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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption 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no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .jfJGTx .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .jfJGTx ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .jfJGTx ol li{margin:10px 0;padding-left:10px;word-break:normal;} .jfJGTx ol li a{word-break:break-all;} .jfJGTx ol li .reflinks{display:block;} .jfJGTx ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .jfJGTx ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .jfJGTx ol li .reflinks .sep{color:#000000;} .jfJGTx .table-wrapper{width:auto;overflow-x:auto;} .jfJGTx .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .jfJGTx .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 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href="//www.newsama.com/journals/jr/" aria-label="Journal of Robotics">机器人杂志</一个>/<一个class="sc-htpNat bUhGXt link sc-cpHetk jUUanO breadCrumb" href="//www.newsama.com/journals/jr/contents/year/2012/" aria-label="2012">2012年</一个>/<年代p一个nclass="sc-nrwXf drSekm">文章</年代p一个n> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 comSpQ threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-ePZHVD kXdKQA section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</gydF4y2Babutton> <div class="sc-jtRlXQ dncNEX static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-lkqHmb yGOZn sc-jeCdPy eVPlap left_section_menu"> <p>在这一页上</pgydF4y2Ba> <span class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#abstract" aria-label="">文摘</一个></span> <span class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#introduction" aria-label="">介绍</一个></span> <span class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#conclusion" aria-label="">结论</一个></span> <span class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#references" aria-label="">引用</一个></span> <span class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#copyright" aria-label="">版权</一个></span> </div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-iBEsjs kOIDmJ article_header_class"> <p class="sc-fcdeBU jSVooP article_type">研究文章|<gydF4y2Ba!-- -->开放获取</pgydF4y2Ba> <div class="sc-gmeYpB edbFGD article_citation"> 体积<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- --> <span class="sc-RcBXQ euBwsC">|</年代p一个n>文章的ID<gydF4y2Ba!-- --> 634758年<gydF4y2Ba!-- --> <span class="sc-RcBXQ euBwsC">|</年代p一个n> <a class="sc-htpNat bUhGXt link sc-iSDuPN kDGfWF" href="https://doi.org/10.1155/2012/634758" aria-label="Doi-link">https://doi.org/10.1155/2012/634758</一个> </div> <div class="sc-jKVCRD kVmHSX article_full_citation"> <div class="sc-LKuAh eHdRBi isHide"> <p>f . Ababsa Zendjebil, J.-Y。迪迪埃,m . Mallem<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> ”<年代p一个nclass="adjust-article-svg-size">智能定位使用新的传感器协会户外增强现实系统的框架</年代p一个n>”,<gydF4y2Ba!-- --><i>机器人杂志</我>,<gydF4y2Ba!-- --> 卷。<gydF4y2Ba!-- -->2012年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 文章的ID<gydF4y2Ba!-- -->634758年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 15<gydF4y2Ba!-- -->   页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- --> https://doi.org/10.1155/2012/634758</pgydF4y2Ba> </div> <button class="sc-iAyFgw irxuxk sc-kaNhvL hZfccF" color="">显示引用</gydF4y2Babutton> </div> <h1 class="sc-gPEVay iUuzmH sc-kZmsYB blFFOf article_title adjust-article-svg-size heading-title">智能定位使用新的传感器协会户外增强现实系统的框架</gydF4y2Bah1> </div> <div class="sc-kQsIoO ilXkOX article_authors"> <hr class="sc-iQtOjA bpnzQO hr__author"> <span class=""><b>f . Ababsa</gydF4y2Bab><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-gPzReC kIRihs icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a>,<年代up>1</年代up></span> <span class="">即Zendjebil<gydF4y2Ba!-- -->,<年代up>1</年代up></span> <span class="">J.-Y。迪迪埃<gydF4y2Ba!-- -->,<年代up>1</年代up> 和</年代p一个n> <span class="">m . Mallem<一个class="sc-htpNat bUhGXt link" href="http://orcid.org/0000-0002-2471-7028" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-jrIrqw kSCjIU" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a><sup>1</年代up></span> <div class="sc-iybRtq hqlWOa isHide"> <p><sup>1</年代up><span>Laboratoire IBISC EA 4526年,大学d 'Evry-Val-d 'Essonne, 40 Pelvoux街,91020埃夫里市,法国</年代p一个n></p> </div> <button class="sc-iAyFgw irxuxk sc-hjRWVT erRKjF" color="">显示更多</gydF4y2Babutton> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</gydF4y2Bab>Huosheng胡</gydF4y2Badiv> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代p一个n> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2012年2月17日</年代p一个n> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</年代p一个n> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2012年5月28日</年代p一个n> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代p一个n> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2012年6月15日</年代p一个n> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代p一个n> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">02年9月2012年</年代p一个n> </div> </div> </div> <article class="sc-hzDEsm jfJGTx article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</gydF4y2Bah4> <p>增强现实(AR)旨在加强我们的现实世界中,通过添加虚拟元素没有明显的自然如:计算机生成图像、虚拟对象,文字,符号,图形,声音,气味。真实/虚拟注册的质量主要取决于3 d相机姿态估计的准确性。在本文中,我们提出了一个户外原始实时定位系统基于“增大化现实”技术相结合三种异构传感器:相机、GPS和惯性传感器。该系统分为两个模块:主模块是基于视觉的;它估计用户的位置使用markerless跟踪方法。视觉跟踪失败时,系统自动切换到辅助定位模块组成的GPS和惯性传感器。</pgydF4y2Ba> <span class="end-abs"></span> <h4 id="introduction">1。介绍</gydF4y2Bah4> <p>结合多种传感器的想法不是最近的。第一个多传感器系统的出现与机器人应用程序,例如,在[<一个href="#B1">1</一个>]Vieville等人提出把相机与一个惯性传感器自动纠正自主移动机器人的路径。这个想法已经利用这最后一年的社区混合现实。几个工作提出融合视觉和惯性传感器的数据,使用卡尔曼滤波器(<一个href="#B2">2</一个>- - - - - -<一个href="#B6">6</一个>)或一个特定的过滤器(<一个href="#B7">7</一个>,<一个href="#B8">8</一个>]。策略包括在合并后所有数据从传感器定位相机预测/修正模型。惯性传感器提供的数据(陀螺仪、磁力计等)通常是用来预测的3 d运动相机然后使用应用技术调整和完善。卡尔曼滤波器通常执行数据融合实现。卡尔曼滤波是一种递归滤波器估计线性动态系统的状态从一系列的噪声测量。递归估计意味着只有以前的时间步的估计状态和当前测量需要计算当前状态的估计。所以,没有历史的观察和/或估计是必需的。</pgydF4y2Ba> <p>在[<一个href="#B2">2</一个>]你等人开发了一个混合传感器结合视觉系统有三个陀螺仪来估计在室外环境中相机的方向。他们的视觉跟踪允许精炼获得的估计。Ababsa[描述的系统<一个href="#B5">5</一个>结合一个edge-based跟踪与惯性测量(线性加速度、角速度,磁场)。视觉跟踪是用来精确的3 d定位而惯性传感器补偿错误由于突然的运动和闭塞。重力和磁场的测量是用来限制漂移问题。陀螺仪采用自动重置跟踪过程。两个传感器提供的数据结合使用一个恒定的速度模型扩展的卡尔曼滤波器。最近[<一个href="#B9">9</一个>),同一作者提出用GPS位置初始化时视觉跟踪失败。因此,初始化的视觉跟踪是通过定义一个搜索区域由一个椭圆以GPS的位置。</pgydF4y2Ba> <p>最近,Bleser和斯特里克(<一个href="#B6">6</一个>]提出结合texture-based追踪惯性传感器。相机姿势预计从加速器提供的数据使用一个扩展卡尔曼滤波器(EKF)。为了估计姿势,EKF保险丝2 d / 3 d对应获得的图像分析和惯性传感器的惯性测量获得。CAD模型的渲染(变形补丁)是用预测的姿势。这允许调整迭代变形补丁在当前图像二维运动估计和更新的估计滤波器。自然特征点跟踪KLT(金卢卡斯预)追踪。运动模型假定恒定加速度和恒定的角速度。这种方法需要离线准备生成变形环境的CAD模型。胡锦涛et al。(<一个href="#B10">10</一个>]提出结合摄像头,GPS和惯性陀螺仪传感器。融合方法是基于PPM(参数化模型匹配算法)。道路形状模型来源于数字地图与GPS的位置,并与道路特征提取匹配真实图像。融合是基于预估控制理论。检查数据完整性后,GPS数据将开始一个新的循环和重置陀螺的综合。陀螺的预测将被反馈到陀螺集成模块动态校正因子。当图像特征跟踪失败时,陀螺的预测数据是用于相机姿态估计。Ababsa和Mallem<一个href="#B8">8</一个>)提出了粒子滤波而不是卡尔曼滤波器。粒子滤波器(PF),也被称为蒙特卡罗方法的顺序的,复杂的技术评估模型是基于模拟。PFs通常用于估计贝叶斯模型。他们代表的另一种选择扩展卡尔曼滤波器,其优势在于,他们方法最优贝叶斯估计使用足够的样本。Ababsa等人从fiducial-based合并数据方法和惯性数据(陀螺仪和加速度计)。他们的融合算法是基于粒子滤波和采样重要性重采样(先生)。两个传感器有不同的采样频率,作者实现了两种互补的过滤器。因此,如果没有数据视觉(例如,阻塞),系统只使用惯性传感器的数据,反之亦然。Aron et al。<一个href="#B11">11</一个>]利用惯性传感器估计摄像机的方向只有当视觉跟踪失败。方向允许跟踪视觉元素通过定义一个搜索区域的图像进行特征匹配。从这组单应性估计估计摄像机构成匹配特性。惯性传感器的误差考虑优化的搜索区域。与阿伦等人提出的方法。<一个href="#B11">11</一个>)只有估计摄像机方向,麦迪et al。<一个href="#B12">12</一个>)使用了一个惯性传感器估计位置和方向。多通道系统允许跟踪基准和处理遮挡通过结合几个传感器和技术环境中根据现有的条件。当目标被部分遮挡时,系统使用一个基于点跟踪。存在完全闭塞的基准点,惯性传感器有助于克服视觉失败。然而,从加速度的估计位置随时间漂移导致跟踪失败。结合传感器后,援助方案似乎更有趣的数据融合。的确,援助方法使得系统更加智能,它可以适应不同的情况,使用在每次只有可用的传感器提供的数据。</pgydF4y2Ba> <p>在本研究工作中,我们感兴趣的是开发一个原始定位系统结合三个异构传感器(相机、GPS和IMU)为了提高准确性和鲁棒性。我们的目标是进行三维定位的一个通用的解决方案,3 d可视化和交互适应几个户外环境。本文的其余部分组织如下:部分<一个href="#sec2">2</一个>致力于我们的混合定位系统的概述。节<一个href="#sec3">3</一个>的配方,我们给相机姿态估计问题在使用点的特性。部分<一个href="#sec3">3</一个>和<一个href="#sec4">4</一个>,将详细描述我们提出混合定位系统。部分<一个href="#sec5">5</一个>提出了一些进行实验,结果在现实条件下在室外环境中。节中我们得出结论<一个href="#sec5">5</一个>并提出未来的工作。</pgydF4y2Ba> <h4 id="hybrid-localization-system-overview">2。混合定位系统概述</gydF4y2Bah4> <p>我们的定位系统是可穿戴和组成的平板电脑,一个惯性测量单元(IMU),一个摄像头和一个GPS接收器(见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig1/" target="_blank">1</一个>)。乌兹别克斯坦伊斯兰运动严格耦合和相机用来估计摄像机旋转。我们使用了一个Xsens MTi传感器包含陀螺仪、加速度计和磁力计。MTi的优点是,它包含一个内部数字信号处理器运行实时传感器融合算法提供一个可靠的三维定位估计。MTi在100 Hz同步测量的数据。视觉上,我们选择了uEye ui - 2220 - re - c CCD相机与6毫米镜头非常紧凑,低成本,适合户外环境。彩色图像的分辨率为768×576像素的帧率25 Hz流使用一个USB 2.0连接电脑。特林布尔GPS探路者ProXT接收机安装在用户提供GPS测量。ProXT接收器集成了一个多路径拒绝技术提供一个分表准确性。它的更新速度大约是1 Hz。 The ProXT receiver uses a Bluetooth wireless connection, to communicate with the computer. The three sensors providing measurements to the system are synchronized in hardware and runs at different rates.</p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.001" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.001.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 我们的混合跟踪器的传感器组件。</gydF4y2Batable> </div> </div> </div> <p>这几个传感器之间的定位系统使用一个援助计划,因此它是划分为两个子系统:一个主要子系统和辅助。主要的子系统对应基于视觉的定位。只有当使用的辅助子系统视觉跟踪失败;它由GPS和惯性传感器。这种混合系统不断的位置和姿态估计的观点,即使在视觉失败。图<一个href="//www.newsama.com/journals/jr/2012/634758/fig2/" target="_blank">2</一个>提供了一个流程图来描述三维定位过程使用提出的援助方案。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.002" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.002.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 系统的数据流程图。</gydF4y2Batable> </div> </div> </div> <h4 id="vision-based-localization-system">3所示。应用定位系统</gydF4y2Bah4> <h5 id="sec3.1">3.1。相机的姿势问题公式化</gydF4y2Bah5> <p>在这篇文章中,我们假设一个校准相机和透视投影模型。如果一个点的坐标<年代vgheight="15.65" id="M1" style="vertical-align:-2.29482pt;width:51.75px;" version="1.1" viewbox="0 0 51.75 15.65" width="51.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.65)"> <g transform="translate(72,-59.48)"> <text transform="matrix(1,0,0,-1,-71.95,61.82)"> <tspan style="font-size: 12.50px; 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" x="12.040389" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.23,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.75,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-20.34,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.87,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-5.42,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是由:<年代p一个nclass="equation" id="EEq1"> <svg height="16.5375" id="M5" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,174.8,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.75,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.45,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.280106" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,216.69,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.69,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.216871" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="251.42999" y="0.63"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="255.59351" y="0.63"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="261.845" y="0.63"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="20.200001" id="M6" style="vertical-align:-4.4302pt;width:97.650002px;" version="1.1" viewbox="0 0 97.650002 20.200001" width="97.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.2)"> <g transform="translate(72,-55.84)"> <text transform="matrix(1,0,0,-1,-71.95,60.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.715551" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.919439" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.72,65.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.3000002"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.6,60.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-21.09,65.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.3000002"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.96,60.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-5.45,65.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.3000002"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.33,60.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,2.84,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="18.700001" id="M7" style="vertical-align:-4.74141pt;width:89.037498px;" version="1.1" viewbox="0 0 89.037498 18.700001" width="89.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7)"> <g transform="translate(72,-57.04)"> <text transform="matrix(1,0,0,-1,-71.95,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.543869" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-41.49,58.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.17,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-27.05,58.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.21,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.09,58.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.22,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.06,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>翻译是一个旋转矩阵,向量,分别。<年代vgheight="10.325" id="M8" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="10.325" id="M9" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>描述刚体变换从世界坐标系到摄像机坐标系和与相机精确的参数相关的问题。</pgydF4y2Ba> <p>让像点<年代vgheight="16.8125" id="M10" style="vertical-align:-3.2316pt;width:90.012497px;" version="1.1" viewbox="0 0 90.012497 16.8125" width="90.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8125)"> <g transform="translate(72,-58.55)"> <text transform="matrix(1,0,0,-1,-71.95,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,58.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.01,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.88,58.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.66,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.12,58.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-18.9,61.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-3.28,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>的投影<年代vgheight="11.55" id="M11" style="vertical-align:-3.2316pt;width:12.8375px;" version="1.1" viewbox="0 0 12.8375 11.55" width="12.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>归一化图像平面上。