</米i> <mi> 米</米i> <mn> 2</米n></米年代ubsup> </mrow> </mfenced> </mrow> </math> </inline-formula>和<在line-formula id="inf9"> <math id="m9"> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> ⁡</米o> <mi> 罪</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ,</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ,</米o> <mn> 0</米n></米row> </mfenced> </mrow> </math> </inline-formula>,点的瞬时倾斜范围的目标<在line-formula id="inf10"> <math id="m10"> <mrow> <mi> P</米i> </mrow> </math> </inline-formula>相对于雷达的APC,</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e1"> <mrow> <mi> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <msqrt> <mrow> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi mathvariant="normal"> x</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> −</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> ⁡</米o> <mi> 罪</米i> <mo> ⁡</米o> <mi> θ</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> +</米o> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> v</米i> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> +</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> −</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> +</米o> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 罪</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> +</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi> z</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </msqrt> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 1</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf11"> <math id="m12"> <mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </math> </inline-formula>是瞬时倾斜范围<在line-formula id="inf12"> <math id="m13"> <mrow> <mi> 一个</米i> </mrow> </math> </inline-formula>来<在line-formula id="inf13"> <math id="m14"> <mrow> <mi> P</米i> </mrow> </math> </inline-formula>在最初的时候,<在line-formula id="inf14"> <math id="m15"> <mrow> <msub> <mi> t</米i> <mi> 米</米i> </msub> </mrow> </math> </inline-formula>缓慢的时间,<在line-formula id="inf15"> <math id="m16"> <mrow> <mi> ϕ</米i> </mrow> </math> </inline-formula>大萧条是角。为进一步分析,1)是泰勒级数展开。</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e2"> <mrow> <mi> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> −</米o> <mi> v</米i> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> −</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi> x</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> ⁡</米o> <mi> 罪</米i> <mo> ⁡</米o> <mi> θ</米i> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> −</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> +</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi> z</米i> </msub> <mo> ⁡</米o> <mi> 罪</米i> <mo> ⁡</米o> <mi> φ</米i> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> +</米o> <mfrac> <mrow> <msup> <mi> v</米i> <mn> 2</米n></米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> −</米o> <msup> <mi> 因为</米i> <mrow> <mtext> </mtext> <mn> 2</米n></米row> </msup> <mo> ⁡</米o> <mi> θ</米i> <msup> <mi> 因为</米i> <mrow> <mtext> </mtext> <mn> 2</米n></米row> </msup> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mfenced> </mrow> </mrow> <mrow> <mn> 2</米n><米年代ub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </mfrac> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> +</米o> <mi> ο</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 2</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="indent"></p> <div class="DottedLine"></div> <div class="Imageheaders"> 图1</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g001.jpg" name="Figure1" target="_blank"><img id="F1" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g001.jpg"></a> <p><b>图1</gydF4y2B一个b>。一个前瞻性的成像几何模型的匀加速平台。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0">根据图像几何,倾斜范围变化不仅随着时间缓慢,但也与斜视角度<在line-formula id="inf16"> <math id="m18"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>大萧条,角<在line-formula id="inf17"> <math id="m19"> <mrow> <mi> ϕ</米i> </mrow> </math> </inline-formula>,因为光束扫描在方位维的变化<在line-formula id="inf18"> <math id="m20"> <mrow> <mi> ϕ</米i> </mrow> </math> </inline-formula>可以忽略,认为是常数<在line-formula id="inf19"> <math id="m21"> <mrow> <msub> <mi> ϕ</米i> <mn> 0</米n></米年代ub> </mrow> </math> </inline-formula>第二项<一个href="#e2">(2)</一个>代表步行范围由于初始速度,第三,第四,第五条款意味着由于曲率加速度范围。远距离成像和前瞻性的成像条件下,两者兼而有之<在line-formula id="inf20"> <math id="m22"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>和<在line-formula id="inf21"> <math id="m23"> <mrow> <mi> ϕ</米i> </mrow> </math> </inline-formula>都很小,所以sin<在line-formula id="inf22"> <math id="m24"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>和<在line-formula id="inf23"> <math id="m25"> <mrow> <mi> ϕ</米i> </mrow> </math> </inline-formula>也小。同时,平台向前飞行时,横向加速度很小,所以横向加速度的影响范围迁移可以忽略。由于CPI是小和<在line-formula id="inf24"> <math id="m26"> <mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ≫</米o> <mi> v</米i> <msub> <mi> t</米i> <mi> 米</米i> </msub> </mrow> </math> </inline-formula>第六,高阶项可以忽略。2)可以近似</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e3"> <mrow> <mi> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> ≈</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> −</米o> <mi> v</米i> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> <mo> −</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 3</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="indent"></p> <h3 class="pt0">2.2迁移和多普勒频移范围</h3><pcgydF4y2B一个lass="mb0">假设单脉冲雷达传输linear-frequency-modulation (lem)脉冲信号;传输信号的时域表达式可以表示</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e4"> <mrow> <mi> x</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> t</米i> </mrow> </mfenced> </mrow> <mo> =</米o> <mi> δ</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> t</米i> <mo> −</米o> <mi> 米</米i> <msub> <mi> T</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mn> 2</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mi> t</米i> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 4</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf25"> <math id="m29"> <mrow> <mi> δ</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> t</米i> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>代表了啁啾脉冲,<在line-formula id="inf26"> <math id="m30"> <mrow> <mi> 米</米i> </mrow> </math> </inline-formula>代表了脉冲序列号码,<在line-formula id="inf27"> <math id="m31"> <mrow> <msub> <mi> T</米i> <mi> r</米i> </msub> </mrow> </math> </inline-formula>代表了脉冲重复间隔(PRI),<在line-formula id="inf28"> <math id="m32"> <mrow> <msub> <mi> f</米i> <mi> c</米i> </msub> </mrow> </math> </inline-formula>代表了中心频率。