卡尔曼滤波_matlab_其他_其他下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"><head><meta charset="utf-8"><meta name="generator" content="pdf2htmlEX"><meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/base.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/4852278/raw.css"><script src="https://csdnimg.cn/release/download_crawler_static/js/compatibility.min.js"></script><script src="https://csdnimg.cn/release/download_crawler_static/js/pdf2htmlEX.min.js"></script><script>try{pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({});}catch(e){}</script><title></title></head><body><div id="sidebar" style="display: none"><div id="outline"></div></div><div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/4852278/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">卡尔曼滤波器介绍</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">Greg<span class="_ _0"> </span>W<span class="_ _1"></span>elc<span class="_ _2"></span>h</div><div class="t m0 x3 h4 y3 ff3 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x4 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">and<span class="_ _0"> </span>Gary<span class="_ _0"> </span>Bishop</div><div class="t m0 x5 h4 y3 ff3 fs2 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6 h3 y4 ff2 fs1 fc0 sc0 ls0 ws0">TR<span class="_ _0"> </span>95-041</div><div class="t m0 x7 h3 y5 ff2 fs1 fc0 sc0 ls0 ws0">Departmen<span class="_ _2"></span>t<span class="_ _0"> </span>of<span class="_ _0"> </span>Computer<span class="_ _0"> </span>Science</div><div class="t m0 x8 h3 y6 ff2 fs1 fc0 sc0 ls0 ws0">Univ<span class="_ _2"></span>ersit<span class="_ _2"></span>y<span class="_ _0"> </span>of<span class="_ _0"> </span>North<span class="_ _0"> </span>Carolina<span class="_ _0"> </span>at<span class="_ _0"> </span>Chap<span class="_ _3"></span>el<span class="_ _0"> </span>Hill</div><div class="t m0 x9 h4 y7 ff3 fs2 fc0 sc0 ls0 ws0">3</div><div class="t m0 xa h3 y8 ff2 fs1 fc0 sc0 ls0 ws0">Chap<span class="_ _3"></span>el<span class="_ _0"> </span>Hill,<span class="_ _0"> </span>NC<span class="_ _0"> </span>27599-3175</div><div class="t m0 xb h5 y9 ff1 fs1 fc0 sc0 ls0 ws0">翻译：姚旭晨</div><div class="t m0 xc h5 ya ff1 fs1 fc0 sc0 ls0 ws0">更新日期<span class="ff2">:<span class="_ _4"> </span>2006</span>年<span class="ff2">7</span>月<span class="ff2">24</span>日，星期一</div><div class="t m0 xd h5 yb ff1 fs1 fc0 sc0 ls0 ws0">中文版更新日期：<span class="ff2">2007</span>年<span class="ff2">1</span>月<span class="ff2">8</span>日，星期一</div><div class="t m0 xe h6 yc ff4 fs3 fc0 sc0 ls0 ws0">摘要</div><div class="t m0 xf h7 yd ff5 fs3 fc0 sc0 ls0 ws0">1960<span class="ff1">年，卡尔曼发表了他著名的用递归方法解决离散数据线性滤波</span></div><div class="t m0 x10 h7 ye ff1 fs3 fc0 sc0 ls0 ws0">问题<span class="_ _3"></span>的论<span class="_ _3"></span>文<span class="_ _3"></span>。从<span class="_ _3"></span>那以<span class="_ _3"></span>后，<span class="_ _3"></span>得益<span class="_ _3"></span>于<span class="_ _3"></span>数字<span class="_ _3"></span>计算<span class="_ _3"></span>技术<span class="_ _3"></span>的进<span class="_ _3"></span>步<span class="_ _3"></span>，卡<span class="_ _3"></span>尔曼<span class="_ _3"></span>滤波<span class="_ _3"></span>器</div><div class="t m0 x10 h7 yf ff1 fs3 fc0 sc0 ls0 ws0">已成为推广研究和应用的主题，尤其是在自主或协助导航领域。</div><div class="t m0 xf h7 y10 ff1 fs3 fc0 sc0 ls0 ws0">卡尔曼滤波器由一系列递归数学公式描述。它们提供了一种高效可</div><div class="t m0 x10 h7 y11 ff1 fs3 fc0 sc0 ls0 ws0">计算<span class="_ _3"></span>的方<span class="_ _3"></span>法<span class="_ _3"></span>来估<span class="_ _3"></span>计过<span class="_ _3"></span>程的<span class="_ _3"></span>状态<span class="_ _3"></span>，<span class="_ _3"></span>并使<span class="_ _3"></span>估计<span class="_ _3"></span>均方<span class="_ _3"></span>误差<span class="_ _3"></span>最<span class="_ _3"></span>小。<span class="_ _3"></span>卡尔<span class="_ _3"></span>曼滤<span class="_ _3"></span>波</div><div class="t m0 x10 h7 y12 ff1 fs3 fc0 sc0 ls0 ws0">器应<span class="_ _3"></span>用广<span class="_ _3"></span>泛<span class="_ _3"></span>且功<span class="_ _3"></span>能强<span class="_ _3"></span>大：<span class="_ _3"></span>它可<span class="_ _3"></span>以<span class="_ _3"></span>估计<span class="_ _3"></span>信号<span class="_ _3"></span>的过<span class="_ _3"></span>去和<span class="_ _3"></span>当<span class="_ _3"></span>前状<span class="_ _3"></span>态，<span class="_ _3"></span>甚至<span class="_ _3"></span>能</div><div class="t m0 x10 h7 y13 ff1 fs3 fc0 sc0 ls0 ws0">估计将来的状态，即使并不知道模型的确切性质。