使用摄像机针孔模型之间的关系<年代vgheight="11.525" id="M12" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.525" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.525)"> <g transform="translate(72,-62.78)"> <text transform="matrix(1,0,0,-1,-71.95,66.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="11.55" id="M13" style="vertical-align:-3.2316pt;width:12.8375px;" version="1.1" viewbox="0 0 12.8375 11.55" width="12.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是由:<年代p一个nclass="equation" id="EEq2"> <svg height="37.4375" id="M14" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.4375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.4375)"> <g transform="translate(72,-42.05)"> <text transform="matrix(1,0,0,-1,145.88,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,152.13,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,158.82,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.860001" y="-7.25"> 1</gydF4y2Batspan> </text> <g> <path d="m 172.06,59.37 43.49,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,172.06,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,178.36,51.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.29"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,182.48,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,189.43,43.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.43,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.69,43.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,218.83,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.10222" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,240.89,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,246.89,56.25)"> <tspan style="font-size: 12.50px; " x="20.219999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="227.23" y="2.3499999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="231.39349" y="2.3499999"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="237.645" y="2.3499999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>这就是所谓的同线性方程。</pgydF4y2Ba> <p>点约束对应于图像空间误差,它给出了3 d参考点之间的关系,提取相应的2 d图像点和相机参数如下:<年代p一个nclass="equation" id="EEq3"> <svg height="56.450001" id="M15" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 56.450001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,56.45)"> <g transform="translate(72,-26.84)"> <text transform="matrix(1,0,0,-1,83.75,42.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,93.43,49.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="10.29"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,101.68,42.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="-20.309999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.26"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="-6.21"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="16.1"> ⎷</gydF4y2Batspan> </text> <g> <path d="m 128.52,70.71 203.44,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,128.52,33.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.17" y="-9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.107245" y="-9.7299995"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,144.55,39.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,150.55,42.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-10.31"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,169.39,58.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.3000002"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,173.51,53.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,180.46,50.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,186.46,53.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.72,50.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 163.09,46.12 43.94,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,163.31,33.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,169.61,38.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.3000002"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,173.73,33.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,180.69,30.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,186.68,33.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.94,30.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,208.23,33.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,218.33,62.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.98,42.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.34" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.309999" y="-0.1"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.450001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,253.75,39.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,259.75,42.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.55" y="-10.74"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,278.6,58.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.29"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,282.73,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.68,50.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,295.68,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,310.94,50.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 272.29,46.12 43.5,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,272.29,33.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,278.59,38.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.3000002"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,282.72,33.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.67,30.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,295.67,33.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,310.92,30.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,316.98,33.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,327.09,62.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,331.96,42.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="142.16" y="-3.3099999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="146.3235" y="-3.3099999"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="152.575" y="-3.3099999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="16.9125" id="M16" style="vertical-align:-3.2316pt;width:95.212502px;" version="1.1" viewbox="0 0 95.212502 16.9125" width="95.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.9125)"> <g transform="translate(72,-58.47)"> <text transform="matrix(1,0,0,-1,-70.27,62.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.6799999" y="0.28999999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.54,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-54.84,61.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.530407" y="0"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.71,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.49,61.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.07" y="-0.1"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.21" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-17.96,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.74,61.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.89,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是观察到的图像点。</pgydF4y2Ba> <p>姿态估计问题是找到刚性变换(<年代vgheight="12.5375" id="M17" style="vertical-align:-1.76814pt;width:25.700001px;" version="1.1" viewbox="0 0 25.700001 12.5375" width="25.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.5375)"> <g transform="translate(72,-61.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.2522202" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.54147" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>)最适合已知三维参考点与观察到的二维图像点。这通常是通过某种形式的积累误差最小化(最小二乘方法)根据(<一个href="#EEq3">3</一个>)。高斯牛顿或Levenberg-Marquardt方法通常用于此目的(<一个href="#B13">13</一个>,<一个href="#B14">14</一个>]。</pgydF4y2Ba> <h5 id="sec3.3">3.3。讨论</gydF4y2Bah5> <p>3 d-2d特征匹配的关键相机姿态估计和计算机视觉中尚未解决的困难问题。跟踪系统需要一个初始化提供了一组好的3 d-2d匹配点。在实践中,匹配过程的准确性取决于信息的相关性相关的3 d点的识别。一个有趣的方法是定义一个参考补丁在3 d模型相对应的像点分。然后由调整匹配这些引用补丁在那些从当前帧中提取。相关性可以用来测量补丁之间的相似性在[<一个href="#B15">15</一个>]。然而,这种方法并不健壮的针对光照变化。其他方法使用筛选描述符(<一个href="#B16">16</一个>在观察条件下)变化的鲁棒性。筛选的主要缺点是其复杂性和时间消耗高,这使它不适合实时应用程序。在这项工作中,我们提出两种应用初始化的方法。第一个是半自动的,需要用户的干预指导匹配过程;它是用来启动跟踪系统。第二种方法是完全自动化的;执行跟踪时丢失。下一小节将给这些方法的概述。</pgydF4y2Ba> <h5 id="sec3.4">3.4。半自动的初始化方法</gydF4y2Bah5> <p>拟议的半自动初始化方法是在两个步骤:执行环境的线框模型(这里的建筑临街)是第一个渲染,实时的视频流量来自相机,使用一组预定义的构成(见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig3/" target="_blank">3(一个)</一个>)。同时用户移动相机为了使预测模型在其形象。一旦对齐(参见图实现<一个href="//www.newsama.com/journals/jr/2012/634758/fig3/" target="_blank">3 (b)</一个>)用户验证相应的构成和系统切换到匹配步骤为了执行,精度高,3 d-2d点匹配。调整呈现模型允许限制搜索区域的二维点在当前图像。这使得更快的和健壮的方法对离群值。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”634758。fig.003a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.003a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”634758。fig.003b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.003b.jpg"> <br> <strong>(b)</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig3"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”634758。fig.003a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.003a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”634758。fig.003b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.003b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig3"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> (一)模型的环境渲染。(b)预测模型及其之间的手动对齐图像。</gydF4y2Batable> </div> </div> </div> <p>3 d-2d匹配执行如下。一个搜索框定义每个三维模型投影点在图像对齐。兴趣点然后从这些图像中提取的地区。3 d点代表角落在模型中,我们使用哈里斯探测器(<一个href="#B17">17</一个>)为了提取2 d的兴趣点。然后,筛选描述符计算每个提取的哈里斯和相关点。我们选择使用筛选描述符,因为它是scale-rotation不变,允许实时跟踪。参考相关的描述符之间的距离的3 d点描述符提取的2 d点测量和比较。二维点最小化这个距离是选为相应的二维点。我们也使用RANSAC算法(<一个href="#B18">18</一个>]为了检测和删除离群值的匹配,从而增加初始化的准确性。</pgydF4y2Ba> <p>为了验证整个匹配3 d-2d点,我们引入一个一致性测试用作估计相机质量测量姿势。我们假设这个姿势接近时,选择线框模型在图像对齐。让,<年代vgheight="14.925" id="M18" style="vertical-align:-3.22282pt;width:90.550003px;" version="1.1" viewbox="0 0 90.550003 14.925" width="90.550003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.16,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.7,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.34,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.66,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-3.77,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>预定义的摄像机构成,用于模型/图像对齐,和<年代vgheight="13.8625" id="M19" style="vertical-align:-2.37006pt;width:72.212502px;" version="1.1" viewbox="0 0 72.212502 13.8625" width="72.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.890113" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.930502" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.094002" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.822056" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.623688" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.500336" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>相机姿势估计使用一组候选匹配点。随着两个矩阵都是相同的,我们可以写:<年代p一个nclass="equation" id="EEq4"> <svg height="18.4625" id="M20" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.4625)"> <g transform="translate(72,-57.23)"> <text transform="matrix(1,0,0,-1,176.29,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,183.71,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,191.38,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.04,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.38,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="252.74001" y="-0.46000001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="256.9035" y="-0.46000001"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="263.155" y="-0.46000001"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="10.325" id="M21" style="vertical-align:-0.0pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 10.325" width="9.0375004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个<年代vgheight="11.075" id="M22" style="vertical-align:-0.3135pt;width:32.700001px;" version="1.1" viewbox="0 0 32.700001 11.075" width="32.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.804752" y="0"> 4</gydF4y2Batspan> </text> </g> </g> </svg>单位矩阵。</pgydF4y2Ba> <p>矩阵的迹<年代vgheight="17.7875" id="M23" style="vertical-align:-3.22282pt;width:52.150002px;" version="1.1" viewbox="0 0 52.150002 17.7875" width="52.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7875)"> <g transform="translate(72,-57.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.52,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.85,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3390212" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-41.2,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>倾向于4。一致性测试可以制定为:<年代p一个nclass="equation" id="EEq5"> <svg height="19.35" id="M24" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,149.74,61.13)"> <tspan style="font-size: 12.50px; " x="52.009998" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.860001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7523403" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.792728" y="0"> T</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.144493" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.282986" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.834316" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.385651" y="0"> e</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,215.03,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.7,61.13)"> <tspan style="font-size: 12.50px; " x="15.66" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.98" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.007885" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.271889" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="251.42" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="255.5835" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="261.83499" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="10.7375" id="M25" style="vertical-align:-0.13794pt;width:7.9875002px;" version="1.1" viewbox="0 0 7.9875002 10.7375" width="7.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>低于一个阈值,两个矩阵被认为是不同的。</pgydF4y2Ba> <h5 id="sec3.5">3.5。自动初始化方法</gydF4y2Bah5> <p>与上面描述的半自动方法不同,自动初始化过程中,不需要用户干预。系统自动切换到此模式每次跟踪失败,因为噪音、闭塞或图像模糊。