</p><pcgydF4y2B一个lass="mb0">和差通道时域回波的目标范围后脉冲压缩可以表示为</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e5"> <mrow> <mtable columnalign="left"> <mtr> <mtd> <mrow> <msub> <mi> 年代</米i> <mo> Σ</米o> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> ,</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mi> p</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> −</米o> <mfrac> <mrow> <mn> 2</米n><米i> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> <mi> c</米i> </mfrac> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <mi> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> <mo> ,</米o> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> 年代</米i> <mo> Δ</米o> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> ,</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> 一个</米i> <mo> Δ</米o> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mi> p</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> −</米o> <mfrac> <mrow> <mn> 2</米n><米i> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> <mi> c</米i> </mfrac> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> <msub> <mi> f</米i> <mi> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <mi> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> </mtd> </mtr> </mtable> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 5</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf29"> <math id="m34"> <mrow> <msub> <mi> 年代</米i> <mo> ∑</米o> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> ,</米o> <mi> 米</米i> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>通道信号之和,<在line-formula id="inf30"> <math id="m35"> <mrow> <msub> <mi> 年代</米i> <mo> Δ</米o> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> ,</米o> <mi> 米</米i> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>的区别是通道信号,<在line-formula id="inf31"> <math id="m36"> <mrow> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>代表和通道的天线模式缓慢的时候,<在line-formula id="inf32"> <math id="m37"> <mrow> <msub> <mi> 一个</米i> <mo> Δ</米o> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>代表了不同通道的天线模式缓慢的时候,<在line-formula id="inf33"> <math id="m38"> <mrow> <mi> p</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> ⋅</米o> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>是标准化的回波包络,<在line-formula id="inf34"> <math id="m39"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> </mrow> </math> </inline-formula>代表着时间快。因为移民和多普勒频移范围和差通道都是一样的,我们只分析通道信号之和。通过一系列傅里叶变换<在line-formula id="inf35"> <math id="m40"> <mrow> <msub> <mi> 年代</米i> <mo> ∑</米o> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> ,</米o> <msub> <mi> t</米i> <mi> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>和应用的原则,固定相(POSP),可以得到信号的频谱</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e6"> <mrow> <mi> 年代</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> <mo> ,</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mi> P</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 6</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf36"> <math id="m42"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </math> </inline-formula>相应的频域吗<在line-formula id="inf37"> <math id="m43"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> </mrow> </math> </inline-formula>,<在line-formula id="inf38"> <math id="m44"> <mrow> <mi> P</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>的傅里叶变换<在line-formula id="inf39"> <math id="m45"> <mrow> <mi> p</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>,用3)6),信号的频谱</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e7"> <mrow> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mi> 年代</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> <mo> ,</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mi> P</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> v</米i> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <msub> <mi> 一个</米i> <mi mathvariant="normal"> y</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> =</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mi> P</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> λ</米i> </mfrac> <mi> v</米i> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> <mi> v</米i> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> </mrow> <mi> λ</米i> </mfrac> <msub> <mi> 一个</米i> <mi mathvariant="normal"> y</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> <msub> <mi> 一个</米i> <mi mathvariant="normal"> y</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mn> 2</米n></米年代ubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 7</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="mb0">交叉耦合阶段术语表示为一系列频率和慢时间函数。第二个指数项显示多普勒频移,第三显示了线性范围由于前行速度行走。第四项意味着额外的多普勒频移,第五表明曲率范围由于向前加速。</p><一个id="h4" name="h4"></a> <h2>3距离迁移校正基础上大量毁灭梯形算法</h2><pcgydF4y2B一个lass="mb15">根据7),线性范围迁移和线性多普勒频移造成的前行速度空变的目标在不同的方向。传统方法弥补空变范围使用梯形变换(走<一个href="#B3">李et al ., 2012</一个>)。</p><h3cgydF4y2Balass="pt0">3.1传统的梯形变换和曲线补偿范围</h3><pcgydF4y2B一个lass="mb0">梯形变换执行纠正走在范围<一个href="#e7">(7)</一个>在前瞻性的成像。解耦关系<在line-formula id="inf40"> <math id="m47"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </math> </inline-formula>和<在line-formula id="inf41"> <math id="m48"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </math> </inline-formula>在<一个href="#e7">(7)</一个>,一个比例因子应用于<在line-formula id="inf42"> <math id="m49"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </math> </inline-formula>,如</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e8"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> =</米o> <mfrac> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfrac> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 8</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">梯形变换(<一个href="#B10">佩里et al ., 1999</一个>)。用8)到7),光谱信号是重塑</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e9"> <mrow> <msub> <mi> 年代</米i> <mn> 1</米n></米年代ub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> <mo> ,</米o> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mi> P</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <mi> v</米i> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mfrac> <msubsup> <mi> f</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfrac> <msub> <mi> 一个</米i> <mi mathvariant="normal"> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 9</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">传统的梯形之间变换消除了耦合在哪里<在line-formula id="inf43"> <math id="m52"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </math> </inline-formula>和<在line-formula id="inf44"> <math id="m53"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </math> </inline-formula>在第二项和补偿不同范围内行走,但是,第三指数项<一个href="#e9">(9)</一个>代表一个剩余之间的耦合<在line-formula id="inf45"> <math id="m54"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </math> </inline-formula>和<在line-formula id="inf46"> <math id="m55"> <mrow> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>介绍了由梯形变换。