</div><div class="t m0 xf h7 y14 ff1 fs3 fc0 sc0 ls0 ws0">这篇文章介绍了离散卡尔曼理论和实用方法，包括卡尔曼滤波器及</div><div class="t m0 x10 h7 y15 ff1 fs3 fc0 sc0 ls0 ws0">其衍<span class="_ _3"></span>生：<span class="_ _3"></span>扩<span class="_ _3"></span>展卡<span class="_ _3"></span>尔曼<span class="_ _3"></span>滤波<span class="_ _3"></span>器的<span class="_ _3"></span>描<span class="_ _3"></span>述和<span class="_ _3"></span>讨论<span class="_ _3"></span>，并<span class="_ _3"></span>给出<span class="_ _3"></span>了<span class="_ _3"></span>一个<span class="_ _3"></span>相对<span class="_ _3"></span>简单<span class="_ _3"></span>的</div><div class="t m0 x10 h7 y16 ff1 fs3 fc0 sc0 ls0 ws0">带图实例。</div><div class="t m0 x11 h8 y17 ff6 fs4 fc1 sc0 ls0 ws0">1</div><div class="t m0 x12 h9 y18 ff7 fs5 fc1 sc0 ls0 ws0">w<span class="_ _2"></span>elch@cs.unc.edu,<span class="_ _5"> </span>h<span class="_ _2"></span>ttp://www.cs.unc.edu/˜welc<span class="_ _2"></span>h</div><div class="t m0 x11 h8 y19 ff6 fs4 fc1 sc0 ls0 ws0">2</div><div class="t m0 x12 h9 y1a ff7 fs5 fc1 sc0 ls0 ws0">gb@cs.unc.edu,<span class="_ _5"> </span>http://www.cs.unc.edu/˜gb</div><div class="t m0 x11 h8 y1b ff6 fs4 fc1 sc0 ls0 ws0">3</div><div class="t m0 x12 ha y1c ff1 fs5 fc1 sc0 ls0 ws0">北卡罗来纳大学教堂山分校，译者注。</div><div class="t m0 x13 hb y1d ff5 fs6 fc1 sc0 ls0 ws0">1</div></div><div class="pi" data-data='{"ctm":[1.611984,0.000000,0.000000,1.611984,0.000000,0.000000]}'></div></div></body></html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/4852278/bg2.jpg"><div class="t m0 x14 hc y1e ff5 fs6 fc1 sc0 ls0 ws0">W<span class="_ _1"></span>elch<span class="_ _6"> </span>&<span class="_ _6"> </span>Bishop,<span class="ff1">卡尔曼滤波器介绍<span class="_ _7"> </span></span>2</div><div class="t m0 x14 hd y1f ff8 fs7 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">离散卡尔曼滤波器</span></div><div class="t m0 x15 hc y20 ff5 fs6 fc0 sc0 ls0 ws0">1960<span class="ff1">年<span class="_ _3"></span>，<span class="_ _3"></span>卡<span class="_ _3"></span>尔<span class="_ _3"></span>曼<span class="_ _3"></span>发<span class="_ _3"></span>表<span class="_ _3"></span>了<span class="_ _3"></span>他<span class="_ _3"></span>著<span class="_ _9"></span>名<span class="_ _3"></span>的<span class="_ _3"></span>用<span class="_ _3"></span>递<span class="_ _3"></span>归<span class="_ _3"></span>方<span class="_ _3"></span>法<span class="_ _3"></span>解<span class="_ _3"></span>决<span class="_ _3"></span>离<span class="_ _9"></span>散<span class="_ _3"></span>数<span class="_ _3"></span>据<span class="_ _3"></span>线<span class="_ _3"></span>性<span class="_ _3"></span>滤<span class="_ _3"></span>波<span class="_ _3"></span>问</span></div><div class="t m0 x14 hc y21 ff1 fs6 fc0 sc0 ls0 ws0">题<span class="_ _3"></span>的<span class="_ _9"></span>论<span class="_ _9"></span>文<span class="_ _0"> </span><span class="ff5">[Kalman60]<span class="_ _6"> </span></span>。<span class="_ _3"></span>从<span class="_ _9"></span>那<span class="_ _3"></span>以<span class="_ _9"></span>后<span class="_ _9"></span>，<span class="_ _9"></span>得<span class="_ _9"></span>益<span class="_ _9"></span>于<span class="_ _9"></span>数<span class="_ _9"></span>字<span class="_ _9"></span>计<span class="_ _9"></span>算<span class="_ _9"></span>技<span class="_ _9"></span>术<span class="_ _3"></span>的<span class="_ _9"></span>进<span class="_ _9"></span>步<span class="_ _9"></span>，</div><div class="t m1 x16 he y21 ff1 fs8 fc0 sc0 ls0 ws0">卡<span class="_ _3"></span>尔<span class="_ _9"></span>曼</div><div class="t m1 x14 he y22 ff1 fs8 fc0 sc0 ls0 ws0">滤<span class="_ _9"></span>波<span class="_ _9"></span>器</div><div class="t m0 x17 hc y22 ff1 fs6 fc0 sc0 ls0 ws0">已<span class="_ _9"></span>成<span class="_ _9"></span>为<span class="_ _a"></span>推<span class="_ _9"></span>广<span class="_ _9"></span>研<span class="_ _a"></span>究<span class="_ _9"></span>和<span class="_ _9"></span>应<span class="_ _a"></span>用<span class="_ _9"></span>的<span class="_ _9"></span>主<span class="_ _a"></span>题<span class="_ _9"></span>，<span class="_ _9"></span>尤<span class="_ _a"></span>其<span class="_ _9"></span>是<span class="_ _9"></span>在<span class="_ _a"></span>自<span class="_ _9"></span>主<span class="_ _9"></span>或<span class="_ _a"></span>协<span class="_ _9"></span>助<span class="_ _9"></span>导<span class="_ _a"></span>航<span class="_ _9"></span>领<span class="_ _9"></span>域<span class="_ _a"></span>。</div><div class="t m0 x14 hc y23 ff5 fs6 fc0 sc0 ls0 ws0">[Ma<span class="_ _2"></span>yb<span class="_ _3"></span>ec<span class="_ _2"></span>k79]<span class="_ _5"> </span><span class="ff1">的第一章给<span class="_ _3"></span>出了一个非<span class="_ _3"></span>常“友好”<span class="_ _3"></span>的介绍，更<span class="_ _3"></span>全面的讨论<span class="_ _3"></span>可以</span></div><div class="t m0 x14 hc y24 ff1 fs6 fc0 sc0 ls0 ws0">参<span class="_ _3"></span>考<span class="_ _6"> </span><span class="ff5">[Sorenson70]<span class="_ _5"> </span></span>，<span class="_ _3"></span>后<span class="_ _9"></span>者<span class="_ _3"></span>还<span class="_ _3"></span>包<span class="_ _3"></span>含<span class="_ _3"></span>了<span class="_ _9"></span>一<span class="_ _3"></span>些<span class="_ _3"></span>非<span class="_ _3"></span>常<span class="_ _3"></span>有<span class="_ _3"></span>趣<span class="_ _9"></span>的<span class="_ _3"></span>历<span class="_ _3"></span>史<span class="_ _3"></span>故<span class="_ _3"></span>事<span class="_ _9"></span>。