这种方法执行如下(见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig4/" target="_blank">4</一个>)。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.004" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.004.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 自动初始化方法。</gydF4y2Batable> </div> </div> </div> <p>让<年代vgheight="14.3625" id="M26" style="vertical-align:-3.2316pt;width:13.8125px;" version="1.1" viewbox="0 0 13.8125 14.3625" width="13.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是对应的参考系之前的最后一个捕获的图像跟踪失败。几个相关的信息帧即:相机的姿势<年代vgheight="14.3625" id="M27" style="vertical-align:-3.2316pt;width:13.4375px;" version="1.1" viewbox="0 0 13.4375 14.3625" width="13.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和3 d-2d匹配点的集合。这个想法是为了产生新的3 d-2d匹配点之间的引用和当前帧。</pgydF4y2Ba> <p>为此,我们第一个项目上的3 d点当前帧使用参考相机的姿势<年代vgheight="14.3625" id="M28" style="vertical-align:-3.2316pt;width:13.4375px;" version="1.1" viewbox="0 0 13.4375 14.3625" width="13.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>生成预测研究领域。这些图像区域,名叫补丁,都集中在预计的3 d点和矩形形状。相对应的兴趣点然后筛选特征提取在这些补丁和那些从参考系中提取和匹配。我们也使用RANSAC算法为了丢弃离群值。找到3 d-2d当前帧的匹配点,我们只需要确定转换映射中定义的兴趣点在当前图像中提取参考图像。我们假设这个变换是一个单应性因为两帧之间的运动是没有意义的。</pgydF4y2Ba> <p>让<年代vgheight="16.2875" id="M29" style="vertical-align:-4.77652pt;width:22.700001px;" version="1.1" viewbox="0 0 22.700001 16.2875" width="22.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.03,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>单应性,<年代vgheight="11.05" id="M30" style="vertical-align:-3.2316pt;width:15.25px;" version="1.1" viewbox="0 0 15.25 11.05" width="15.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="12.975" id="M31" style="vertical-align:-4.77652pt;width:16.75px;" version="1.1" viewbox="0 0 16.75 12.975" width="16.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>兴趣点提取参考和当前帧<年代vgheight="14.3625" id="M32" style="vertical-align:-3.2316pt;width:13.8125px;" version="1.1" viewbox="0 0 13.8125 14.3625" width="13.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vgheight="16.2875" id="M33" style="vertical-align:-4.77652pt;width:15.3125px;" version="1.1" viewbox="0 0 15.3125 16.2875" width="15.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,分别。之间的关系<年代vgheight="11.05" id="M34" style="vertical-align:-3.2316pt;width:15.25px;" version="1.1" viewbox="0 0 15.25 11.05" width="15.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vgheight="12.975" id="M35" style="vertical-align:-4.77652pt;width:16.75px;" version="1.1" viewbox="0 0 16.75 12.975" width="16.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="16.2875" id="M36" style="vertical-align:-4.77652pt;width:22.700001px;" version="1.1" viewbox="0 0 22.700001 16.2875" width="22.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.03,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>被定义为:<年代p一个nclass="equation" id="EEq6"> <svg height="17.1625" id="M37" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.1625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1625)"> <g transform="translate(72,-58.27)"> <text transform="matrix(1,0,0,-1,173.8,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,182.68,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,190.58,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.53,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.46,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.69,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.91,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="232.21001" y="1.13"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="236.3735" y="1.13"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="242.625" y="1.13"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>一旦单应性估计,我们把它应用到二维图像点相关的3 d模型点的参考系,为了改变当前图像。这允许更新3 d和2 d之间的对应点为当前图像,因此重启自动跟踪过程。</pgydF4y2Ba> <h5 id="sec3.6">3.6。视觉跟踪</gydF4y2Bah5> <p>一旦初始化视觉系统的视觉跟踪就可以开始。估计摄像机的姿势,我们必须保持2 d / 3 d匹配每个当前视图。这可以通过使用一个2 d分帧到帧跟踪。从一帧跟踪由以下特点<年代vgheight="9.125" id="M38" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>1到另一个框架<年代vgheight="9.125" id="M39" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。可以使用几种方法,如相关匹配方法;然而他们在计算时间非常昂贵。实时追踪二维特性,选择的方法必须迅速、准确。为KLT跟踪器(<一个href="#B19">19</一个>可以采用)。该算法使用了一个光流计算跟踪特征点或一组预定义的点从之前的形象<年代vgheight="14.3375" id="M40" style="vertical-align:-3.21404pt;width:24.637501px;" version="1.1" viewbox="0 0 24.637501 14.3375" width="24.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.95,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7393761" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7344961" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>当前图像<年代vgheight="14.3375" id="M41" style="vertical-align:-3.21404pt;width:11.675px;" version="1.1" viewbox="0 0 11.675 14.3375" width="11.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.95,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。因此,该算法跟踪相关的一组二维点可见3 d点。简而言之,2 d点是在附近搜索的立场观点<年代vgheight="9.125" id="M42" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>1基于最小化的亮度差异。尽量减少计算时间,KLT跟踪器使用当前视图的金字塔的图像。因此,在粗级别跟踪完成,然后传播到最好的。这允许功能后,在很长很精确的距离。快速、准确的方法,但是它要求跟踪点总是可见的。因此,方法不能处理遮挡。</pgydF4y2Ba> <h4 id="imu-gps-localization-system">4所示。IMU-GPS定位系统</gydF4y2Bah4> <p>这个子系统,取代了建立这一失败时定位系统。的位置和姿态视觉子系统替换的GPS接收器提供的绝对位置和方向的惯性传感器。使用辅助子系统不限于取代视觉子系统。辅助子系统还用于初始化视觉子系统。此外,从这个子系统的位置和姿态,我们可以测量的准确性3 d定位估计的视觉子系统通过定义一些置信区间。辅助子系统由两个模块组成:预测和修正。预测模块是用来预测精度定位系统的错误。它是基于两子系统之间误差的在线培训。一旦定位系统切换到辅助子系统、误差预计高斯模型和用于改善后提供的位置和姿态的GPS和惯性传感器。两部分组成系统不断相互交互。 Also, the use of GPS for position estimation solves the problem of inertial sensor’s drift, which is used only for orientation estimation.</p> <h5 id="sec4.1">4.1。传感器校准</gydF4y2Bah5> <p>在我们的混合动力系统中,每个传感器提供的数据在自己的参考系。惯性传感器计算身体参考系之间的取向与当地水平坐标系。同时,地球参考系的GPS位置表达WGS84(世界大地系统)所定义的标准。注册,我们需要估计不断的相机的姿势与世界坐标系到摄像机坐标系。因此,提供的3 d定位IMU-GPS系统必须与摄像机坐标系。几个传感器必须一致统一参考系以相同的位置和方向的观点。所以,混合传感器必须校准,确定几个传感器之间的关系,从而统一测量。IMU-GPS系统的准确性取决于校准过程的准确性。我们已经开发出一种原始标定方法以计算几个转换精度高。我们的方法分为两个校准过程。 The first one consists in estimating the relationship between inertial sensor and camera (Inertial/Camera calibration). The second one estimates the transformation which maps the GPS position to the camera position (GPS/Camera transformation).</p> <h6 id="sec4.1.1">以下4.4.1。惯性/相机校正</gydF4y2Bah6> <p>为了推导出相机的取向方向的惯性传感器,我们需要估计参考帧之间的转换连接到相机和惯性传感器。使用参考框架见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig5/" target="_blank">5</一个>。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.005" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.005.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 惯性/相机:参考帧配置。</gydF4y2Batable> </div> </div> </div> <p>让<年代vgheight="14.4125" id="M43" style="vertical-align:-3.27548pt;width:32.137501px;" version="1.1" viewbox="0 0 32.137501 14.4125" width="32.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>世界坐标系的旋转<年代vgheight="14.4125" id="M44" style="vertical-align:-3.27548pt;width:24.799999px;" version="1.1" viewbox="0 0 24.799999 14.4125" width="24.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>对摄像机坐标系<年代vgheight="14.375" id="M45" style="vertical-align:-3.24037pt;width:20.525px;" version="1.1" viewbox="0 0 20.525 14.375" width="20.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。<年代vgheight="14.375" id="M46" style="vertical-align:-3.24037pt;width:25.887501px;" version="1.1" viewbox="0 0 25.887501 14.375" width="25.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>代表的旋转<年代vgheight="14.2375" id="M47" style="vertical-align:-3.13504pt;width:18.549999px;" version="1.1" viewbox="0 0 18.549999 14.2375" width="18.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>对摄像机坐标系<年代vgheight="14.375" id="M48" style="vertical-align:-3.24037pt;width:20.525px;" version="1.1" viewbox="0 0 20.525 14.375" width="20.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。车身骨架之间的旋转<年代vgheight="14.2375" id="M49" style="vertical-align:-3.13504pt;width:18.549999px;" version="1.1" viewbox="0 0 18.549999 14.2375" width="18.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="14.375" id="M50" style="vertical-align:-3.24037pt;width:20.5625px;" version="1.1" viewbox="0 0 20.5625 14.375" width="20.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>而著称<年代vgheight="14.375" id="M51" style="vertical-align:-3.24037pt;width:25.8125px;" version="1.1" viewbox="0 0 25.8125 14.375" width="25.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。最后,<年代vgheight="14.4125" id="M52" style="vertical-align:-3.27548pt;width:32.825001px;" version="1.1" viewbox="0 0 32.825001 14.4125" width="32.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>代表了世界坐标系的旋转<年代vgheight="14.4125" id="M53" style="vertical-align:-3.27548pt;width:24.799999px;" version="1.1" viewbox="0 0 24.799999 14.4125" width="24.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>关于<年代vgheight="14.375" id="M54" style="vertical-align:-3.24037pt;width:20.5625px;" version="1.1" viewbox="0 0 20.5625 14.375" width="20.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。旋转<年代vgheight="14.375" id="M55" style="vertical-align:-3.24037pt;width:25.8125px;" version="1.1" viewbox="0 0 25.8125 14.375" width="25.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是由惯性传感器和<年代vgheight="14.4125" id="M56" style="vertical-align:-3.27548pt;width:32.137501px;" version="1.1" viewbox="0 0 32.137501 14.4125" width="32.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>从相机姿势估计获得。因此,我们需要计算旋转<年代vgheight="14.375" id="M57" style="vertical-align:-3.24037pt;width:25.887501px;" version="1.1" viewbox="0 0 25.887501 14.375" width="25.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="14.4125" id="M58" style="vertical-align:-3.27548pt;width:32.825001px;" version="1.1" viewbox="0 0 32.825001 14.4125" width="32.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。几帧之间的关系表达的是:<年代p一个nclass="equation" id="EEq7"> <svg height="16.5375" id="M59" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,144.5,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.75,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,173.58,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,194.87,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,209.01,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,224.62,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.69,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.3,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,271.21,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="202.91" y="0.63"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="207.0735" y="0.63"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="213.325" y="0.63"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>在这种情况下,惯性/相机标定过程由估计的旋转矩阵<年代vgheight="14.375" id="M60" style="vertical-align:-3.24037pt;width:25.887501px;" version="1.1" viewbox="0 0 25.887501 14.375" width="25.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>并推导出矩阵<年代vgheight="14.4125" id="M61" style="vertical-align:-3.27548pt;width:32.825001px;" version="1.1" viewbox="0 0 32.825001 14.4125" width="32.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。我们假设<年代vgheight="10.325" id="M62" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>设在的<年代vgheight="14.375" id="M63" style="vertical-align:-3.24037pt;width:20.5625px;" version="1.1" viewbox="0 0 20.5625 14.375" width="20.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>框架是指向上沿纵向和共线的<年代vgheight="10.325" id="M64" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>设在世界坐标系<年代vgheight="14.4125" id="M65" style="vertical-align:-3.27548pt;width:24.799999px;" version="1.1" viewbox="0 0 24.799999 14.4125" width="24.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(图<一个href="//www.newsama.com/journals/jr/2012/634758/fig6/" target="_blank">6</一个>)。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig6"> <div class="floats-partial-content fig-content-fig6"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.006" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.006.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="14.4125" id="M66" style="vertical-align:-3.27548pt" version="1.1" viewbox="0 0 24.799999 14.4125" width="24.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg> <svg height="14.2375" id="M67" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 18.549999 14.2375" width="18.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg> <table> 世界坐标系之间的关系gydF4y2Ba和全球惯性参考系gydF4y2Ba。</gydF4y2Batable> </div> </div> </div> <p>因此,这个配置意味着矩阵<年代vgheight="14.4125" id="M68" style="vertical-align:-3.27548pt;width:32.825001px;" version="1.1" viewbox="0 0 32.825001 14.4125" width="32.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>对应于一个单一的旋转在吗<年代vgheight="10.325" id="M69" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>设在一个角<我><i>θ</我></i>。因此,矩阵<年代vgheight="14.4125" id="M70" style="vertical-align:-3.27548pt;width:32.825001px;" version="1.1" viewbox="0 0 32.825001 14.4125" width="32.