</p><pcgydF4y2B一个lass="mb0">高波段雷达满足<在line-formula id="inf47"> <math id="m56"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ≪</米o> <msub> <mi> f</米i> <mi> c</米i> </msub> </mrow> </math> </inline-formula>,因为<在line-formula id="inf48"> <math id="m57"> <mrow> <mi> 一个</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mo> ≈</米o> <mi> 一个</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi> 米</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>,<在line-formula id="inf49"> <math id="m58"> <mrow> <mrow> <msubsup> <mi> f</米i> <mi> c</米i> <mn> 2</米n></米年代ubsup> <mo> /</米o> <mrow> <msub> <mi> f</米i> <mi> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </mrow> <mo> =</米o> <mrow> <msub> <mi> f</米i> <mi> c</米i> </msub> <mo> /</米o> <mrow> <mn> 1</米n><米o> +</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> /</米o> <msub> <mi> f</米i> <mi> c</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </mrow> <mo> ≈</米o> <msub> <mi> f</米i> <mi> c</米i> </msub> <mo> ×</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> −</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> /</米o> <msub> <mi> f</米i> <mi> c</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> f</米i> <mi> c</米i> </msub> <mo> −</米o> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </math> </inline-formula>9)可以近似</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e10"> <mtable class="align" columnalign="left"> <mtr> <mtd columnalign="right"> <msubsup> <mi> 年代</米i> <mn> 1</米n><米o> ′</米o> </msubsup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> </mtd> <mtd columnalign="left"> <mo> =</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mi> P</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <mi> v</米i> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd columnalign="right"></mtd> <mtd columnalign="left"> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> <mi> c</米i> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> 。</米o> </mtd> </mtr> </mtable> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 10</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="mb0">在第四指数曲率补偿范围,提出了一种频域系数解耦<在line-formula id="inf50"> <math id="m60"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </math> </inline-formula>和<在line-formula id="inf51"> <math id="m61"> <mrow> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>(<一个href="#B16">2011年夏,</一个>)。补偿因素是表达的</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e11"> <mrow> <mi> H</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mo> =</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> <mi> c</米i> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 11</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="mb0">考虑到前线地区的倾斜角度通常是不足的<在line-formula id="inf52"> <math id="m63"> <mrow> <mrow> <mn> 15</米n><米o> °</米o> </mrow> </mrow> </math> </inline-formula>的变化,<在line-formula id="inf53"> <math id="m64"> <mrow> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> </mrow> </math> </inline-formula>很小。因此,曲率的目标范围的差异在不同的方向可以忽略。补偿因素是简化为</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e12"> <mrow> <mi> H</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mo> =</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> <mi> c</米i> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 12</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="indent">因此,范围可以操纵在频域曲线补偿。通过乘以<一个href="#e10">(10)</一个>,我们可以获得</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e13"> <mtable class="align" columnalign="left"> <mtr> <mtd columnalign="right"> <msub> <mi> 年代</米i> <mn> 2</米n></米年代ub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> </mtd> <mtd columnalign="left"> <mo> =</米o> <msubsup> <mi> 年代</米i> <mn> 1</米n><米o> ′</米o> </msubsup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> <mi> c</米i> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ≈</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mi> P</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> </mfenced> </mrow> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd columnalign="right"></mtd> <mtd columnalign="left"> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <mi> v</米i> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> ×</米o> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 2</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> <mo> 。</米o> </mtd> </mtr> </mtable> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 13</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="mb0">进行傅里叶反变换(13),收益率</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e14"> <mrow> <msup> <mi> 年代</米i> <mo> ′</米o> </msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> ,</米o> <mi> 米</米i> </mrow> </mfenced> </mrow> <mo> =</米o> <msub> <mi> 一个</米i> <mi> Σ</米i> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mi> p</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mover accent="true"> <mi> t</米i> <mo> ^</米o> </mover> <mo> −</米o> <mfrac> <mrow> <mn> 2</米n><米年代ub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> <mi> c</米i> </mfrac> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mo> −</米o> <mi mathvariant="normal"> j</米i> <mfrac> <mrow> <mn> 4</米n><米i> π</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> R</米i> <mn mathvariant="normal"> 0</米n></米年代ub> <mo> −</米o> <mi> v</米i> <msubsup> <mi> t</米i> <mi mathvariant="normal"> 米</米i> <mo> ′</米o> </msubsup> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> <mo> −</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> t</米i> <mi> 米</米i> <mo> ′</米o> </msubsup> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 14</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="mb0">信封的倾斜范围表明,空变范围迁移已经纠正使用梯形变换和曲线补偿范围。然而,指数项意味着加速度引入一个额外的多普勒频移。</p><h3cgydF4y2Balass="pt0">3.2才梯形算法对多普勒模糊补偿</h3><pcgydF4y2B一个lass="mb0">高波段雷达,作为系统的脉冲重复频率远小于多普勒质心,发生多普勒模糊。多普勒模糊的校正必须结合梯形变换。多普勒模糊数的依赖的一个限制梯形变换(<一个href="#B18">张和曾庆红,2005</一个>)(<gydF4y2B一个一个href="#B6">李,2006</一个>),<gydF4y2B一个在line-formula id="inf54"> <math id="m68"> <mrow> <mi> F</米i> </mrow> </math> </inline-formula>是一个整数定义为</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e15"> <mrow> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> c</米i> </mrow> </msub> <mo> =</米o> <mi> F</米i> <mo> ×</米o> <msub> <mi> F</米i> <mi mathvariant="normal"> R</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> n</米i> </mrow> </msub> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> n</米i> </mrow> </msub> </mrow> </mfenced> </mrow> <mo> <</米o> <mfrac> <mrow> <msub> <mi> F</米i> <mi mathvariant="normal"> R</米i> </msub> </mrow> <mrow> <mn> 2</米n></米row> </mfrac> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 15</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf55"> <math id="m70"> <mrow> <msub> <mi> F</米i> <mi> R</米i> </msub> </mrow> </math> </inline-formula>代表PRF,<在line-formula id="inf56"> <math id="m71"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> n</米i> </mrow> </msub> </mrow> </math> </inline-formula>代表的多普勒质心测量多普勒模糊的情况下,<在line-formula