<span class="_ _3"></span>更<span class="_ _3"></span>广<span class="_ _3"></span>泛<span class="_ _3"></span>的<span class="_ _9"></span>参</div><div class="t m0 x14 hc y25 ff1 fs6 fc0 sc0 ls0 ws0">考包括<span class="_ _5"> </span><span class="ff5">[Gelb74,<span class="_ _6"> </span>Grewal93,<span class="_ _6"> </span>Ma<span class="_ _2"></span>yb<span class="_ _3"></span>ec<span class="_ _2"></span>k79,<span class="_ _0"> </span>Lewis86,<span class="_ _6"> </span>Bro<span class="_ _2"></span>wn92,<span class="_ _0"> </span>Jacobs93]<span class="_ _b"> </span><span class="ff1">。</span></span></div><div class="t m0 x14 hf y26 ff4 fs1 fc0 sc0 ls0 ws0">被估计的过程信号</div><div class="t m0 x15 hc y27 ff1 fs6 fc0 sc0 ls0 ws0">卡尔曼<span class="_ _3"></span>滤波器<span class="_ _3"></span>用于估<span class="_ _3"></span>计离散<span class="_ _3"></span>时间过<span class="_ _3"></span>程的状<span class="_ _3"></span>态变量<span class="_ _6"> </span><span class="ff9">x<span class="_ _c"> </span><span class="ffa">∈<span class="_ _c"> </span><</span></span></div><div class="t m0 x18 h10 y28 ffb fs2 fc0 sc0 ls0 ws0">n</div><div class="t m0 x19 hc y27 ff1 fs6 fc0 sc0 ls0 ws0">。这个<span class="_ _3"></span>离散时</div><div class="t m0 x14 hc y29 ff1 fs6 fc0 sc0 ls0 ws0">间过程由以下离散随机差分方程描述：</div><div class="t m0 x1a h11 y2a ff9 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x1b h10 y2b ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1c hb y2a ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">Ax</span></div><div class="t m0 x1d h4 y2b ffb fs2 fc0 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x4 hb y2a ff5 fs6 fc0 sc0 ls0 ws0">+<span class="_ _b"> </span><span class="ff9">B<span class="_ _3"></span>u</span></div><div class="t m0 x1e h4 y2b ffb fs2 fc0 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x1f hb y2a ff5 fs6 fc0 sc0 ls0 ws0">+<span class="_ _b"> </span><span class="ff9">w</span></div><div class="t m0 x20 h4 y2b ffb fs2 fc0 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x21 hb y2a ff9 fs6 fc0 sc0 ls0 ws0">,<span class="_ _d"> </span><span class="ff5">(1.1)</span></div><div class="t m0 x15 hc y2c ff1 fs6 fc0 sc0 ls0 ws0">定义观测变量<span class="_ _5"> </span><span class="ff9">z<span class="_ _c"> </span><span class="ffa">∈<span class="_ _c"> </span><</span></span></div><div class="t m0 x22 h10 y2d ffb fs2 fc0 sc0 ls0 ws0">m</div><div class="t m0 x23 hc y2c ff1 fs6 fc0 sc0 ls0 ws0">，得到量测方程：</div><div class="t m0 xb h11 y2e ff9 fs6 fc0 sc0 ls0 ws0">z</div><div class="t m0 x24 h10 y2f ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x25 hb y2e ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">H<span class="_ _a"></span>x</span></div><div class="t m0 x26 h10 y2f ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x27 hb y2e ff5 fs6 fc0 sc0 ls0 ws0">+<span class="_ _b"> </span><span class="ff9">v</span></div><div class="t m0 x28 h10 y2f ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x29 hb y2e ff9 fs6 fc0 sc0 ls0 ws0">.<span class="_ _e"> </span><span class="ff5">(1.2)</span></div><div class="t m0 x15 hc y30 ff1 fs6 fc0 sc0 ls0 ws0">随机信<span class="_ _3"></span>号<span class="_ _5"> </span><span class="ff9">w</span></div><div class="t m0 x2a h10 y31 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x2b hc y30 ff1 fs6 fc0 sc0 ls0 ws0">和<span class="_ _5"> </span><span class="ff9">v</span></div><div class="t m0 x2 h10 y31 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x2c hc y30 ff1 fs6 fc0 sc0 ls0 ws0">分别表<span class="_ _3"></span>示过程<span class="_ _3"></span>激励噪<span class="_ _3"></span>声</div><div class="t m0 x2d h4 y32 ff3 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x2e hc y30 ff1 fs6 fc0 sc0 ls0 ws0">和观测<span class="_ _3"></span>噪声。<span class="_ _3"></span>假设它<span class="_ _3"></span>们为相</div><div class="t m0 x14 hc y33 ff1 fs6 fc0 sc0 ls0 ws0">互独立，正态分布的白色噪声：</div><div class="t m0 x2f hb y34 ff9 fs6 fc0 sc0 ls0 ws0">p<span class="ff5">(</span>w<span class="_ _3"></span><span class="ff5">)<span class="_ _5"> </span><span class="ffa">∼<span class="_ _c"> </span></span></span>N<span class="_ _f"></span><span class="ff5">(0</span>,<span class="_ _10"> </span>Q<span class="ff5">)</span>,<span class="_ _11"> </span><span class="ff5">(1.3)</span></div><div class="t m0 x30 hb y35 ff9 fs6 fc0 sc0 ls0 ws0">p<span class="ff5">(</span>v<span class="_ _3"></span><span class="ff5">)<span class="_ _5"> </span><span class="ffa">∼<span class="_ _c"> </span></span></span>N<span class="_ _f"> </span><span class="ff5">(0</span>,<span class="_ _10"> </span>R<span class="ff5">)</span>.