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>可以表示如下:<年代p一个nclass="equation" id="EEq8"> <svg height="48.1875" id="M71" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.1875)"> <g transform="translate(72,-33.45)"> <text transform="matrix(1,0,0,-1,122.6,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.86,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,152.24,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="128.67999" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.139999" y="-13.13"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.691332" y="-13.13"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.942833" y="-13.13"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.133495" y="-13.13"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.296997" y="-13.13"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.848568" y="-13.13"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.988503" y="-13.13"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.64106" y="-13.13"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.504723" y="-13.13"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.98056" y="-13.13"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.55906" y="-13.13"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="105.72256" y="-13.13"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="112.27412" y="-13.13"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="122.42656" y="-13.13"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.18" y="-0.63"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.043667" y="-0.63"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.519501" y="-0.63"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.098" y="-0.63"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.261497" y="-0.63"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.813068" y="-0.63"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.279282" y="-0.63"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.830612" y="-0.63"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.082115" y="-0.63"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.272781" y="-0.63"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.43628" y="-0.63"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="107.98785" y="-0.63"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="122.41631" y="-0.63"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.950001" y="11.88"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.099998" y="11.88"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="122.42049" y="11.88"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="140.87" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="321.88" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="326.04349" y="0"> 8</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="332.29501" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>假设<年代vgheight="18.549999" id="M72" style="vertical-align:-3.90353pt;width:145.9375px;" version="1.1" viewbox="0 0 145.9375 18.549999" width="145.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.55)"> <g transform="translate(72,-57.16)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.93,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.62,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="8.79"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-15.33,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.817015" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.108906" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.31015" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.561653" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.775402" y="0"> 3</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<年代vgheight="18.549999" id="M73" style="vertical-align:-3.90353pt;width:20.625px;" version="1.1" viewbox="0 0 20.625 18.549999" width="20.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.55)"> <g transform="translate(72,-57.16)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.85,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="8.79"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是<年代vgheight="9.9250002" id="M74" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>th的列<年代vgheight="14.375" id="M75" style="vertical-align:-3.24037pt;width:25.8125px;" version="1.1" viewbox="0 0 25.8125 14.375" width="25.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>矩阵。方程(<一个href="#EEq8">8</一个>)可以写成:<年代p一个nclass="equation" id="EEq9"> <svg height="75.025002" id="M76" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 75.025002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,75.025)"> <g transform="translate(72,-11.98)"> <text transform="matrix(1,0,0,-1,53.72,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,62.97,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,57.19,28.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.889999" y="0.07"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,84.33,24.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.47,28.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,109.93,33.06)"> <tspan style="font-size: 8.75px; " x="0" y="9.3299999"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,127.2,28.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,136.46,24.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,150.59,28.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162.05,33.06)"> <tspan style="font-size: 8.75px; " x="0" y="9.3299999"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,179.33,28.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.58,24.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.72,28.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3390212" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,214.17,33.06)"> <tspan style="font-size: 8.75px; " x="0" y="9.3299999"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.47,25.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.98" y="7.2199998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="131.63" y="7.2199998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.09" y="-15.64"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.641333" y="-15.64"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.892834" y="-15.64"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.083496" y="-15.64"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.246998" y="-15.64"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.798569" y="-15.64"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.938499" y="-15.64"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.591057" y="-15.64"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.454727" y="-15.64"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.930557" y="-15.64"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.50906" y="-15.64"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="108.67255" y="-15.64"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.22413" y="-15.64"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="125.36406" y="-15.64"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.120001" y="-3.1400001"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.983667" y="-3.1400001"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.459499" y="-3.1400001"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.037998" y="-3.1400001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.201496" y="-3.1400001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.753071" y="-3.1400001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.219284" y="-3.1400001"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.770615" y="-3.1400001"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.02211" y="-3.1400001"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.22528" y="-3.1400001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.38878" y="-3.1400001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="110.94035" y="-3.1400001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="125.36881" y="-3.1400001"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.900002" y="9.3699999"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="92.050003" y="9.3699999"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="125.3705" y="9.3699999"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="248.64999" y="-13.25"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="252.81349" y="-13.25"> 9</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="259.065" y="-13.25"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>然后,<年代p一个nclass="equation" id="EEq10"> <svg height="58.224998" id="M77" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 58.224998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,58.225)"> <g transform="translate(72,-25.42)"> <text transform="matrix(1,0,0,-1,55.65,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,64.91,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,59.13,34.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.4" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,87.78,31.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,101.92,34.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,113.38,39.85)"> <tspan style="font-size: 8.75px; " x="0" y="9.3199997"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,127.45,34.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3600001" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.599998" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.290001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.72" y="-6.8800001"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.271332" y="-6.8800001"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.522833" y="-6.8800001"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.713497" y="-6.8800001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.876995" y="-6.8800001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.42857" y="-6.8800001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.76" y="5.6199999"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.623667" y="5.6199999"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.099501" y="5.6199999"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.677998" y="5.6199999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.841499" y="5.6199999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.39307" y="5.6199999"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,199.99,31.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,214.13,34.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.58,39.85)"> <tspan style="font-size: 8.75px; " x="0" y="9.3199997"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.66,34.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3499999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.169998" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.860001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.72" y="-6.8800001"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.360052" y="-6.8800001"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.223721" y="-6.8800001"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.699554" y="-6.8800001"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.290554" y="-6.8800001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.454056" y="-6.8800001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.005627" y="-6.8800001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.01" y="5.6199999"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.561333" y="5.6199999"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.812832" y="5.6199999"> 年代</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.003498" y="5.6199999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.166996" y="5.6199999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.718567" y="5.6199999"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,320.77,31.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,334.91,34.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,346.36,39.85)"> <tspan style="font-size: 8.75px; " x="0" y="9.3199997"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,357.66,29.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="110.21" y="-15.66"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="114.3735" y="-15.66"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="120.625" y="-15.66"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="126.8765" y="-15.66"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>从(<一个href="#EEq10">10</一个>我们可以推断出:<年代p一个nclass="equation" id="EEq11"> <svg height="19.2875" id="M78" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.2875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.2875)"> <g transform="translate(72,-56.57)"> <text transform="matrix(1,0,0,-1,167.86,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,172.96,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="9.3500004"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.79,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,214.08,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,228.22,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.68,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="9.3199997"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,467.87,61.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>我们重写这个方程的线性形式<年代vgheight="10.7375" id="M79" style="vertical-align:-0.13794pt;width:61.825001px;" version="1.1" viewbox="0 0 61.825001 10.7375" width="61.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.740317" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.091841" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.445045" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.472931" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,所以:<年代p一个nclass="equation" id="EEq12"> <svg height="69.512497" id="M80" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 69.512497" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,69.5125)"> <g transform="translate(72,-16.39)"> <text transform="matrix(1,0,0,-1,116.04,59.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎛</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="10.75"> ⎜</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="21.5"> ⎜</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="32.25"> ⎜</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="42.939999"> ⎝</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.6300001" y="4.21"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.48" y="1.7"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,132.62,62.68)"> <tspan style="font-size: 8.75px; " x="0" y="9.3199997"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.92,55.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,149.77,65.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,176.74,57.68)"> <tspan style="font-size: 12.50px; " x="-40.790001" y="17.85"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-14.28" y="20.360001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-8.4300003" y="17.85"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.784786" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,173.41,44.84)"> <tspan style="font-size: 8.75px; " x="0" y="9.3299999"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,184.71,37.