id="inf57"> <math id="m72"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> </mrow> </msub> </mrow> </math> </inline-formula>代表实际的主光束回波多普勒质心,表达的</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e16"> <mrow> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> c</米i> </mrow> </msub> <mo> =</米o> <mfrac> <mrow> <mn> 2</米n><米i> v</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> <mi> c</米i> </mfrac> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 16</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="indent">一般来说,<在line-formula id="inf58"> <math id="m74"> <mrow> <mi> F</米i> </mrow> </math> </inline-formula>是通过</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e17"> <mrow> <mi> F</米i> <mo> =</米o> <mrow> <mfenced open="〈" close="〉" separators="|"> <mrow> <mfrac> <mrow> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> c</米i> </mrow> </msub> </mrow> <mrow> <msub> <mi> F</米i> <mi mathvariant="normal"> R</米i> </msub> </mrow> </mfrac> </mrow> </mfenced> </mrow> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 17</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf59"> <math id="m76"> <mrow> <mfenced open="〈" close="〉" separators="|"> <mrow> <mo> ⋅</米o> </mrow> </mfenced> </mrow> </math> </inline-formula>是一种舍入操作符。<在line-formula id="inf60"> <math id="m77"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> w</米i> </mrow> </msub> </mrow> </math> </inline-formula>代表主光束回波的多普勒带宽和表达的是(<一个href="#B11">理查兹,2005</一个>)</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e18"> <mrow> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> w</米i> </mrow> </msub> <mo> =</米o> <mrow> <mfenced open="{" close="" separators="|"> <mrow> <mtable columnalign="center"> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn> 2</米n><米i> v</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> <mi> c</米i> </mfrac> <mi> 罪</米i> <mo> ⁡</米o> <mi> θ</米i> </mrow> </mtd> <mtd> <mrow> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <mi> θ</米i> </mrow> </mfenced> </mrow> <mo> ></米o> <mfrac> <mrow> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> </mrow> <mrow> <mn> 2</米n></米row> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn> 2</米n><米i> v</米i> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> −</米o> <mi> 因为</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> θ</米i> <mo> +</米o> <mfrac> <mrow> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> </mrow> <mrow> <mn> 2</米n></米row> </mfrac> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> </mrow> </mtd> <mtd> <mrow> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <mi> θ</米i> </mrow> </mfenced> </mrow> <mo> <</米o> <mfrac> <mrow> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> </mrow> <mrow> <mn> 2</米n></米row> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mfenced> </mrow> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 18</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf61"> <math id="m79"> <mrow> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> </mrow> </math> </inline-formula>是3 dB波束宽度。根据(16)和(18)的增加<在line-formula id="inf62"> <math id="m80"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>多普勒质心减少,而多普勒宽度增加,说明<一个href="#F2">图2</一个>。</p><dgydF4y2B一个iv class="DottedLine"></div> <div class="Imageheaders"> 图2</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g002.jpg" name="Figure2" target="_blank"><img id="F2" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g002.jpg"></a> <p><b>图2</gydF4y2B一个b>。原理图生成的剩余速度解多普勒模糊。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0"> <inline-formula id="inf63"> <math id="m81"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> <mn> 0</米n></米row> </msub> </mrow> </math> </inline-formula>和<在line-formula id="inf64"> <math id="m82"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> n</米i> <mn> 0</米n></米row> </msub> </mrow> </math> </inline-formula>代表实际的多普勒质心和目标的多普勒质心测量<在line-formula id="inf65"> <math id="m83"> <mrow> <mrow> <mn> 0</米n><米o> °</米o> </mrow> </mrow> </math> </inline-formula>,分别。同样的,<在line-formula id="inf66"> <math id="m84"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> <mi> θ</米i> </mrow> </msub> </mrow> </math> </inline-formula>和<在line-formula id="inf67"> <math id="m85"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> n</米i> <mi> θ</米i> </mrow> </msub> </mrow> </math> </inline-formula>代表真正的多普勒质心和目标的多普勒质心测量<在line-formula id="inf68"> <math id="m86"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>,分别。在扫描模式下,多普勒模糊数的方向是用来弥补双方的所有目标的回声。因此,残留误差为目标的多普勒质心<在line-formula id="inf69"> <math id="m87"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>发生。如果<在line-formula id="inf70"> <math id="m88"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> n</米i> <mn> 0</米n></米row> </msub> </mrow> </math> </inline-formula>是更重要的比<在line-formula id="inf71"> <math id="m89"> <mrow> <mo> −</米o> <mrow> <msub> <mi> F</米i> <mi mathvariant="normal"> R</米i> </msub> <mo> /</米o> <mn> 2</米n></米row> </mrow> </math> </inline-formula>、多普勒模糊数的变化可能发生的目标除了飞行路径,产生剩余速度,如图所示<一个href="#F2">图2</一个>。</p><pcgydF4y2B一个lass="mb0">自<在line-formula id="inf72"> <math id="m90"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> <mn> 0</米n></米row> </msub> </mrow> </math> </inline-formula>只是比<在line-formula id="inf73"> <math id="m91"> <mrow> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> F</米i> <mo> +</米o> <mn> 0.5</米n></米row> </mfenced> </mrow> <msub> <mi> F</米i> <mi> R</米i> </msub> </mrow> </math> </inline-formula>多普勒模糊数是圆形的<在line-formula id="inf74"> <math id="m92"> <mrow> <mi> F</米i> <mo> +</米o> <mn> 1</米n></米row> </math> </inline-formula>,因为实际的多普勒模糊数为目标<在line-formula id="inf75"> <math id="m93"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>是<在line-formula id="inf76"> <math id="m94"> <mrow> <mi> F</米i> </mrow> </math> </inline-formula>,它可能会转向<在line-formula id="inf77"> <math id="m95"> <mrow> <msubsup> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> <mi> θ</米i> </mrow> <mo> ′</米o> </msubsup> </mrow> </math> </inline-formula>,这意味着额外的速度误差。