<span class="_ _12"> </span><span class="ff5">(1.4)</span></div><div class="t m0 x15 hc y36 ff1 fs6 fc0 sc0 ls0 ws0">实际系<span class="_ _3"></span>统中，</div><div class="t m1 x31 he y36 ff1 fs8 fc0 sc0 ls0 ws0">过程激<span class="_ _3"></span>励噪声<span class="_ _3"></span>协方差<span class="_ _3"></span>矩阵</div><div class="t m0 x1f hc y36 ff9 fs6 fc0 sc0 ls0 ws0">Q<span class="_ _5"> </span><span class="ff1">和</span></div><div class="t m1 x32 he y36 ff1 fs8 fc0 sc0 ls0 ws0">观测噪<span class="_ _3"></span>声协方<span class="_ _3"></span>差矩阵</div><div class="t m0 x33 hc y36 ff9 fs6 fc0 sc0 ls0 ws0">R<span class="_ _5"> </span><span class="ff1">可</span></div><div class="t m0 x14 hc y37 ff1 fs6 fc0 sc0 ls0 ws0">能会随每次迭代计算而变化。但在这儿我们假设它们是常数。</div><div class="t m0 x15 hc y38 ff1 fs6 fc0 sc0 ls0 ws0">当控制函数<span class="ff9">u</span></div><div class="t m0 x34 h4 y39 ffb fs2 fc0 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x35 hc y38 ff1 fs6 fc0 sc0 ls0 ws0">或过程激励噪声<span class="_ _b"> </span><span class="ff9">w</span></div><div class="t m0 x36 h4 y39 ffb fs2 fc0 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x37 hc y38 ff1 fs6 fc0 sc0 ls0 ws0">为零时，差分方程<span class="ff5">1.1</span>中的<span class="_ _b"> </span><span class="ff9">n<span class="_ _b"> </span><span class="ffa">×<span class="_ _b"> </span></span>n</span></div><div class="t m0 x14 hc y3a ff1 fs6 fc0 sc0 ls0 ws0">阶增益矩阵<span class="_ _b"> </span><span class="ff9">A<span class="_ _b"> </span></span>将上一时刻<span class="_ _b"> </span><span class="ff9">k<span class="_ _b"> </span><span class="ffa">−<span class="_ _10"> </span><span class="ff5">1<span class="_ _b"> </span></span></span></span>的状态线性映射到当前时刻<span class="_ _b"> </span><span class="ff9">k<span class="_ _5"> </span></span>的状态。实际</div><div class="t m0 x14 hc y3b ff1 fs6 fc0 sc0 ls0 ws0">中<span class="_ _b"> </span><span class="ff9">A<span class="_ _5"> </span></span>可能随时间变化，但在这儿假设为常数。<span class="ff9">n<span class="_ _13"> </span><span class="ffa">×<span class="_ _13"> </span></span>l<span class="_ _5"> </span></span>阶矩阵<span class="_ _b"> </span><span class="ff9">B<span class="_ _6"> </span></span>代表可选的控</div><div class="t m0 x14 hc y3c ff1 fs6 fc0 sc0 ls0 ws0">制输<span class="_ _3"></span>入<span class="_ _5"> </span><span class="ff9">u<span class="_ _c"> </span><span class="ffa">∈<span class="_ _6"> </span><</span></span></div><div class="t m0 x38 h10 y3d ffb fs2 fc0 sc0 ls0 ws0">l</div><div class="t m0 x39 hc y3c ff1 fs6 fc0 sc0 ls0 ws0">的增益<span class="_ _3"></span>。量<span class="_ _3"></span>测方程<span class="ff5">1.2</span>中<span class="_ _3"></span>的<span class="_ _5"> </span><span class="ff9">m<span class="_ _b"> </span><span class="ffa">×<span class="_ _b"> </span></span>n<span class="_ _5"> </span></span>阶<span class="_ _3"></span>矩阵<span class="_ _5"> </span><span class="ff9">H<span class="_ _0"> </span></span>表示<span class="_ _3"></span>状态变<span class="_ _3"></span>量<span class="_ _5"> </span><span class="ff9">x</span></div><div class="t m0 x3a h10 y3e ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x14 hc y3f ff1 fs6 fc0 sc0 ls0 ws0">对测量变量<span class="_ _5"> </span><span class="ff9">z</span></div><div class="t m0 x3b h10 y40 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x39 hc y3f ff1 fs6 fc0 sc0 ls0 ws0">的增益。实际中<span class="_ _b"> </span><span class="ff9">H<span class="_ _0"> </span></span>可能随时间变化，但在这儿假设为常数。</div><div class="t m0 x14 hf y41 ff4 fs1 fc0 sc0 ls0 ws0">滤波器的计算原型</div><div class="t m0 x15 hc y42 ff1 fs6 fc0 sc0 ls0 ws0">定义<span class="_ _6"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x3c h12 y43 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x3c h10 y44 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x3b hb y42 ffa fs6 fc0 sc0 ls0 ws0">∈<span class="_ _5"> </span><</div><div class="t m0 x3d h10 y45 ffb fs2 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc hc y42 ff1 fs6 fc0 sc0 ls0 ws0">（</div><div class="t m0 x3e h12 y45 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x3f hc y42 ff1 fs6 fc0 sc0 ls0 ws0">代表先验，<span class="ff5">ˆ</span>代表估计）为在已知第<span class="_ _b"> </span><span class="ff9">k<span class="_ _c"> </span></span>步以前状态情</div><div class="t m0 x14 hc y46 ff1 fs6 fc0 sc0 ls0 ws0">况下第<span class="_ _5"> </span><span class="ff9">k<span class="_ _c"> </span></span>步<span class="_ _3"></span>的</div><div class="t m1 x8 he y46 ff1 fs8 fc0 sc0 ls0 ws0">先验</div><div class="t m0 xc hc y46 ff1 fs6 fc0 sc0 ls0 ws0">状态估<span class="_ _3"></span>计。