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,190.56,47.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.53,39.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-14.28" y="20.35"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-8.4300003" y="17.84"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-81.580002" y="17.84"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-40.795216" y="17.84"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,214.2,26.99)"> <tspan style="font-size: 8.75px; " x="0" y="9.3199997"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.5,19.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.35,29.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.06,59.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎞</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="10.75"> ⎟</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="21.5"> ⎟</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="32.25"> ⎟</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="42.939999"> ⎠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.4099998" y="18.309999"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.761524" y="18.309999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.102224" y="18.309999"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.142612" y="18.309999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,283.31,46.07)"> <tspan style="font-size: 8.75px; " x="0" y="9.3599997"> 3</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,299.67,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="168.2" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="172.36349" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="178.61501" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="184.8665" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="22.387501" id="M81" style="vertical-align:-4.57706pt;width:227.8625px;" version="1.1" viewbox="0 0 227.8625 22.387501" width="227.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3875)"> <g transform="translate(72,-54.09)"> <text transform="matrix(1,0,0,-1,-71.95,58.7)"> <tspan style="font-size: 12.50px; " x="25.389999" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.63,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.06,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 1</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.33,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.76,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 1</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.03,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.46,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 1</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.27,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,10.84,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 2</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,22.57,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.14,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 2</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,37.87,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,41.44,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 2</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,53.17,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,56.74,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 3</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.47,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,72.04,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 3</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.77,59.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,87.34,63.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="4.1950922" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.6100001"> 3</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.1259999" y="6.6100001"> 3</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,97.68,56.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,103.53,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。我们需要至少3矩阵<年代vgheight="14.375" id="M82" style="vertical-align:-3.24037pt;width:25.8125px;" version="1.1" viewbox="0 0 25.8125 14.375" width="25.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="14.4125" id="M83" style="vertical-align:-3.27548pt;width:32.137501px;" version="1.1" viewbox="0 0 32.137501 14.4125" width="32.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为了估计<年代vgheight="14.375" id="M84" style="vertical-align:-3.24037pt;width:25.887501px;" version="1.1" viewbox="0 0 25.887501 14.375" width="25.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>使用至少意味着二乘算法。一旦矩阵<年代vgheight="14.375" id="M85" style="vertical-align:-3.24037pt;width:25.887501px;" version="1.1" viewbox="0 0 25.887501 14.375" width="25.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>计算矩阵我们可以推断出什么<年代vgheight="14.4125" id="M86" style="vertical-align:-3.27548pt;width:32.825001px;" version="1.1" viewbox="0 0 32.825001 14.4125" width="32.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>使用(<一个href="#EEq1">1</一个>),所以:<年代p一个nclass="equation" id="EEq13"> <svg height="18.8375" id="M87" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.8375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.8375)"> <g transform="translate(72,-56.93)"> <text transform="matrix(1,0,0,-1,144.5,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.75,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,174.13,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.42,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.2009602" y="9.1499996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,209.5,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.11,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.0699997"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="9.0699997"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.25,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3390212" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.85,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,271.21,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="196.66" y="-0.11"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="200.8235" y="-0.11"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="207.075" y="-0.11"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="213.32649" y="-0.11"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>两个矩阵的估计<年代vgheight="14.375" id="M88" style="vertical-align:-3.24037pt;width:25.887501px;" version="1.1" viewbox="0 0 25.887501 14.375" width="25.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="14.4125" id="M89" style="vertical-align:-3.27548pt;width:32.825001px;" version="1.1" viewbox="0 0 32.825001 14.4125" width="32.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.4239678" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>完成脱机,允许系统实时估计摄像机的旋转只使用方向矩阵的惯性传感器。这是非常重要的视觉跟踪失败时恢复相机的姿势。</pgydF4y2Ba> <h6 id="sec4.1.2">4.1.2。GPS /相机校正</gydF4y2Bah6> <p>第二校准过程估计刚性变换(旋转+翻译),将GPS位置映射到本地世界参照系<年代vgheight="14.4125" id="M90" style="vertical-align:-3.27548pt;width:24.799999px;" version="1.1" viewbox="0 0 24.799999 14.4125" width="24.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig6/" target="_blank">6</一个>)。在我们的例子中,表达的位置由GPS接收器提供学位。兰伯特圆锥投影是必要的表达的GPS位置米。这个投影最小化的扭曲和适应区域实验(即完成。、法国)。这套装置的兰伯特圆锥投影在地球球锥。让<年代vgheight="13.3125" id="M91" style="vertical-align:-5.04861pt;width:23.5875px;" version="1.1" viewbox="0 0 23.5875 13.3125" width="23.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.3125)"> <g transform="translate(72,-61.35)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> p</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7519999" y="0"> 年代</gydF4y2Batspan> </text> </g> </g> </svg>相机位置的GPS接收器和地球参考系和表达<年代vgheight="11.0375" id="M92" style="vertical-align:-3.22281pt;width:26.612499px;" version="1.1" viewbox="0 0 26.612499 11.0375" width="26.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.8858881" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.7717762" y="0"> 米</gydF4y2Batspan> </text> </g> </g> </svg>相机的位置在当地世界参照系。之间的关系<年代vgheight="13.3125" id="M93" style="vertical-align:-5.04861pt;width:23.5875px;" version="1.1" viewbox="0 0 23.5875 13.3125" width="23.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.3125)"> <g transform="translate(72,-61.35)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> p</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7519999" y="0"> 年代</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="11.0375" id="M94" style="vertical-align:-3.22281pt;width:26.612499px;" version="1.1" viewbox="0 0 26.612499 11.0375" width="26.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.8858881" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.7717762" y="0"> 米</gydF4y2Batspan> </text> </g> </g> </svg>然后给出了:<年代p一个nclass="equation" id="EEq14"> <svg height="17.362499" id="M95" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.362499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.3625)"> <g transform="translate(72,-58.11)"> <text transform="matrix(1,0,0,-1,161.91,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,168.02,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.8858881" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.7717762" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,186.57,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.068275" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.4198" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.11,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> p</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7519999" y="0"> 年代</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.54,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.25366" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="229.33" y="1.27"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="233.4935" y="1.27"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="239.745" y="1.27"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="245.99651" y="1.27"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="11.0375" id="M96" style="vertical-align:-3.22281pt;width:26.612499px;" version="1.1" viewbox="0 0 26.612499 11.0375" width="26.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.8858881" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.7717762" y="0"> 米</gydF4y2Batspan> </text> </g> </g> </svg>使用相机标定参数计算如下:<年代vgheight="18.775" id="M97" style="vertical-align:-4.21953pt;width:125.475px;" version="1.1" viewbox="0 0 125.475 18.775" width="125.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.775)"> <g transform="translate(72,-56.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.8858881" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.7717762" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.28,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-17.43,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.0699997"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="9.0699997"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,1.71,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3390212" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.97,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。</pgydF4y2Ba> <p>最后,刚性变换获得通过最小化以下准则:<年代p一个nclass="equation" id="EEq15"> <svg height="48.349998" id="M98" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.35)"> <g transform="translate(72,-33.32)"> <text transform="matrix(1,0,0,-1,144.56,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,138.66,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,140.19,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,154.81,51.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.71"> 为</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.54" y="1.85"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,167.46,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,167.46,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.8858881" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.7717762" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,185.32,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.34" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.200001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.215384" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.579411" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,227.01,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,227.01,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> p</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7519999" y="0"> 年代</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,242.45,49.67)"> <tspan style="font-size: 12.50px; " x="15.25" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.110001" y="-1.85"> 为</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.110001" y="1.86"> 为</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,272.18,57.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.05,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="190.82001" y="0.14"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="194.98351" y="0.14"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="201.235" y="0.14"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="207.4865" y="0.14"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>为了简化问题,我们使用了轴和角度<年代vgheight="22.987499" id="M99" style="vertical-align:-2.21957pt;width:39.012501px;" version="1.1" viewbox="0 0 39.012501 22.987499" width="39.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.9875)"> <g transform="translate(72,-53.61)"> <text transform="matrix(1,0,0,-1,-71.95,55.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.33,65.