因此,错误的多普勒模糊数引入了剩余<在line-formula id="inf78"> <math id="m96"> <mrow> <mo> Δ</米o> <mi> v</米i> </mrow> </math> </inline-formula>可以表达的</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e19"> <mrow> <mo> Δ</米o> <mi> v</米i> <mo> =</米o> <msup> <mi> v</米i> <mo> ′</米o> </msup> <mo> −</米o> <mi> v</米i> <mo> =</米o> <mfrac> <mrow> <mi> c</米i> <mo> ⋅</米o> <msubsup> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> c</米i> <mi mathvariant="normal"> θ</米i> </mrow> <mo> ′</米o> </msubsup> </mrow> <mrow> <mn> 2</米n><米年代ub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mfrac> <mo> −</米o> <mfrac> <mrow> <mi> c</米i> <mo> ⋅</米o> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> c</米i> <mi mathvariant="normal"> θ</米i> </mrow> </msub> </mrow> <mrow> <mn> 2</米n><米年代ub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mfrac> <mo> =</米o> <mfrac> <mrow> <mi> c</米i> <mo> ⋅</米o> <msub> <mi> F</米i> <mi mathvariant="normal"> R</米i> </msub> </mrow> <mrow> <mn> 2</米n><米年代ub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mfrac> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 19</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf79"> <math id="m98"> <mrow> <msup> <mi> v</米i> <mo> ′</米o> </msup> </mrow> </math> </inline-formula>从平台相关的速度目标的多普勒质心是什么<在line-formula id="inf80"> <math id="m99"> <mrow> <msubsup> <mi> f</米i> <mrow> <mi mathvariant="italic"> 直流</米i> <mi> θ</米i> </mrow> <mrow> <mo> ′</米o> </mrow> </msubsup> </mrow> </math> </inline-formula>残留率越大,范围越大位置错误。</p><pcgydF4y2B一个lass="mb0">一大批杀害梯形算法解决范围位置误差引起的多普勒模糊补偿。假设抽样序列的长度在缓慢的时间维度<在line-formula id="inf81"> <math id="m100"> <mrow> <mi> 米</米i> <mo> =</米o> <mi> P</米i> <mo> ×</米o> <mi> 问</米i> </mrow> </math> </inline-formula>。通过采样下来原始序列使用一个整数<在line-formula id="inf82"> <math id="m101"> <mrow> <mi> 问</米i> </mrow> </math> </inline-formula>,回波序列是摧毁均匀<在line-formula id="inf83"> <math id="m102"> <mrow> <mi> 米</米i> </mrow> </math> </inline-formula>子,如所示<一个href="#F3">图3</一个>。每个子由<在line-formula id="inf84"> <math id="m103"> <mrow> <mi> P</米i> </mrow> </math> </inline-formula>采样点,指数<在line-formula id="inf85"> <math id="m104"> <mrow> <mi> p</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> p</米i> <mo> =</米o> <mn> 1、2</米n><米o> ,</米o> <mo> …</米o> <mo> ,</米o> <mi> P</米i> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>子形成的秩序<在line-formula id="inf86"> <math id="m105"> <mrow> <msub> <mi> P</米i> <mn> 1</米n></米年代ub> <mo> ,</米o> <msub> <mi> P</米i> <mn> 2</米n></米年代ub> <mo> ,</米o> <mo> …</米o> <mo> ,</米o> <msub> <mi> P</米i> <mi> 问</米i> </msub> </mrow> </math> </inline-formula>,见<一个href="#F3">图3</一个>。</p><dgydF4y2B一个iv class="DottedLine"></div> <div class="Imageheaders"> 图3</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g003.jpg" name="Figure3" target="_blank"><img id="F3" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g003.jpg"></a> <p><b>图3</gydF4y2B一个b>。原理图的序列和重新排列。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0">为每个子<在line-formula id="inf87"> <math id="m106"> <mrow> <msub> <mi> P</米i> <mi> 问</米i> </msub> </mrow> </math> </inline-formula>,空间采样率<在line-formula id="inf88"> <math id="m107"> <mrow> <msub> <mi> F</米i> <mi> R</米i> </msub> </mrow> </math> </inline-formula>是减少了<在line-formula id="inf89"> <math id="m108"> <mrow> <mi> 问</米i> </mrow> </math> </inline-formula>次了。然后梯形变换是操纵子来补偿范围走路。尽管多普勒模糊数的变化不可避免,一个低<在line-formula id="inf90"> <math id="m109"> <mrow> <msub> <mi> F</米i> <mi> R</米i> </msub> </mrow> </math> </inline-formula>意味着更少的残留多普勒模糊。例如,当模糊数量改变<在line-formula id="inf91"> <math id="m110"> <mrow> <mi> F</米i> </mrow> </math> </inline-formula>来<在line-formula id="inf92"> <math id="m111"> <mrow> <mi> F</米i> <mo> +</米o> <mn> 1</米n></米row> </math> </inline-formula>、剩余速度<在line-formula id="inf93"> <math id="m112"> <mrow> <mo> Δ</米o> <msup> <mi> v</米i> <mo> ′</米o> </msup> </mrow> </math> </inline-formula>就变成了</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e20"> <mrow> <mo> Δ</米o> <msup> <mi> v</米i> <mo> ′</米o> </msup> <mo> =</米o> <mfrac> <mrow> <mi> c</米i> <mo> ⋅</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> F</米i> <mi mathvariant="normal"> R</米i> </msub> <mo> /</米o> <mi> 问</米i> </mrow> </mfenced> </mrow> </mrow> <mrow> <mn> 2</米n><米年代ub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mfrac> <mo> =</米o> <mfrac> <mrow> <mo> Δ</米o> <mi> v</米i> </mrow> <mi> 问</米i> </mfrac> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 20.</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="mb0">剩余速度降低<在line-formula id="inf94"> <math id="m114"> <mrow> <mi> 问</米i> </mrow> </math> </inline-formula>与传统方法相比。通过设置一个合适的<在line-formula id="inf95"> <math id="m115"> <mrow> <mi> 问</米i> </mrow> </math> </inline-formula>确保实现多个样本在每个梁的位置,剩余可以有限范围走半个距离分辨率单元来实现准确的目标定位。步行范围调整后,子重整旗鼓根据逆过程,如图所示<一个href="#F3">图3</一个>。</p><pcgydF4y2B一个lass="mb0">由于实际信号处理是数字化,频率和缓慢的时间范围的数据需要被表示为离散变量。提出了三种方法来实现梯形变换(<一个href="#B13">王、赵,2011年</一个>):SINC插值,DFT-IFFT, CZT。因为CZT的计算复杂度远远小于其他两个方法,用于实现梯形变换。这个过程可以表示如下:</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e21"> <mrow> <mi> 年代</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> <mo> ,</米o> <msub> <mi> z</米i> <mi mathvariant="normal"> 米</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <msup> <mi> W</米i> <mrow> <msup> <mi> 米</米i> <mn> 2</米n></米年代up> <mo> /</米o> <mn> 2</米n></米row> </msup> <mrow> <mfenced open="[" close="]" separators="|"> <mrow> <mi> g</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> </mrow> </mfenced> </mrow> <mo> ∗</米o> <mi> h</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 21</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf96"> <math id="m117"> <mrow> <mi> W</米i> <mo> =</米o> <msup> <mi> e</米i> <mrow> <mo> −</米o> <mi> j</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mrow> <msub> <mi> f</米i> <mi> c</米i> </msub> <mo> +</米o> <msub> <mi> f</米i> <mi> r</米i> </msub> </mrow> <mo> /</米o> <msub> <mi> f</米i> <mi> c</米i> </msub> </mrow> </mfenced> </mrow> <mrow> <mrow> <mn> 2</米n><米i> π</米i> </mrow> <mo> /</米o> <mi> 米</米i> </mrow> </mrow> </msup> </mrow> </math> </inline-formula>,<在line-formula id="inf97"> <math id="m118"> <mrow> <mi> g</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> </mrow> </mfenced> </mrow> <mo> =</米o> <mi> 年代</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <mi> 米</米i> </mrow> </mfenced> </mrow> <msup> <mi> W</米i> <mrow> <msup> <mi> 米</米i> <mn> 2</米n></米年代up> <mo> /</米o> <mn> 2</米n></米row> </msup> </mrow> </math> </inline-formula>,<在line-formula id="inf98"> <math id="m119"> <mrow> <mi> h</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> </mrow> </mfenced> </mrow> <mo> =</米o> <msup> <mi> W</米i> <msup> <mo> −</米o> <mrow> <msup> <mi> 米</米i> <mn> 2</米n></米年代up> <mo> /</米o> <mn> 2</米n></米row> </msup> </msup> </mrow> </math> </inline-formula>,<在line-formula id="inf99"> <math id="m120"> <mrow> <mn> 0</米n><米o> ≤</米o> <mi> 米</米i> <mo> ≤</米o> <mi> 米</米i> <mo> −</米o> <mn> 1</米n></米row> </math> </inline-formula>,<在line-formula id="inf100"> <math id="m121"> <mrow> <mi> 米</米i> </mrow> </math> </inline-formula>数据的长度吗<在line-formula id="inf101"> <math id="m122"> <mrow> <mi> 年代</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <mi> 米</米i> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>执行逆FFT(21),在多普勒模糊的情况下,可以写成的梯形变换</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e22"> <mrow> <msub> <mi> 年代</米i> <mn> 1</米n></米年代ub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi> r</米i> </msub> <mo> ,</米o> <msup> <mi> 米</米i> <mo> ′</米o> </msup> </mrow> </mfenced> </mrow> <mo> =</米o> <mi mathvariant="normal"> 我</米i> <mi mathvariant="normal"> F</米i> <mi mathvariant="normal"> F</米i> <mi mathvariant="normal"> T</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 年代</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> f</米i> <mi mathvariant="normal"> r</米i> </msub> <mo> ,</米o> <msub> <mi> z</米i> <mi> 米</米i> </msub> </mrow> </mfenced> </mrow> <mi> 经验值</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> j</米i> <mn> 2</米n><米i mathvariant="normal"> π</米i> <mi> F</米i> <msup> <mi> 米</米i> <mo> ′</米o> </msup> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 22</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里<在line-formula id="inf102"> <math id="m124"> <mrow> <mi> F</米i> </mrow> </math> </inline-formula>多普勒模糊数。