定<span class="_ _3"></span>义<span class="_ _6"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x40 h10 y47 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x26 hb y46 ffa fs6 fc0 sc0 ls0 ws0">∈<span class="_ _c"> </span><</div><div class="t m0 x41 h10 y48 ffb fs2 fc0 sc0 ls0 ws0">n</div><div class="t m0 x42 hc y46 ff1 fs6 fc0 sc0 ls0 ws0">为已知<span class="_ _3"></span>测量变<span class="_ _3"></span>量<span class="_ _5"> </span><span class="ff9">z</span></div><div class="t m0 x43 h10 y47 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x44 hc y46 ff1 fs6 fc0 sc0 ls0 ws0">时第<span class="_ _5"> </span><span class="ff9">k<span class="_ _c"> </span></span>步的</div><div class="t m1 x14 he y49 ff1 fs8 fc0 sc0 ls0 ws0">后验</div><div class="t m0 x15 hc y49 ff1 fs6 fc0 sc0 ls0 ws0">状态估计。由此定义</div><div class="t m1 x45 he y49 ff1 fs8 fc0 sc0 ls0 ws0">先验</div><div class="t m0 x30 hc y49 ff1 fs6 fc0 sc0 ls0 ws0">估计误差和</div><div class="t m1 x46 he y49 ff1 fs8 fc0 sc0 ls0 ws0">后验</div><div class="t m0 x47 hc y49 ff1 fs6 fc0 sc0 ls0 ws0">估计误差：</div><div class="t m0 x48 h11 y4a ff9 fs6 fc0 sc0 ls0 ws0">e</div><div class="t m0 x49 h12 y4b ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x49 h10 y4c ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4a hb y4a ffa fs6 fc0 sc0 ls0 ws0">≡<span class="_ _5"> </span><span class="ff9">x</span></div><div class="t m0 x4b h10 y4d ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4c hb y4a ffa fs6 fc0 sc0 ls0 ws0">−<span class="_ _5"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x4d h12 y4b ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x4d h10 y4c ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x42 h11 y4a ff9 fs6 fc0 sc0 ls0 ws0">,</div><div class="t m0 x1d h11 y4e ff9 fs6 fc0 sc0 ls0 ws0">e</div><div class="t m0 x4e h10 y4f ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4f hb y4e ffa fs6 fc0 sc0 ls0 ws0">≡<span class="_ _5"> </span><span class="ff9">x</span></div><div class="t m0 x50 h10 y4f ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x51 hb y4e ffa fs6 fc0 sc0 ls0 ws0">−<span class="_ _5"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x52 h10 y4f ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x11 h8 y50 ff6 fs4 fc1 sc0 ls0 ws0">1</div><div class="t m0 x12 ha y51 ff1 fs5 fc1 sc0 ls0 ws0">原文为<span class="_ _13"> </span><span class="ff7">pro<span class="_ _3"></span>cess<span class="_ _c"> </span>noise</span>，本该翻译作过程<span class="_ _3"></span>噪声，由时间序列信号模型的观点，平稳<span class="_ _3"></span>随机序</div><div class="t m0 x14 ha y52 ff1 fs5 fc1 sc0 ls0 ws0">列可以看成是由典型噪声源激励线性系统产生，故译作过程激励噪声。</div><div class="t m0 x1d hb y1d ff5 fs6 fc1 sc0 ls0 ws0">UNC-Chap<span class="_ _3"></span>el<span class="_ _6"> </span>Hill,<span class="_ _0"> </span>TR<span class="_ _6"> </span>95-041,<span class="_ _0"> </span>July<span class="_ _6"> </span>24,<span class="_ _0"> </span>2006</div></div><div class="pi" data-data='{"ctm":[1.611984,0.000000,0.000000,1.611984,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/4852278/bg3.jpg"><div class="t m0 x14 hc y1e ff5 fs6 fc1 sc0 ls0 ws0">W<span class="_ _1"></span>elch<span class="_ _6"> </span>&<span class="_ _6"> </span>Bishop,<span class="ff1">卡尔曼滤波器介绍<span class="_ _7"> </span></span>3</div><div class="t m1 x14 he y53 ff1 fs8 fc0 sc0 ls0 ws0">先验</div><div class="t m0 x15 hc y53 ff1 fs6 fc0 sc0 ls0 ws0">估计误差的协方差为：</div><div class="t m0 x53 h11 y54 ff9 fs6 fc0 sc0 ls0 ws0">P</div><div class="t m0 x24 h12 y55 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x54 h10 y56 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x55 hb y54 ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">E<span class="_ _9"></span></span>[<span class="ff9">e</span></div><div class="t m0 x51 h12 y55 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x51 h10 y56 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1e h11 y54 ff9 fs6 fc0 sc0 ls0 ws0">e</div><div class="t m0 x56 h12 y55 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x56 h10 y56 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x57 h10 y57 ffb fs2 fc0 sc0 ls0 ws0">T</div><div class="t m0 x29 hb y54 ff5 fs6 fc0 sc0 ls0 ws0">]<span class="ff9">,<span class="_ _15"> </span></span>(1.5)</div><div class="t m1 x14 he y58 ff1 fs8 fc0 sc0 ls0 ws0">后验</div><div class="t m0 x15 hc y58 ff1 fs6 fc0 sc0 ls0 ws0">估计误差的协方差为：</div><div class="t m0 xb h11 y59 ff9 fs6 fc0 sc0 ls0 ws0">P</div><div class="t m0 x49 h10 y5a ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x55 hb y59 ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">E<span class="_ _9"></span></span>[<span class="ff9">e</span></div><div class="t m0 x51 h10 