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> →</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.38,56.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.6199999" y="0.41999999"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.821248" y="0.41999999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.37282" y="0.41999999"> )</gydF4y2Batspan> </text> </g> </g> </svg>来表示旋转矩阵<年代vgheight="10.325" id="M100" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#B20">20.</一个>]。这允许细分优化问题分成两个子问题,一个旋转的估计,一个用于翻译向量。</pgydF4y2Ba> <h5 id="sec4.2">4.2。定位误差预测</gydF4y2Bah5> <p>提供的3 d定位估计的组合GPS和惯性传感器估计不准确,那么应用。产生的计算误差在本地化过程中是很重要的。事实上,它允许量化测量的质量以提高3 d定位估计IMU-GPS定位系统提供的。错误代表之间的抵消相机姿势和位置和姿态推断从GPS和惯性传感器。当视觉上失败时,必须预测这个错误。,错误与高斯过程建模为回归(<一个href="#B21">21</一个>]。生成样本的高斯过程是一个随机过程,可以作为先验概率分布在贝叶斯推理功能。</pgydF4y2Ba> <p>我们是<年代vgheight="11.0125" id="M101" style="vertical-align:-3.20526pt;width:81.925003px;" version="1.1" viewbox="0 0 81.925003 11.0125" width="81.925003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.2,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.11,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-43.24,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.36,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>一组训练数据相关联<年代vgheight="11" id="M102" style="vertical-align:-3.20526pt;width:79.400002px;" version="1.1" viewbox="0 0 79.400002 11" width="79.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.87,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.46,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.59,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.38,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在哪里<年代vgheight="14.7125" id="M103" style="vertical-align:-3.2316pt;width:63px;" version="1.1" viewbox="0 0 63 14.7125" width="63" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.06,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.82,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。我们的目标是预测价值<年代vgheight="11.3625" id="M104" style="vertical-align:-3.49493pt;width:26.9px;" version="1.1" viewbox="0 0 26.9 11.3625" width="26.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>相关的数据<年代vgheight="11.375" id="M105" style="vertical-align:-3.49493pt;width:27.75px;" version="1.1" viewbox="0 0 27.75 11.375" width="27.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.375)"> <g transform="translate(72,-62.9)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。我们考虑<年代vgheight="15.05" id="M106" style="vertical-align:-3.49493pt;width:104.6px;" version="1.1" viewbox="0 0 104.6 15.05" width="104.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.05)"> <g transform="translate(72,-59.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.22,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.32,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.45,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.46,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>一组(<年代vgheight="11.325" id="M107" style="vertical-align:-0.51414pt;width:33.362499px;" version="1.1" viewbox="0 0 33.362499 11.325" width="33.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9896574" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.329878" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>)随机变量与零均值高斯分布和协方差矩阵<年代vgheight="14.825" id="M108" style="vertical-align:-3.49493pt;width:28.9px;" version="1.1" viewbox="0 0 28.9 14.825" width="28.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.15,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>如:<年代p一个nclass="equation" id="EEq16"> <svg height="38.575001" id="M109" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,157.16,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,164.97,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,183.66,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.16" y="-7.8499999"> Σ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.62,58.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,232.42,61.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-27.35" y="14.46"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,212.5,51.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.19,46.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.87,43.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,247.09,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.46" y="-7.3299999"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="220.78" y="-7.3299999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="224.9435" y="-7.3299999"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="231.19499" y="-7.3299999"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="237.4465" y="-7.3299999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="11.0125" id="M110" style="vertical-align:-3.20526pt;width:14.525px;" version="1.1" viewbox="0 0 14.525 11.0125" width="14.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.27,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是<年代vgheight="8.7875004" id="M111" style="vertical-align:-0.3135pt;width:32.612499px;" version="1.1" viewbox="0 0 32.612499 8.7875004" width="32.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.7875)"> <g transform="translate(72,-64.97)"> <text transform="matrix(1,0,0,-1,-71.95,65.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9896574" y="0"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.767242" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>矩阵,<年代vgheight="7.0124998" id="M112" style="vertical-align:-0.0pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 7.0124998" width="9.4125004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个<年代vgheight="7.1374998" id="M113" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>列向量和<年代vgheight="11.375" id="M114" style="vertical-align:-3.49493pt;width:27.5px;" version="1.1" viewbox="0 0 27.5 11.375" width="27.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.375)"> <g transform="translate(72,-62.9)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.27,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>是一个标量。如果<年代vgheight="11" id="M115" style="vertical-align:-3.20526pt;width:79.400002px;" version="1.1" viewbox="0 0 79.400002 11" width="79.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.87,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.46,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.59,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.38,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>观察到的变量相关<年代vgheight="11.0125" id="M116" style="vertical-align:-3.20526pt;width:81.925003px;" version="1.1" viewbox="0 0 81.925003 11.0125" width="81.925003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.2,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.11,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-43.24,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.36,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>然后条件分布<年代vgheight="15.05" id="M117" style="vertical-align:-3.49493pt;width:110.4625px;" version="1.1" viewbox="0 0 110.4625 15.05" width="110.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.05)"> <g transform="translate(72,-59.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.4267821" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-53.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.45,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.39,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,12.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>产生高斯分布:<年代p一个nclass="equation" id="EEq17"> <svg height="53.662498" id="M118" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 53.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,53.6625)"> <g transform="translate(72,-29.07)"> <text transform="matrix(1,0,0,-1,148.87,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,156.11,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.79,55.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.107244" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="7.389864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.77,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.93,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.64,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.32,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,227.52,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,149.39,35.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,156.73,40.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.62" y="9.0200005"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.79,29.38)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="3.107244" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="7.389864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.77,35.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.18,32.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.18,35.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.95,40.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.66,35.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,246.46,40.58)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,257.33,35.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.4267821" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="210.53999" y="-11.83"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="214.70351" y="-11.83"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="220.955" y="-11.83"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="227.2065" y="-11.83"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<年代vgheight="17.725" id="M119" style="vertical-align:-3.20526pt;width:131.39999px;" version="1.1" viewbox="0 0 131.39999 17.725" width="131.39999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.725)"> <g transform="translate(72,-57.82)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.75,66.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.43,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.02,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.15,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-18.74,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.87,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,17.34,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,22.19,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.35,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<年代vgheight="15.05" id="M120" style="vertical-align:-3.49493pt;width:145.1375px;" version="1.1" viewbox="0 0 145.1375 15.05" width="145.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.05)"> <g transform="translate(72,-59.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-46.58,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.579218" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> v</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.258221" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.421719" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.96,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,13.26,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,39.89,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<年代vgheight="15.05" id="M121" style="vertical-align:-3.49493pt;width:115.1375px;" version="1.1" viewbox="0 0 115.1375 15.05" width="115.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.05)"> <g transform="translate(72,-59.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-58.58,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.579218" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> v</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.258221" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.421719" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.96,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,1.26,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,12.68,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,15.9,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="16.637501" id="M122" style="vertical-align:-4.77652pt;width:107.9625px;" version="1.1" viewbox="0 0 107.9625 16.637501" width="107.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.15,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-53.53,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> v</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.258221" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.421719" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-5.68,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.73,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,10.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。之间的协方差<年代vgheight="11.025" id="M123" style="vertical-align:-3.2316pt;width:11.9px;" version="1.1" viewbox="0 0 11.9 11.025" width="11.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.025)"> <g transform="translate(72,-63.18)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="12.95" id="M124" style="vertical-align:-4.77652pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 12.95" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.95)"> <g transform="translate(72,-61.64)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>之间的协方差是一样的吗<年代vgheight="11.05" id="M125" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<年代vgheight="12.975" id="M126" style="vertical-align:-4.77652pt;width:14.25px;" version="1.1" viewbox="0 0 14.25 12.975" width="14.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>呼呼的声音是由:<年代p一个nclass="equation" id="eq18"> <svg height="50.887501" id="M127" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.887501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.8875)"> <g transform="translate(72,-31.29)"> <text transform="matrix(1,0,0,-1,97.18,47.62)"> <tspan style="font-size: 12.50px; " x="24.309999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.16" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> v</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,134.22,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,137.44,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,149.52,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.95,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.52"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.130001" y="-9.7700005"> 1</gydF4y2Batspan> </text> <g> <path d="m 176.51,50.74 53.