</p><pcgydF4y2B一个lass="mb0">大量毁灭的流程图显示为梯形算法<一个href="#F4">图4</一个>。</p><dgydF4y2B一个iv class="DottedLine"></div> <div class="Imageheaders"> 图4</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g004.jpg" name="Figure4" target="_blank"><img id="F4" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g004.jpg"></a> <p><b>图4</gydF4y2B一个b>。大量毁灭梯形算法的流程图。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0">范围压缩和运动补偿后,我们利用多普勒的估计来实现单脉冲和差测量前瞻性成像(<一个href="#B5">李et al ., 2021</一个>)。第一,目标多样性是解决利用不同平台之间的相对运动引起的多普勒变化在不同的方向和目标。方位角度测量精度高的多普勒估计得到使用和差摘要技术。随后,和信道估计的强度投影到图像平面上根据范围和角度测量。</p><h3cgydF4y2Balass="pt0">3.3在多普勒质心加速度的影响及其补偿</h3><pcgydF4y2B一个lass="mb0">演示了前瞻性的成像几何模型<一个href="#F1">图1</一个>,当加速度<在line-formula id="inf103"> <math id="m125"> <mrow> <mi> 一个</米i> <mo> =</米o> <mn> 0</米n></米row> </math> </inline-formula>,平台正均匀。一个目标的多普勒频移位于方位角,<在line-formula id="inf104"> <math id="m126"> <mrow> <mi> θ</米i> </mrow> </math> </inline-formula>,被定义为<一个href="#e16">(16)</一个>。然而,如果平台在一个恒定的加速度运动,多普勒频移是受到加速度的影响,如图所示<一个href="#e14">(14)</一个>。在CPI,主光束回波的多普勒质心也各不相同。为了解决这一问题,1)扩展到泰勒级数<在line-formula id="inf105"> <math id="m127"> <mrow> <msub> <mi> t</米i> <mi> c</米i> </msub> </mrow> </math> </inline-formula>CPI的平均时间。</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e23"> <mrow> <mi> R</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> −</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <mi> 一个</米i> <mo> +</米o> <mi> B</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> −</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> </mfenced> </mrow> <mo> +</米o> <mi> C</米i> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> −</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> <mo> +</米o> <mi> ο</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> 米</米i> </msub> <mo> −</米o> <msub> <mi> t</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </mfenced> </mrow> <mo> ,</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 23</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">在哪里</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e24"> <mrow> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mi> 一个</米i> <mo> =</米o> <msqrt> <mrow> <msubsup> <mi> R</米i> <mn> 0</米n><米n>2</gydF4y2Ba米n></米年代ubsup> <mo> +</米o> <msubsup> <mi> R</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <mo> −</米o> <mn> 2</米n><米年代ub> <mi> R</米i> <mn> 0</米n></米年代ub> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </msqrt> <mo> ≈</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> −</米o> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi> B</米i> <mo> =</米o> <mfrac> <mrow> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <msub> <mi> v</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> −</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <msub> <mi> v</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> <msqrt> <mrow> <msubsup> <mi> R</米i> <mn> 0</米n><米n>2</gydF4y2Ba米n></米年代ubsup> <mo> +</米o> <msubsup> <mi> R</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <mo> −</米o> <mn> 2</米n><米年代ub> <mi> R</米i> <mn> 0</米n></米年代ub> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </msqrt> </mfrac> <mo> ≈</米o> <mo> −</米o> <msub> <mi> v</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi> C</米i> <mo> =</米o> <mfrac> <mrow> <mn> 1</米n></米row> <mrow> <mn> 2</米n></米row> </mfrac> <mo> ⋅</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mfrac> <mrow> <msubsup> <mi> v</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <mo> +</米o> <mi> 一个</米i> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> −</米o> <mi> 一个</米i> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> <msqrt> <mrow> <msubsup> <mi> R</米i> <mn> 0</米n><米n>2</gydF4y2Ba米n></米年代ubsup> <mo> +</米o> <msubsup> <mi> R</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <mo> −</米o> <mn> 2</米n><米年代ub> <mi> R</米i> <mn> 0</米n></米年代ub> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </msqrt> </mfrac> <mo> −</米o> <mfrac> <mrow> <msubsup> <mi> v</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> −</米o> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> <msup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msubsup> <mi> R</米i> <mn> 0</米n><米n>2</gydF4y2Ba米n></米年代ubsup> <mo> +</米o> <msubsup> <mi> R</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <mo> −</米o> <mn> 2</米n><米年代ub> <mi> R</米i> <mn> 0</米n></米年代ub> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> </mfenced> </mrow> <mrow> <mn> 3</米n><米o> /</米o> <mn> 2</米n></米row> </msup> </mfrac> </mrow> </mfenced> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> ≈</米o> <mfrac> <mrow> <msubsup> <mi> v</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> −</米o> <msup> <mi> 因为</米i> <mrow> <mtext> </mtext> <mn> 2</米n></米row> </msup> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <msup> <mrow> <mi> 因为</米i> <mo> ⁡</米o> <mtext> </mtext> </mrow> <mrow> <mtext> </mtext> <mn> 2</米n></米row> </msup> <mi> φ</米i> </mrow> </mfenced> </mrow> <mo> −</米o> <mi> 一个</米i> <msub> <mi> R</米i> <mn> 0</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> φ</米i> </mrow> <mrow> <mn> 2</米n><米年代ub> <mi> R</米i> <mn> 0</米n></米年代ub> </mrow> </mfrac> <mo> ,</米o> </mrow> </mtd> </mtr> </mtable> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 24</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">和<在line-formula id="inf106"> <math id="m130"> <mrow> <msub> <mi> R</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> =</米o> <mi> v</米i> <msub> <mi> t</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> +</米o> <mrow> <mn> 1</米n><米o> /</米o> <mn> 2</米n></米row> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msubsup> <mi> t</米i> <mi mathvariant="normal"> c</米i> <mn> 2</米n></米年代ubsup> </mrow> </math> </inline-formula>,<在line-formula id="inf107"> <math id="m131"> <mrow> <msub> <mi> v</米i> <mi> c</米i> </msub> <mo> =</米o> <mi> v</米i> <mo> +</米o> <msub> <mi> 一个</米i> <mi> y</米i> </msub> <msub> <mi> t</米i> <mi> c</米i> </msub> </mrow> </math> </inline-formula>在居民消费价格指数(CPI)的平均速度。