y5a ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x58 h11 y59 ff9 fs6 fc0 sc0 ls0 ws0">e</div><div class="t m0 x59 h10 y5a ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x5a h10 y5b ffb fs2 fc0 sc0 ls0 ws0">T</div><div class="t m0 x5b hb y59 ff5 fs6 fc0 sc0 ls0 ws0">]<span class="ff9">,<span class="_ _16"> </span></span>(1.6)</div><div class="t m0 x15 hc y5c ff1 fs6 fc0 sc0 ls0 ws0">式<span class="ff5">1.7</span>构<span class="_ _3"></span>造<span class="_ _3"></span>了<span class="_ _3"></span>卡<span class="_ _3"></span>尔<span class="_ _3"></span>曼<span class="_ _3"></span>滤<span class="_ _3"></span>波<span class="_ _9"></span>器<span class="_ _3"></span>的<span class="_ _3"></span>表<span class="_ _3"></span>达<span class="_ _3"></span>式<span class="_ _3"></span>：</div><div class="t m1 x52 he y5c ff1 fs8 fc0 sc0 ls0 ws0">先<span class="_ _3"></span>验</div><div class="t m0 x2e hc y5c ff1 fs6 fc0 sc0 ls0 ws0">估<span class="_ _3"></span>计<span class="_ _0"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x5c h12 y5d ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x5c h10 y5e ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x5d hc y5c ff1 fs6 fc0 sc0 ls0 ws0">和<span class="_ _3"></span>加<span class="_ _3"></span>权<span class="_ _3"></span>的<span class="_ _3"></span>测<span class="_ _3"></span>量<span class="_ _3"></span>变<span class="_ _9"></span>量</div><div class="t m0 x14 h11 y5f ff9 fs6 fc0 sc0 ls0 ws0">z</div><div class="t m0 x5e h10 y60 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x5f hc y5f ff1 fs6 fc0 sc0 ls0 ws0">及其<span class="_ _3"></span>预<span class="_ _3"></span>测<span class="_ _5"> </span><span class="ff9">H<span class="_ _10"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></span></div><div class="t m0 x60 h12 y61 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x60 h10 y62 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x61 hc y5f ff1 fs6 fc0 sc0 ls0 ws0">之差<span class="_ _3"></span>的<span class="_ _3"></span>线性<span class="_ _3"></span>组合<span class="_ _3"></span>构<span class="_ _3"></span>成了</div><div class="t m1 x62 he y5f ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">后</span><span class="fc2 sc0">验</span></div><div class="t m0 x63 hc y5f ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">状</span><span class="fc2 sc0">态</span><span class="_ _3"></span><span class="fc2 sc0">估</span><span class="_ _3"></span><span class="fc2 sc0">计</span><span class="_ _6"> </span><span class="ff5"><span class="fc2 sc0">ˆ</span><span class="_ _14"></span><span class="ff9"><span class="fc2 sc0">x</span></span></span></div><div class="t m0 x64 h10 y60 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 x65 hc y5f ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">。</span>式<span class="ff5">1.7</span>的<span class="_ _3"></span>理<span class="_ _3"></span>论解</div><div class="t m0 x14 hc y63 ff1 fs6 fc0 sc0 ls0 ws0">释请参看“滤波器的概率原型”一节。</div><div class="t m0 x66 hb y64 ff5 fs6 fc0 sc0 ls0 ws0">ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 x67 h10 y65 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x68 hb y64 ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _0"> </span>ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 x6 h12 y66 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x6 h10 y67 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4f hb y64 ff5 fs6 fc0 sc0 ls0 ws0">+<span class="_ _13"> </span><span class="ff9">K<span class="_ _a"></span></span>(<span class="ff9">z</span></div><div class="t m0 x58 h10 y65 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x69 hb y64 ffa fs6 fc0 sc0 ls0 ws0">−<span class="_ _13"> </span><span class="ff9">H<span class="_ _10"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></span></div><div class="t m0 x2e h12 y66 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x2e h10 y67 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x32 hb y64 ff5 fs6 fc0 sc0 ls0 ws0">)<span class="_ _17"> </span>(1.7)</div><div class="t m0 x15 hc y68 ff1 fs6 fc0 sc0 ls0 ws0">式<span class="ff5">1.7</span>中测量变量及其预测之差<span class="_ _5"> </span><span class="ff5">(<span class="ff9">z</span></span></div><div class="t m0 x4b h10 y69 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4c hb y68 ffa fs6 fc0 sc0 ls0 ws0">−<span class="_ _b"> </span><span class="ff9">H<span class="_ _18"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></span></div><div class="t m0 x6a h12 y6a ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x6a h10 y6b ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x6b hc y68 ff5 fs6 fc0 sc0 ls0 ws0">)<span class="_ _5"> </span><span class="ff1">被称为测量过程的</span></div><div class="t m1 x6c he y6c ff1 fs8 fc0 sc0 ls0 ws0">革新</div><div class="t m0 x33 hc y6c ff1 fs6 fc0 sc0 ls0 ws0">或</div><div class="t m1 x6d he y6c ff1 fs8 fc0 sc0 ls0 ws0">残</div><div class="t m1 x14 he y6d ff1 fs8 fc0 sc0 ls0 ws0">余</div><div class="t m0 x6e hc y6d ff1 fs6 fc0 sc0 ls0 ws0">。