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,176.51,37.81)"> <tspan style="font-size: 12.50px; " x="24.76" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.76" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.889999" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.889999" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.415719" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.26" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.924099" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.26432" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,233.18,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.4479518" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.443072" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="15.193472" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="17.915344" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="23.910463" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="27.314993" y="0"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.63,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,240.35,33.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,264.33,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,271.2,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,278.83,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,292.06,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.095264" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="14.817136" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="20.812256" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.216784" y="0"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,318.53,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="149.34" y="-0.89999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="153.50349" y="-0.89999998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="159.755" y="-0.89999998"> 8</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="166.0065" y="-0.89999998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>在我们的案例中<年代vgheight="11.05" id="M128" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>代表了GPS的位置或方向矩阵给惯性传感器,和<年代vgheight="9.8625002" id="M129" style="vertical-align:-2.29482pt;width:7.875px;" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>就是我们想要预测错误定位。在视觉跟踪,之间的抵消IMU-GPS定位系统和应用定位系统是在线培训记录的步骤。训练数据是用来学习样本协方差函数。视觉跟踪失败时,高斯过程预测抵消由GPS和惯性传感器。这抵消所代表的平均误差,用于正确估计三维定位。事实上,高斯过程允许计算<年代vgheight="13.8625" id="M130" style="vertical-align:-2.37006pt;width:47.362499px;" version="1.1" viewbox="0 0 47.362499 13.8625" width="47.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.1139669" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.942286" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.743917" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.620567" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>定位误差的可能性。这似然函数是高斯分布,与均值和方差<年代vgheight="7.1624999" id="M131" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>给出了基于高斯过程的地图。在我们的例子中,均值和方差是用来计算估计的误差椭圆定位。</pgydF4y2Ba> <h4 id="real-time-operating">5。实时操作</gydF4y2Bah4> <p>我们使用有限状态机定位系统运行方案(见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig7/" target="_blank">7</一个>)。有限状态机是一种抽象模型组成的有限数量的状态,这些状态之间的转换,和行动。这张图主要用于可计算性理论和形式语言,并允许运行在实时高精度。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig7"> <div class="floats-partial-content fig-content-fig7"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.007" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.007.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 状态机的三维定位系统的操作。</gydF4y2Batable> </div> </div> </div> <p>提出了状态机由三个州:辅助优势状态,初始化状态和视觉优势的状态。不同状态之间的转换如下:在初始化状态,辅助子系统提供了一个估计的姿势(1),这估计是精制与视觉子系统(2),当视觉跟踪失败,辅助子系统接管估计3 d定位(3)。自从辅助子系统比视觉子系统,不准确的估计是考虑预测误差修正。此后,估计是用来初始化视觉跟踪(4)。</pgydF4y2Ba> <p>我们定义了三个标准来量化的质量估计使用视觉跟踪构成。如果这些标准之一是不验证,构成被拒绝和系统切换到辅助子系统。</pgydF4y2Ba> <h5 id="sec5.1">5.1。数量的跟踪点</gydF4y2Bah5> <p>2 d / 3 d匹配点的数量影响最小化过程用来估计的准确性相机姿势。事实上,我们有一个大的2 d / 3 d匹配点,估计姿势越准确,反之亦然。为此,我们定义了一个最小数量的匹配。低于这个阈值,它被认为是无法估计与视觉子系统构成。</pgydF4y2Ba> <h5 id="sec5.2">5.2。投影误差</gydF4y2Bah5> <p>匹配点的数量不足以确保姿态估计的准确性;还可以使用投影误差准则。这个错误代表的平均平方3 d的投影点之间的区别使用估计姿势和2 d点。如果误差很大,大于一个经验阈值,构成被认为是错误的。</pgydF4y2Ba> <h5 id="sec5.3">5.3。置信区间</gydF4y2Bah5> <p>辅助子系统提供的数据也可以作为一个指标构成的验证。事实上,从给出的位置和姿态辅助子系统,置信区间的定义。他们由一个椭球为中心的取向提供的惯性传感器和一个椭圆的中心是由2 d位置由GPS。轴的椭圆或椭球可以定义3 *<我>σ</我>(标准偏差之间的抵消相机姿势和辅助评估)或经验。如果构成计算视觉子系统包含在这些置信区间(在椭圆中的位置和取向椭球),姿势是正确的。</pgydF4y2Ba> <h4 id="experiments">6。实验</gydF4y2Bah4> <p>取得了几个实验研究提出了定位系统使用时的行为在户外环境中。第一个实验指出半自动的表演在几个条件初始化方法。图<一个href="//www.newsama.com/journals/jr/2012/634758/fig8/" target="_blank">8</一个>表明这种方法执行良好匹配尽管照明的变化。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig8"> <div class="floats-partial-content fig-content-fig8"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”634758。fig.008a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.008a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”634758。fig.008b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.008b.jpg"> <br> <strong>(b)</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig8"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”634758。fig.008a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.008a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”634758。fig.008b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.008b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig8"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 半自动的方法的性能。</gydF4y2Batable> </div> </div> </div> <p>此外,为了分析误差在匹配的过程中,我们估计之间的平均距离2 d分半自动后获得的初始化步骤和精炼后的2 d分从图像中提取相机姿势。我们发现平均误差等于3.8216标准差1.0873像素的像素。这意味着半自动的方法是非常有效的生成粗略估计2 d-3d通讯,真正帮助跟踪系统快速收敛于最优解。</pgydF4y2Ba> <p>我们也分析了执行时间通过仔细评估所需的处理时间实现半自动初始化过程的每一步。这些计算时间的一个例子是在桌子上<一个href="//www.newsama.com/journals/jr/2012/634758/tab1/" target="_blank">1</一个>。</pgydF4y2Ba> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="2"> <hr></td> </tr> <tr class="thead"> <td align="left">步骤</gydF4y2Batd> <td align="center">次</gydF4y2Batd> </tr> <tr> <td class="thead-hr" colspan="2"> <hr></td> </tr> <tr> <td align="left">手动对齐</gydF4y2Batd> <td align="center">未知的</gydF4y2Batd> </tr> <tr> <td align="left">提取和匹配</gydF4y2Batd> <td align="center">50毫秒</gydF4y2Batd> </tr> <tr> <td align="left">RANSAC</gydF4y2Batd> <td align="center">100毫秒</gydF4y2Batd> </tr> <tr> <td align="left">总(没有手动对齐)</gydF4y2Batd> <td align="center">150毫秒</gydF4y2Batd> </tr> <tr class="table-tr"> <td colspan="2"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 半自动的初始化方法计算时间。</gydF4y2Badiv> </div> </div> <p></p> <p>这个表显示,实现半自动初始化匹配所需的计算时间非常快,使得这种方法特别有效的跟踪系统的初始化阶段。</pgydF4y2Ba> <p>此外,我们还测试了我们的自动初始化方法的性能。我们已经考虑几种不同观点下拍摄的图像。图<一个href="//www.newsama.com/journals/jr/2012/634758/fig9/" target="_blank">9</一个>显示了一些结果。我们可以看到,所有的考虑情况下,参考点(采取的临街建筑)在当前帧匹配。在这个例子中,我们已经考虑共面分。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig9"> <div class="floats-partial-content fig-content-fig9"> <div class="partial-carousel--single-image"> <img alt="(一)参考图像”n一个米e=”634758。fig.009a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009a.jpg"> <br> <strong>(一)参考图像</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b) 1日的结果”n一个米e=”634758。fig.009b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009b.jpg"> <br> <strong>(b) 1日的结果</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(c) 2的结果”n一个米e=”634758。fig.009c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009c.jpg"> <br> <strong>(c) 2的结果</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(d) 3日的结果”n一个米e=”634758。fig.009d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009d.jpg"> <br> <strong>(d) 3日的结果</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig9"> <button class="partial-carousel-dot" aria-label="(a) Reference Image"><img alt="(一)参考图像”n一个米e=”634758。fig.009a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009a.jpg"><br><strong>(一)参考图像</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) 1st result"><img alt="(b) 1日的结果”n一个米e=”634758。fig.009b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009b.jpg"><br><strong>(b) 1日的结果</年代trong></button> <button class="partial-carousel-dot" aria-label="(c) 2nd result"><img alt="(c) 2的结果”n一个米e=”634758。fig.009c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009c.jpg"><br><strong>(c) 2的结果</年代trong></button> <button class="partial-carousel-dot" aria-label="(d) 3rd result"><img alt="(d) 3日的结果”n一个米e=”634758。fig.009d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.009d.jpg"><br><strong>(d) 3日的结果</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig9"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图9</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 匹配结果autometed初始化方法,coplanr点。</gydF4y2Batable> </div> </div> </div> <p>我们也测试了我们的方法对非共面点选择在城堡的塔楼(图<一个href="//www.newsama.com/journals/jr/2012/634758/fig10/" target="_blank">10</一个>)。在这种情况下得到的结果是令人满意的。的确,筛分结合RANSAC算法提供了一种准确、可靠的单应性估计,从而允许优点匹配。匹配的过程,在这种情况下给出了平均误差约1.7823像素的标准差为0.6634像素。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig10"> <div class="floats-partial-content fig-content-fig10"> <div class="partial-carousel--single-image"> <img alt="(一)最初的形象”n一个米e=”634758。fig.0010a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010a.jpg"> <br> <strong>(一)最初的形象</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b) 1日的结果”n一个米e=”634758。fig.0010b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010b.jpg"> <br> <strong>(b) 1日的结果</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(c) 2的结果”n一个米e=”634758。fig.0010c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010c.jpg"> <br> <strong>(c) 2的结果</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(d) 3日的结果”n一个米e=”634758。fig.0010d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010d.jpg"> <br> <strong>(d) 3日的结果</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig10"> <button class="partial-carousel-dot" aria-label="(a) Initial Image"><img alt="(一)最初的形象”n一个米e=”634758。fig.0010a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010a.jpg"><br><strong>(一)最初的形象</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) 1st Result"><img alt="(b) 1日的结果”n一个米e=”634758。fig.0010b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010b.jpg"><br><strong>(b) 1日的结果</年代trong></button> <button class="partial-carousel-dot" aria-label="(c) 2nd Result"><img alt="(c) 2的结果”n一个米e=”634758。fig.0010c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010c.jpg"><br><strong>(c) 2的结果</年代trong></button> <button class="partial-carousel-dot" aria-label="(d) 3rd Result"><img alt="(d) 3日的结果”n一个米e=”634758。fig.0010d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0010d.jpg"><br><strong>(d) 3日的结果</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig10"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图10</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 初始化匹配结果autometed approach-Non coplanr点。</gydF4y2Batable> </div> </div> </div> <p>这种方法的计算时间主要取决于筛选特征提取和匹配。引入一个预测阶段,以限制的研究领域的兴趣点在当前帧大大降低了整个算法的总时间(实际上,它除以两个)。比较其他类似的方法(<一个href="#B15">15</一个>),我们提出了自动初始化技术更加灵活,并提供最好的表演真正的倍。</pgydF4y2Ba> <p>在接下来的实验中,我们评估的性能GPS-IMU定位系统。第一个实验认为一条直线是真实数据。面前的这条线定义起源的起源世界参照系。线采样在几个位置,对每一个样品我们做一些收购,即图像和GPS的位置。传感器安装在三脚架上,以确保更稳定(见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig11/" target="_blank">11</一个>)。参考位置与遥测仪的测量精度约为0.15 m。此外,对于每一个获得图像,我们计算摄像机的位置和方向。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig11"> <div class="floats-partial-content fig-content-fig11"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.0011" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0011.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图11</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig11/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 我们的混合传感器安装在三脚架上。</gydF4y2Batable> </div> </div> </div> <p>从GPS数据和转换期间估计校准步骤,我们推导出绝对位置对世界坐标系相关的真实场景。通过比较不同的估计位置参考位置,我们找到一个意味着抵消(1.8374 m;1.4810米)。相同的GPS位置相对于相机的位置给平均误差等于(1.7321 m;1.4702米)和标准差(1.8314米;1.0116米)。图<一个href="//www.newsama.com/journals/jr/2012/634758/fig12/" target="_blank">12</一个>显示了孔轨迹从GPS和相机位置计算获得相对于参考轨迹。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig12"> <div class="floats-partial-content fig-content-fig12"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.0012" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0012.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图12</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig12/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 直线测试:参考位置和摄像机位置和GPS的位置。</gydF4y2Batable> </div> </div> </div> <p>第二个实验关注连续两个固定位置之间的相对位置。平均参考位置之间的偏移量,获得与全球定位系统(GPS)约为0.7817 m标准差等于1.06米。值是由视觉子系统相似,也就是说,一个偏移量平均约0.8743米标准偏差为0.9524 m。因此,这些结果表明,这两个子系统提供的运动是一致的。第三个实验执行几个连续的录音GPS /摄像机的位置。两个传感器是带时间戳以同步和检索的数据获得在同一时间。远景和GPS的位置没有校正相比,获得了0.9235的错误<年代vgheight="7.1624999" id="M132" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>设在(标准差为0.6669米),0.8170<年代vgheight="9.8625002" id="M133" style="vertical-align:-2.29482pt;width:7.875px;" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>设在(标准差为0.6755米)。此外,为了研究误差预测方法76年我们第一次使用一组数据以连续的方式来执行错误的训练来获得。然后,使用高斯过程与过去30数据预测错误。均值偏移之间的预测错误,真正的一个是(<年代vgheight="14.7" id="M134" style="vertical-align:-3.21404pt;width:78.1875px;" version="1.1" viewbox="0 0 78.1875 14.7" width="78.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.93,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.417639" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.920639" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.172138" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>m;<年代vgheight="14.7" id="M135" style="vertical-align:-3.21404pt;width:77.525002px;" version="1.1" viewbox="0 0 77.525002 14.7" width="77.