假设<在line-formula id="inf108"> <math id="m132"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> </mrow> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi> c</米i> </msub> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>扫描目标的多普勒质心在哪里<在line-formula id="inf109"> <math id="m133"> <mrow> <msub> <mi> t</米i> <mi> c</米i> </msub> </mrow> </math> </inline-formula>,那么它可以重新定义</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e25"> <mrow> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> c</米i> </mrow> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi mathvariant="normal"> c</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <mo> −</米o> <mfrac> <mrow> <mn> 2</米n><米i> B</米i> </mrow> <mi> λ</米i> </mfrac> <mo> =</米o> <mfrac> <mrow> <mn> 2</米n><米年代ub> <mi> v</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <mi> θ</米i> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> <mi> λ</米i> </mfrac> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 25</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="noindent">波长在哪里,因此,多普勒带宽也修改如下:</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e26"> <mrow> <msub> <mi> f</米i> <mrow> <mi mathvariant="normal"> d</米i> <mi mathvariant="normal"> w</米i> </mrow> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> t</米i> <mi> c</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <mrow> <mfenced open="{" close="" separators="|"> <mrow> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn> 2</米n><米年代ub> <mi> v</米i> <mi mathvariant="normal"> c</米i> </msub> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> <mi> c</米i> </mfrac> <mi> 罪</米i> <mo> ⁡</米o> <mi> θ</米i> </mrow> </mtd> <mtd> <mrow> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <mi> θ</米i> </mrow> </mfenced> </mrow> <mo> ></米o> <mfrac> <mrow> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> </mrow> <mrow> <mn> 2</米n></米row> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn> 2</米n><米年代ub> <mi> v</米i> <mi mathvariant="normal"> c</米i> </msub> <msub> <mi> f</米i> <mi mathvariant="normal"> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> <mi> c</米i> </mfrac> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 1</米n><米o> −</米o> <mi> 因为</米i> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> θ</米i> <mo> +</米o> <mfrac> <mrow> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> </mrow> <mrow> <mn> 2</米n></米row> </mfrac> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> </mrow> </mtd> <mtd> <mrow> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <mi> θ</米i> </mrow> </mfenced> </mrow> <mo> <</米o> <mfrac> <mrow> <msub> <mi> θ</米i> <mn> 3</米n></米年代ub> </mrow> <mrow> <mn> 2</米n></米row> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 26</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="mb0">如果执行单脉冲成像基于多普勒的估计和差通道,多普勒参数必须根据计算(25)和(26)。否则,散射的能量在主瓣是错过了,无法衡量的角度准确,导致图像模糊。</p><一个id="h5" name="h5"></a> <h2>4仿真结果</h2><h3cgydF4y2Balass="pt0">4.1点目标成像仿真</h3><pcgydF4y2B一个lass="mb0">单脉冲前视成像算法用于模拟来验证该方法(<一个href="#B5">李et al ., 2021</一个>)。给出了仿真参数<一个href="#T1">表1</一个>。假设雷达传感器安装在一架飞机。速度<在line-formula id="inf110"> <math id="m136"> <mrow> <mi> v</米i> </mrow> </math> </inline-formula>是240米/秒。雷达相干线性调频信号传送<在line-formula id="inf111"> <math id="m137"> <mrow> <mn> 1</米n><米i> μ</米i> <mi mathvariant="normal"> 年代</米i> </mrow> </math> </inline-formula>脉冲宽度和50 MHz带宽。传输信号的中心频率是18 GHz。光束扫描前面场景从-15°15°。扫描照明的脉冲数是2500。现场有3×21点目标在30 m×30 m晶格。每个目标都有一个统一的强度,和现场中心轴(0,1700)米米在地面上。range-compressed数据的信噪比是20 dB,和噪音是一个复杂的正态分布均值为0,方差<在line-formula id="inf112"> <math id="m138"> <mrow> <msup> <mi> σ</米i> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>。角度测量的CPI是32。多普勒估计和差通道重建的CZT和用来测量方位角度的点目标单脉冲成像(<一个href="#B5">李et al ., 2021</一个>)。</p><dgydF4y2B一个iv class="DottedLine"></div> <div class="Imageheaders"> 表1</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-t001.jpg" name="Table1" target="_blank"><img id="T1" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-t001.jpg"></a> <p><b>表1</gydF4y2B一个b>。仿真参数前瞻性扫描雷达。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0"><a href="#F5">图5</一个>比较前瞻性的成像结果使用传统的处理方法和大量毁灭梯形算法。雷达平台遵循统一的运动。目标的多普勒模糊数<在line-formula id="inf117"> <math id="m143"> <mrow> <mi> θ</米i> <mo> =</米o> <mrow> <mn> 0</米n><米o> °</米o> </mrow> </mrow> </math> </inline-formula>是<在line-formula id="inf118"> <math id="m144"> <mrow> <mi> F</米i> <mo> =</米o> <mrow> <mfenced open="〈" close="〉" separators="|"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> <mn> 0</米n></米row> </msub> <mo> /</米o> <msub> <mi> F</米i> <mi> R</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <mn> 12</米n></米row> </math> </inline-formula>,目标的多普勒模糊数<在line-formula id="inf119"> <math id="m145"> <mrow> <mi> θ</米i> <mo> =</米o> <mrow> <mn> 10</米n><米o> °</米o> </mrow> </mrow> </math> </inline-formula>是<在line-formula id="inf120"> <math id="m146"> <mrow> <msub> <mi> F</米i> <mi> θ</米i> </msub> <mo> =</米o> <mrow> <mfenced open="〈" close="〉" separators="|"> <mrow> <msub> <mi> f</米i> <mrow> <mi> d</米i> <mi> c</米i> <mi> θ</米i> </mrow> </msub> <mo> /</米o> <msub> <mi> F</米i> <mi> R</米i> </msub> </mrow> </mfenced> </mrow> <mo> =</米o> <mn> 11</米n></米row> </math> </inline-formula>,这意味着多普勒模糊数的变化发生。产生的剩余速度多普勒模糊数错了<在line-formula id="inf121"> <math id="m147"> <mrow> <mo> Δ</米o> <mi> v</米i> <mo> =</米o> <mrow> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> c</米i> <mo> ⋅</米o> <msub> <mi> F</米i> <mi> R</米i> </msub> </mrow> </mfenced> </mrow> <mo> /</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 2</米n><米年代ub> <mi> f</米i> <mi> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mrow> <mo> =</米o> <mn> 20.8</米n><米row> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>,目标指向<在line-formula id="inf122"> <math id="m148"> <mrow> <mrow> <mfenced open="|" close="|" separators="|"> <mrow> <mi> θ</米i> </mrow> </mfenced> </mrow> <mo> ≠</米o> <mrow> <mn> 0</米n><米o> °</米o> </mrow> </mrow> </math> </inline-formula>患有残留率,及其位移范围约他们的方位角度成正比。的成像结果<一个href="#F5">图5一个</一个>验证剩余速度的影响范围位置错误。的成像结果大量毁灭梯形算法所示<一个href="#F5">图5 b</一个>。的因素是<在line-formula id="inf123"> <math id="m149"> <mrow> <mi> 问</米i> <mo> =</米o> <mn> 25</米n></米row> </math> </inline-formula>。因此,剩余速度降低<在line-formula id="inf124"> <math id="m150"> <mrow> <mo> Δ</米o> <msup> <mi> v</米i> <mo> ′</米o> </msup> <mo> =</米o> <mrow> <mrow> <mo> Δ</米o> <mi> v</米i> </mrow> <mo> /</米o> <mi> 问</米i> </mrow> <mo> =</米o> <mrow> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> c</米i> <mo> ⋅</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mi> F</米i> <mi> R</米i> </msub> <mo> /</米o> <mi> 问</米i> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> <mo> /</米o> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mn> 2</米n><米年代ub> <mi> f</米i> <mi> c</米i> </msub> <mo> ⁡</米o> <mi> 因为</米i> <mo> ⁡</米o> <msub> <mi> φ</米i> <mn> 0</米n></米年代ub> </mrow> </mfenced> </mrow> </mrow> <mo> =</米o> <mn> 0.8</米n><米row> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> </mrow> </math> </inline-formula>,多普勒模糊数的变化是在子更严重,例如,多普勒点目标的数量差异<在line-formula id="inf125"> <math id="m151"> <mrow> <mi> θ</米i> <mo> =</米o> <mrow> <mn> 10</米n><米o> °</米o> </mrow> </mrow> </math> </inline-formula>是4。