<span class="_ _3"></span>残<span class="_ _3"></span>余<span class="_ _3"></span>反<span class="_ _3"></span>映<span class="fc2 sc0">了</span><span class="_ _3"></span><span class="fc2 sc0">预</span><span class="_ _3"></span><span class="fc2 sc0">测</span><span class="_ _3"></span><span class="fc2 sc0">值</span><span class="_ _3"></span><span class="fc2 sc0">和</span><span class="_ _3"></span><span class="fc2 sc0">实</span><span class="_ _3"></span><span class="fc2 sc0">际</span><span class="_ _3"></span><span class="fc2 sc0">值</span><span class="_ _3"></span><span class="fc2 sc0">之</span><span class="_ _3"></span><span class="fc2 sc0">间</span><span class="_ _3"></span><span class="fc2 sc0">的</span><span class="_ _3"></span><span class="fc2 sc0">不</span><span class="_ _3"></span><span class="fc2 sc0">一</span><span class="_ _3"></span><span class="fc2 sc0">致</span><span class="_ _3"></span><span class="fc2 sc0">程</span><span class="_ _3"></span><span class="fc2 sc0">度</span><span class="_ _3"></span>。<span class="_ _3"></span>残余<span class="_ _3"></span>为<span class="_ _3"></span>零<span class="_ _3"></span>表<span class="_ _3"></span>明<span class="_ _3"></span>二<span class="_ _3"></span>者<span class="_ _3"></span>完</div><div class="t m0 x14 hc y6e ff1 fs6 fc0 sc0 ls0 ws0">全吻合。</div><div class="t m0 x15 hc y6f ff1 fs6 fc0 sc0 ls0 ws0">式<span class="ff5">1.7</span>中<span class="_ _5"> </span><span class="ff9">n<span class="_ _5"> </span><span class="ffa">×<span class="_ _5"> </span></span>m<span class="_ _5"> </span></span>阶<span class="_ _3"></span>矩<span class="_ _3"></span><span class="fc2 sc0">阵</span><span class="_ _c"> </span><span class="ff9"><span class="fc2 sc0">K</span><span class="_ _0"> </span></span><span class="fc2 sc0">叫</span><span class="_ _3"></span><span class="fc2 sc0">做</span><span class="_ _3"></span><span class="fc2 sc0">残</span><span class="_ _3"></span><span class="fc2 sc0">余</span><span class="_ _3"></span><span class="fc2 sc0">的</span></div><div class="t m1 x56 he y6f ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">增</span><span class="_ _3"></span><span class="fc2 sc0">益</span></div><div class="t m0 x2d hc y6f ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">或</span></div><div class="t m1 x6f he y6f ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">混</span><span class="_ _3"></span><span class="fc2 sc0">合</span><span class="_ _3"></span><span class="fc2 sc0">因</span><span class="_ _3"></span><span class="fc2 sc0">数</span></div><div class="t m0 x65 hc y6f ff1 fs6 fc0 sc0 ls0 ws0">，<span class="_ _3"></span>作<span class="_ _3"></span>用是<span class="_ _3"></span>使<span class="ff5">1.6</span>式</div><div class="t m0 x14 hc y70 ff1 fs6 fc0 sc0 ls0 ws0">中<span class="_ _3"></span>的</div><div class="t m1 x70 he y70 ff1 fs8 fc0 sc0 ls0 ws0">后<span class="_ _3"></span>验</div><div class="t m0 x71 hc y70 ff1 fs6 fc0 sc0 ls0 ws0">估<span class="_ _3"></span>计<span class="_ _3"></span>误<span class="_ _9"></span>差<span class="_ _3"></span>协<span class="_ _9"></span>方<span class="_ _3"></span>差<span class="_ _9"></span>最<span class="_ _3"></span>小<span class="_ _9"></span>。<span class="_ _3"></span>可<span class="_ _9"></span>以<span class="_ _3"></span>通<span class="_ _9"></span>过<span class="_ _3"></span>以<span class="_ _9"></span>下<span class="_ _3"></span>步<span class="_ _9"></span>骤<span class="_ _3"></span>计<span class="_ _9"></span>算<span class="_ _6"> </span><span class="ff9">K<span class="_ _0"> </span></span>：<span class="_ _9"></span>首<span class="_ _3"></span>先<span class="_ _9"></span>将<span class="ff5">1.7</span>式</div><div class="t m0 x14 hc y71 ff1 fs6 fc0 sc0 ls0 ws0">代<span class="_ _3"></span>入<span class="_ _c"> </span><span class="ff9">e</span></div><div class="t m0 x72 h10 y72 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x73 hc y71 ff1 fs6 fc0 sc0 ls0 ws0">的<span class="_ _3"></span>定<span class="_ _3"></span>义<span class="_ _3"></span>式<span class="_ _3"></span>，<span class="_ _3"></span>再<span class="_ _3"></span>将<span class="_ _c"> </span><span class="ff9">e</span></div><div class="t m0 x74 h10 y72 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x75 hc y71 ff1 fs6 fc0 sc0 ls0 ws0">代<span class="_ _3"></span>入<span class="ff5">1.6</span>式<span class="_ _3"></span>中<span class="_ _3"></span>，<span class="_ _3"></span>求<span class="_ _3"></span>得<span class="_ _3"></span>期<span class="_ _3"></span>望<span class="_ _3"></span>后<span class="_ _3"></span>，<span class="_ _3"></span>将<span class="ff5">1.6</span>式<span class="_ _3"></span>中<span class="_ _9"></span>的<span class="_ _c"> </span><span class="ff9">P</span></div><div class="t m0 x76 h10 y72 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x6d hc y71 ff1 fs6 fc0 sc0 ls0 ws0">对</div><div class="t m0 x14 hc y73 ff9 fs6 fc0 sc0 ls0 ws0">K<span class="_ _0"> </span><span class="ff1">求导<span class="_ _3"></span>。