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.24,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.45,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 9</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> 9</gydF4y2Batspan> </text> </g> </g> </svg>)和(<年代vgheight="16.7875" id="M136" style="vertical-align:-4.74141pt;width:77.587502px;" version="1.1" viewbox="0 0 77.587502 16.7875" width="77.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7875)"> <g transform="translate(72,-58.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.71,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.4,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> 7</gydF4y2Batspan> </text> </g> </g> </svg>m;<年代vgheight="16.7875" id="M137" style="vertical-align:-4.74141pt;width:76.9375px;" version="1.1" viewbox="0 0 76.9375 16.7875" width="76.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7875)"> <g transform="translate(72,-58.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.24,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.92,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 9</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> 7</gydF4y2Batspan> </text> </g> </g> </svg>米)(见图<一个href="//www.newsama.com/journals/jr/2012/634758/fig13/" target="_blank">13</一个>)。GPS接收器提供的位置然后使用这个预测误差修正。这允许改善提供的3 d定位辅助子系统。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig13"> <div class="floats-partial-content fig-content-fig13"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.0013" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0013.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图13</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig13/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="7.1624999" id="M138" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg> <table> 预测和估计(定位错误gydF4y2Ba设在)。</gydF4y2Batable> </div> </div> </div> <p>评估惯性传感器的准确性,我们比较了陀螺仪的取向产生视觉计算的姿态估计算法。和几个方向,一段视频在室外环境的表现。两个方向(图具有相同的行为<一个href="//www.newsama.com/journals/jr/2012/634758/fig14/" target="_blank">14</一个>)。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig14"> <div class="floats-partial-content fig-content-fig14"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.0014" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0014.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图14</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig14/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 相机的取向和惯性传感器的方向。</gydF4y2Batable> </div> </div> </div> <p>然而,在某些情况下,我们发现,外部因素会影响惯性测量,尤其是在定义地方参考系<年代vgheight="7.1624999" id="M139" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>设在是当地磁北的方向。这将导致错误的方向估计。为了解决这个问题相关的局部坐标系之间的旋转惯性传感器和世界坐标系是不断重新评估。整个系统的行为也是考验。初始化过程允许有3 d可见的匹配点的三维模型与预测在第一个视图。从这2 d / 3 d匹配的二维点集定义和跟踪帧到帧。对于每一帧,线框模型注册使用的位置和方向从混合定位系统获得。在图<一个href="//www.newsama.com/journals/jr/2012/634758/fig15/" target="_blank">15</一个>,绿色投影得到的位置和方向提供的视觉子系统。线框模型叠加在真实的观点这演示了相机姿态估计的准确性。在红色,得到预测模型提供的位置和方向辅助子系统。图<一个href="//www.newsama.com/journals/jr/2012/634758/fig15/" target="_blank">15</一个>表明,当视觉失败,定位系统切换到辅助子系统提供3 d定位。定位与预测纠正错误,有利于提高估算。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig15"> <div class="floats-partial-content fig-content-fig15"> <div class="partial-carousel--single-image"> <img alt="(一)# 0686”n一个米e=”634758。fig.0015a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015a.jpg"> <br> <strong>(一)# 0686</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b) # 1053”n一个米e=”634758。fig.0015b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015b.jpg"> <br> <strong>(b) # 1053</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(c) # 1054”n一个米e=”634758。fig.0015c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015c.jpg"> <br> <strong>(c) # 1054</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(d) # 1055”n一个米e=”634758。fig.0015d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015d.jpg"> <br> <strong>(d) # 1055</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig15"> <button class="partial-carousel-dot" aria-label="(a) #0686"><img alt="(一)# 0686”n一个米e=”634758。fig.0015a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015a.jpg"><br><strong>(一)# 0686</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) #1053"><img alt="(b) # 1053”n一个米e=”634758。fig.0015b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015b.jpg"><br><strong>(b) # 1053</年代trong></button> <button class="partial-carousel-dot" aria-label="(c) #1054"><img alt="(c) # 1054”n一个米e=”634758。fig.0015c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015c.jpg"><br><strong>(c) # 1054</年代trong></button> <button class="partial-carousel-dot" aria-label="(d) #1055"><img alt="(d) # 1055”n一个米e=”634758。fig.0015d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0015d.jpg"><br><strong>(d) # 1055</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig15"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图15</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig15/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 注册3 d模型的使用姿势获得我们的混合动力系统。</gydF4y2Batable> </div> </div> </div> <p>图<一个href="//www.newsama.com/journals/jr/2012/634758/fig16/" target="_blank">16</一个>表明在遮挡的跟踪点,始终GPS-IMU定位系统提供一个相机的位置和姿态的估计。因此,即使总阻塞发生时,系统可以提供一个粗略的估计3 d定位。不会这样,如果我们只使用相机。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig16"> <div class="floats-partial-content fig-content-fig16"> <div class="partial-carousel--single-image"> <img alt="(一)# 1236”n一个米e=”634758。fig.0016a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016a.jpg"> <br> <strong>(一)# 1236</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b) # 1239”n一个米e=”634758。fig.0016b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016b.jpg"> <br> <strong>(b) # 1239</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(c) # 1245”n一个米e=”634758。fig.0016c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016c.jpg"> <br> <strong>(c) # 1245</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(d) # 1269”n一个米e=”634758。fig.0016d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016d.jpg"> <br> <strong>(d) # 1269</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig16"> <button class="partial-carousel-dot" aria-label="(a) #1236"><img alt="(一)# 1236”n一个米e=”634758。fig.0016a" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016a.jpg"><br><strong>(一)# 1236</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) #1239"><img alt="(b) # 1239”n一个米e=”634758。fig.0016b" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016b.jpg"><br><strong>(b) # 1239</年代trong></button> <button class="partial-carousel-dot" aria-label="(c) #1245"><img alt="(c) # 1245”n一个米e=”634758。fig.0016c" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016c.jpg"><br><strong>(c) # 1245</年代trong></button> <button class="partial-carousel-dot" aria-label="(d) #1269"><img alt="(d) # 1269”n一个米e=”634758。fig.0016d" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0016d.jpg"><br><strong>(d) # 1269</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig16"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图16</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig16/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 注册的3 d模型使用辅助子系统:阻塞情况。</gydF4y2Batable> </div> </div> </div> <p>此外,我们评估我们的三维定位系统的性能在这个城市风光。建筑物的三维模型,它是由定义的120个自然点的三维坐标在世界坐标框架。几个试验在不同的位置被记录下来。数据来自三个传感器包含时间戳,存储在数据文件中。相机姿态估计的视觉跟踪绩效评估作为地面实况。我们定义了一组2 d / 3 d点的对应关系从第一帧序列。兴趣点然后跟踪帧到帧使用KLT特征跟踪算法(<一个href="#B17">17</一个>,<一个href="#B18">18</一个>]。更新2 d / 3 d通讯和用于估计3 d定位。我们已经将我们的方法与使用扩展卡尔曼滤波的数据融合方法。计算结果表明我们的方法的有效性,因为它得到更好的精度。图<一个href="//www.newsama.com/journals/jr/2012/634758/fig17/" target="_blank">17</一个>显示了恢复相机轨迹在世界坐标系统;我们注意轨迹估计定位方法是接近地面真理然后融合估计的数据来自三个传感器。</pgydF4y2Ba> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig17"> <div class="floats-partial-content fig-content-fig17"> <div class="partial-carousel--single-image"> <img alt="" name="634758.fig.0017" src="https://static-01.hindawi.com/articles/jr/volume-2012/634758/figures/634758.fig.0017.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图17</年代p一个n> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jr/2012/634758/fig17/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 世界坐标系统的轨迹。</gydF4y2Batable> </div> </div> </div> <p>最后,表演我们的定位系统比较先进的结果报道DiVerdi和叫喊<一个href="#B22">22</一个>]GroundCam系统也结合了一个摄像头,GPS接收器和一个定位跟踪器。作者运行他们的系统在住宅街区大约90秒和比较估计轨迹hand-labelled地面真理。报告的RMS大约是5.5米。我们运行我们的系统在相似的条件下在我们的制度建设。获得的RMS约1.55米,这表明我们的定位系统产生更好的结果。</pgydF4y2Ba> <h4 id="conclusion">7所示。结论</gydF4y2Bah4> <p>在本文中,我们提出了一个原始三维摄像机定位使用多传感器技术的解决方案。该系统结合了一个摄像头,GPS和惯性传感器;它的目的是在户外工作环境。而不是融合所有数据,该系统是基于一个援助计划。它是由两部分组成的工作以互补的方式,由一个有限状态机控制允许连续三维定位。视觉子系统,代表主要部分,使用积分视觉跟踪。一旦愿景失败,系统切换到辅助子系统组成的GPS /惯性传感器。辅助子系统不太准确的视觉子系统,特别是GPS定位。因此,预测执行阶段提高辅助子系统的准确性。提供的3 d定位两个子系统是用来学习,在线,错误由辅助子系统。 The two subsystems interact continuously to each other. The obtained results are quite satisfactory with respect to the purpose of Mobile Augmented Reality systems. They have shown that the proposed system has quite good accuracy compared to other approaches.</p> <p>系统测试在室外环境中,并展示了其适应能力几个条件发生在这样的环境中。例如,当总阻塞发生的场景模型,辅助系统接管3 d定位估计直到视力开始运行。然而,增加整个系统的健壮性和效率,改善必须在几个部分。实际上,在实现的方法,建立跟踪点必须总是可见的。挑战之一是开发一个跟踪方法可以处理视觉遮挡和更新通过添加自动跟踪的集合点,实时,新的可见点。此外,其他markerless跟踪方法可以结合edge-based等点追踪方法(<一个href="#B23">23</一个>)或基于基准点的方法(<一个href="#B24">24</一个>,<一个href="#B25">25</一个>)提高应用姿态估计的准确性。同时,融合过程可以优化如果我们考虑摄像机的运动动态的IMU传感器。另一方面,实验表明,GPS信号可以阻碍当用户附近的建筑物。因此,当系统切换到辅助子系统,位置无法估计。这个问题可以解决通过添加其他类型的定位传感器,可以取代GPS(射频识别、无线等)。主要的想法是开发一个无处不在的跟踪系统组成的一个网络互补的传感器可以分别征集和实时的情况下发生的环境。</pgydF4y2Ba> </div> <div class="xml-content"> <h4 class="references" id="references">引用</gydF4y2Bah4> <ol> <li id="B1">t . Vieville f . 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Williams&publication_year=1997" target="_blank">谷歌学术搜索</一个></span></li> <li id="B22">DiVerdi和t .叫喊“GroundCam:跟踪移动混合现实形态,”<我>学报IEEE国际会议上虚拟现实(VR ' 07)</我>2007年3月,页75 - 82。<年代p一个nclass="reflinks">视图:<一个href="https://doi.org/10.1109/VR.2007.352466">出版商的网站</一个><span class="sep">|</年代p一个n><a href="https://scholar.google.com/scholar_lookup?title=GroundCam:%20a%20tracking%20modality%20for%20mobile%20mixed%20reality&author=S. DiVerdi &author=T. Höllerer" target="_blank">谷歌学术搜索</一个></span></li> <li id="B23">f . Ababsa和m . Mallem健壮的相机姿势估计结合跟踪,2 d / 3 d点和线”<我>IEEE国际研讨会工业电子学报》(ISIE ' 08)</我>剑桥大学,页774 - 779年,英国,2008年7月。<年代p一个nclass="reflinks">视图:<一个href="https://doi.org/10.1109/ISIE.2008.4676964">出版商的网站</一个><span class="sep">|</年代p一个n><a href="https://scholar.google.com/scholar_lookup?title=Robust%20camera%20pose%20estimation%20combining%202D/3D%20points%20and%20lines%20tracking&author=F. Ababsa &author=M. Mallem" target="_blank">谷歌学术搜索</一个></span></li> <li id="B24">f . Ababsa和m . Mallem”,一个健壮的圆形基准检测技术和实时3 d相机追踪,”<我>多媒体杂志</我>,3卷,不。4、41、2008页。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=A%20robust%20circular%20fiducial%20detection%20technique%20and%20real-time%203D%20camera%20tracking&author=F. Ababsa &author=M. Mallem&publication_year=2008" target="_blank">谷歌学术搜索</一个></span></li> <li id="B25">j.y.迪迪埃·f·Ababsa, m . Mallem”混合相机姿势估计基准点本地化技术和正交迭代算法,结合广场”<我>国际期刊的图像和图形</我>,8卷,不。1,第188 - 169页,2008。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Hybrid%20camera%20pose%20estimation%20combining%20square%20fiducials%20localisation%20technique%20and%20orthogonal%20iteration%20algorithm&author=J. Y. Didier&author=F. Ababsa&author=&author=M. Mallem&publication_year=2008" target="_blank">谷歌学术搜索</一个></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</gydF4y2Bah4> <p>版权©2012 F。Ababsa等。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</pgydF4y2Ba> </div> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 kgAKHb hrTitleRef">更多相关文章</gydF4y2Bah4> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 ghauYU"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-keVrkP cMXuwG article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-elJkPf 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height="24"><span class="text">下载引用</年代p一个n></span><span class="sc-htoDjs bqeMOy sc-kTUwUJ fKwwpq fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-elJkPf ghbfGn sc-exkUMo ikaeWC ref_desktop" href="//www.newsama.com/journals/jr/2012/634758.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-jtRfpW drOnJN" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引用</年代p一个n></span><span class="sc-htoDjs bqeMOy sc-kTUwUJ fKwwpq fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-iYUSvU xdFeU article_bottom_toolbar"> <div class="sc-cHSUfg hlwZCh accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-iNhVCk fhBqDd" title="" role="presentation" 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height="24"><span class="sc-bfYoXt jLRaNL">下载其他格式</年代p一个n><span class="sc-gbOuXE kvCIiS">更多的</年代p一个n></span> <span class="sc-htoDjs bMdQcY sc-eAKXzc bmKKdh icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-cTjmhe fEoWte"> <a class="sc-htpNat bUhGXt link sc-cugefK irOfVO open_panel" href="//www.newsama.com/downloads/journals/jr/2012/634758.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-fnwBNb gUqhXf"> ePub</gydF4y2Badiv><img alt="" class="sc-EHOje jOLhQl sc-iNhVCk fhBqDd" title="" role="presentation" 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height="24"><span class="sc-bfYoXt jLRaNL">订单打印副本</年代p一个n><span class="sc-gbOuXE kvCIiS">订单</年代p一个n></span><span class="sc-htoDjs kNoiZu sc-eAKXzc bmKKdh right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-bFADNz dxRcBT"> <div class="sc-cqpYsc bTgkQB"> <div> 的观点<年代p一个n>1875年</年代p一个n> </div> <div> 下载<年代p一个n>1176年</年代p一个n> </div> </div> <div> <div class="sc-hBbWxd exhBez"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2012/634758" data-style="small_circle"></span>引用</gydF4y2Badiv> </div> </div> <nav class="sc-Rmtcm hZsedb sc-dRFtgE evqjui" id="toolbar__iconNav"> <h3 class="sc-csuQGl idXHYp">分享文章</gydF4y2Bah3> <ul class="sc-bRBYWo keayzM"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2012/634758&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" 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