但范围造成的残余率还不到一半距离分辨率单元由于轻微的剩余速度和短CPI。因此,目标定位准确,所示<一个href="#F5">图5 b</一个>。</p><dgydF4y2B一个iv class="DottedLine"></div> <div class="Imageheaders"> 图5</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g005.jpg" name="Figure5" target="_blank"><img id="F5" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g005.jpg"></a> <p><b>图5</gydF4y2B一个b>。比较均匀运动平台的图像结果。<gydF4y2B一个b>(一)</gydF4y2B一个b>传统的梯形变换。<gydF4y2B一个b>(B)</gydF4y2B一个b>大量毁灭梯形算法。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0"><a href="#F6">图6</一个>验证的有效性范围在恒定加速度曲线补偿策略。<一个href="#F6">图6 a, B</一个>目前的成像结果与不同的加速度由传统的梯形变换处理。因为多普勒模糊数的变化和曲率范围,定位误差范围明显的图像。<一个href="#F6">图6 c, E</一个>对比成像结果处理的大量毁灭与加速度等于梯形算法<在line-formula id="inf126"> <math id="m152"> <mrow> <mn> 10</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>。在<一个href="#F6">图6 c</一个>,由于曲率加速度范围不补偿。由于轻微的加速度,曲率范围<一个href="#F6">图6 c</一个>并不明显。因此,大量毁灭梯形变换工作。当加速度增加<在line-formula id="inf127"> <math id="m153"> <mrow> <mn> 50</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>没有曲线补偿范围,成像结果<一个href="#F6">图6 d</一个>呈现明显的曲率。和范围曲线补偿可以消除重大加速度的影响目标的信封,如图所示<一个href="#F6">图6 f</一个>。仿真结果表明大量毁灭梯形变换的有效性和范围曲线补偿加速度恒定的动作。</p><dgydF4y2B一个iv class="DottedLine"></div> <div class="Imageheaders"> 图6</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g006.jpg" name="Figure6" target="_blank"><img id="F6" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g006.jpg"></a> <p><b>图6</gydF4y2B一个b>。匀加速运动平台的图像结果的比较。<gydF4y2B一个b>(一)</gydF4y2B一个b>传统的梯形变换在<在line-formula id="inf128"> <math id="m154"> <mrow> <mi> 一个</米i> <mo> =</米o> <mn> 10</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula><b>(B)</gydF4y2B一个b>传统的梯形变换在<在line-formula id="inf129"> <math id="m155"> <mrow> <mi> 一个</米i> <mo> =</米o> <mn> 50</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>。<gydF4y2B一个b>(C)</gydF4y2B一个b>大量毁灭梯形算法没有曲线补偿范围(<在line-formula id="inf130"> <math id="m156"> <mrow> <mi> 一个</米i> <mo> =</米o> <mn> 10</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>)。<gydF4y2B一个b>(D)</gydF4y2B一个b>大量毁灭梯形算法没有曲线补偿范围(<在line-formula id="inf131"> <math id="m157"> <mrow> <mi> 一个</米i> <mo> =</米o> <mn> 50</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>)。<gydF4y2B一个b>(E)</gydF4y2B一个b>大量毁灭(梯形算法和曲线补偿范围<在line-formula id="inf132"> <math id="m158"> <mrow> <mi> 一个</米i> <mo> =</米o> <mn> 10</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>)。<gydF4y2B一个b>(F)</gydF4y2B一个b>大量毁灭(梯形算法和曲线补偿范围<在line-formula id="inf133"> <math id="m159"> <mrow> <mi> 一个</米i> <mo> =</米o> <mn> 50</米n><米年代up> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi> 米</米i> <mo> /</米o> <mi> 年代</米i> </mrow> </mfenced> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>)。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0">我们比较概要范围的目标指向的方位距离地面-300米,1700米的范围<一个href="#F6">图6 b, D, F</一个>,分别。标准化范围配置文件被五次插值。在<一个href="#F7">图7</一个>概要文件,红色代表的曲线加工使用传统的梯形变换,在实际的位移范围约为3米。蓝线代表的曲线轮廓加工使用大量毁灭梯形变换,位移是无形的。在<一个href="#F7">图7 b</一个>红色曲线代表点在目标范围<一个href="#F6">图6 d</一个>。蓝色曲线代表的点目标范围<一个href="#F6">图6 f</一个>。没有曲率补偿范围,目标将会抵消3 m,导致偏差范围的定位。积分旁瓣比(ISLR)计算:</p><dgydF4y2B一个iv class="equationImageholder"> <math id="e27"> <mrow> <mi mathvariant="normal"> 我</米i> <mi mathvariant="normal"> 年代</米i> <mi mathvariant="normal"> l</米i> <mi mathvariant="normal"> R</米i> <mo> =</米o> <mn> 10</米n><米年代ub> <mi> 日志</米i> <mrow> <mtext> </mtext> <mn> 10</米n></米row> </msub> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mfrac> <mrow> <msub> <mi> P</米i> <mtext> 总</米text></米年代ub> <mo> −</米o> <msub> <mi> P</米i> <mtext> 主要</米text></米年代ub> </mrow> <msub> <mi> P</米i> <mtext> 主要</米text></米年代ub> </mfrac> </mrow> </mfenced> </mrow> <mo> 。</米o> </mrow> <mspace width="5em"></mspace> <mo stretchy="false"> (</米o> <mn> 27</米n><米o stretchy="false"> )</米o> </math> <div class="clear"></div> </div> <p class="indent"></p> <div class="DottedLine"></div> <div class="Imageheaders"> 图7</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g007.jpg" name="Figure7" target="_blank"><img id="F7" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g007.jpg"></a> <p><b>图7</gydF4y2B一个b>。范围的目标概要文件轴(范围1700米,方位−300米)。<gydF4y2B一个b>(一)</gydF4y2B一个b>比较传统的梯形变换和大量毁灭梯形算法。<gydF4y2B一个b>(B)</gydF4y2B一个b>只有大量毁灭和死亡梯形算法的比较。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0">在<一个href="#F7">图7</一个>的ISLR传统梯形变换是-9.93分贝,而大量毁坏的ISLR梯形算法−14.65 dB。在<一个href="#F7">图7 b</一个>,只有大量毁灭的ISLR−14.34 dB。的能量大量毁灭梯形算法更为集中和有更好的聚焦效果。</p><h3cgydF4y2Balass="pt0">4.2现场模拟验证</h3><pcgydF4y2B一个lass="mb0">点目标仿真验证才梯形算法的有效性。本节演示了该方法在重建一个扩展目标的可行性。模拟,ku波段SAR图像作为原始场景,和这张照片down-sampled 10 3 m×3 m像素分辨率,如图所示<一个href="#F8">图8</一个>。红色虚线代表道路的实际范围的位置在图像的边缘。图像中心是在地面位置(01700)m。根据生成的回波数据模拟参数<一个href="#T1">表1</一个>与加速度等于<在line-formula id="inf134"> <math id="m161"> <mrow> <mn> 50</米n><米年代up> <mrow> <mtext></mtext> <mi mathvariant="normal"> 米</米i> <mo> /</米o> <mi mathvariant="normal"> 年代</米i> </mrow> <mn> 2</米n></米年代up> </mrow> </math> </inline-formula>。<一个href="#F8">图8 b, C</一个>显示range-compressed和差通道的数据矩阵,分别。图像结果绘制在dB规模。</p><dgydF4y2B一个iv class="DottedLine"></div> <div class="Imageheaders"> 图8</dgydF4y2B一个iv> <div class="FigureDesc"> <a href="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g008.jpg" name="Figure8" target="_blank"><img id="F8" alt="www.雷竞技rebatfrontiersin.orggydF4y2B一个" class="lazy" data-src="//www.thespel.com/files/Articles/1074053/frsip-02-1074053-HTML/image_m/frsip-02-1074053-g008.jpg"></a> <p><b>图8</gydF4y2B一个b>。在模拟场景中校正结果的比较。<gydF4y2B一个b>(一)</gydF4y2B一个b>原始ku波段SAR地图。<gydF4y2B一个b>(B)</gydF4y2B一个b>的数据矩阵和通道。<gydF4y2B一个b>(C)</gydF4y2B一个b>不同渠道的数据矩阵。<gydF4y2B一个b>(D)</gydF4y2B一个b>传统的梯形变换。<gydF4y2B一个b>(E)</gydF4y2B一个b>大量毁灭梯形算法没有曲线补偿范围。<gydF4y2B一个b>(F)</gydF4y2B一个b>大量毁灭梯形算法和曲线补偿范围。</p></dgydF4y2B一个iv> <div class="clear"></div> <div class="DottedLine"></div> <p class="mb0"><a href="#F8">图8 d</一个>介绍了图像处理的结果与传统的梯形变换。道路边缘扭曲和散焦,因为space-varying多普勒频移和加速度。补偿范围目标是严重的大方位角度。<一个href="#F8">图8 e</一个>是成像结果处理大量毁灭梯形算法没有曲线补偿范围。道路边缘的变形仍明显由于曲率范围。<一个href="#F8">图8 f</一个>证明了大批杀害梯形算法结合曲线补偿范围可以重建现场准确。实验结果验证了该方法的有效性。</p><一个id="h6" name="h6"></a> <h2>5的结论</h2><pcgydF4y2B一个lass="mb15">当机载平台采用前瞻性的成像扫描模式,平台运动导致范围和多普勒频移走在目标积累时间。当梯形变换用于范围修正走,两边的点目标可能受到多普勒模糊数的变化。提出了大批杀害梯形算法,它可以减少的脉冲重复频率,从而减少剩余速度和实现一个精确的位置范围。此外,我们分析的影响范围曲率引起的加速度和多普勒频移与恒定加速度运动平台的成像结果。才梯形算法引入了一个频域系数补偿曲率范围。仿真结果验证了该方法的有效性。</p><一个id="h7" name="h7"></a> <h2>数据可用性圣</h2></dgydF4y2B一个iv> </div> </div> </div> </main> </div> </div> </div> </div> </div> </body> </html>

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