<span class="_ _3"></span>并使<span class="_ _3"></span>一<span class="_ _3"></span>阶导<span class="_ _3"></span>数<span class="_ _3"></span>为<span class="_ _3"></span>零从<span class="_ _3"></span>而<span class="_ _3"></span>解得<span class="_ _c"> </span></span>K<span class="_ _0"> </span><span class="ff1">值<span class="_ _3"></span>。<span class="_ _3"></span>详细<span class="_ _3"></span>推<span class="_ _3"></span>导清<span class="_ _3"></span>参<span class="_ _3"></span>照<span class="_ _c"> </span><span class="ff5">[Ma<span class="_ _2"></span>yb<span class="_ _3"></span>ec<span class="_ _2"></span>k79,</span></span></div><div class="t m0 x14 hc y74 ff5 fs6 fc0 sc0 ls0 ws0">Bro<span class="_ _2"></span>wn92,<span class="_ _0"> </span>Jacobs93]<span class="_ _b"> </span><span class="ff1">。<span class="_ _5"> </span><span class="ff9">K<span class="_ _c"> </span></span>的一种表示形式为：</span></div><div class="t m0 x77 h11 y75 ff9 fs6 fc0 sc0 ls0 ws0">K</div><div class="t m0 x22 h10 y76 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x78 hb y75 ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">P</span></div><div class="t m0 x79 h12 y77 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 xb h10 y78 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x7a h11 y75 ff9 fs6 fc0 sc0 ls0 ws0">H</div><div class="t m0 x7b h10 y79 ffb fs2 fc0 sc0 ls0 ws0">T</div><div class="t m0 x7c hb y75 ff5 fs6 fc0 sc0 ls0 ws0">(<span class="ff9">H<span class="_ _a"></span>P</span></div><div class="t m0 x27 h12 y77 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x7d h10 y78 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x59 h11 y75 ff9 fs6 fc0 sc0 ls0 ws0">H</div><div class="t m0 x28 h10 y79 ffb fs2 fc0 sc0 ls0 ws0">T</div><div class="t m0 x63 hb y75 ff5 fs6 fc0 sc0 ls0 ws0">+<span class="_ _13"> </span><span class="ff9">R<span class="_ _3"></span></span>)</div><div class="t m0 x7e h4 y79 ffc fs2 fc0 sc0 ls0 ws0">−<span class="ff3">1</span></div><div class="t m0 x78 hb y7a ff5 fs6 fc0 sc0 ls0 ws0">=</div><div class="t m0 x7f h11 y7b ff9 fs6 fc0 sc0 ls0 ws0">P</div><div class="t m0 x7b h12 y7c ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x80 h10 y7d ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x7c h11 y7b ff9 fs6 fc0 sc0 ls0 ws0">H</div><div class="t m0 x4b h10 y7e ffb fs2 fc0 sc0 ls0 ws0">T</div><div class="t m0 x81 h11 y7f ff9 fs6 fc0 sc0 ls0 ws0">H<span class="_ _a"></span>P</div><div class="t m0 x25 h12 y80 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x4e h10 y81 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4f h11 y7f ff9 fs6 fc0 sc0 ls0 ws0">H</div><div class="t m0 x82 h10 y82 ffb fs2 fc0 sc0 ls0 ws0">T</div><div class="t m0 x83 hb y7f ff5 fs6 fc0 sc0 ls0 ws0">+<span class="_ _13"> </span><span class="ff9">R</span></div><div class="t m0 x41 hb y7a ff9 fs6 fc0 sc0 ls0 ws0">.<span class="_ _19"> </span><span class="ff5">(1.8)</span></div><div class="t m0 x15 hc y83 ff1 fs6 fc0 sc0 ls0 ws0">由<span class="ff5">1.8</span>式可知，观测噪声协方差<span class="_ _b"> </span><span class="ff9">R<span class="_ _b"> </span></span>越小，残余的增益越大<span class="_ _b"> </span><span class="ff9">K<span class="_ _c"> </span></span>越大。特别</div><div class="t m0 x14 hc y84 ff1 fs6 fc0 sc0 ls0 ws0">地，<span class="_ _b"> </span><span class="ff9">R<span class="_ _5"> </span></span>趋向于零时，有：</div><div class="t m0 x79 hb y85 ff5 fs6 fc0 sc0 ls0 ws0">lim</div><div class="t m0 x53 h10 y86 ffb fs2 fc0 sc0 ls0 ws0">R</div><div class="t m0 x54 h13 y87 ffd fs4 fc0 sc0 ls0 ws0">k</div><div class="t m0 x49 h4 y86 ffc fs2 fc0 sc0 ls0 ws0">→<span class="ff3">0</span></div><div class="t m0 x84 h11 y85 ff9 fs6 fc0 sc0 ls0 ws0">K</div><div class="t m0 x40 h10 y88 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x85 hb y85 ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">H</span></div><div class="t m0 x52 h4 y89 ffc fs2 fc0 sc0 ls0 ws0">−<span class="ff3">1</span></div><div class="t m0 x86 h11 y85 ff9 fs6 fc0 sc0 ls0 ws0">.</div><div class="t m0 x15 hc y8a ff1 fs6 fc0 sc0 ls0 ws0">另一<span class="_ _3"></span>方<span class="_ _3"></span>面，</div><div class="t m1 x87 he y8a ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">先</span><span class="fc2 sc0">验</span></div><div class="t m0 x88 hc y8a ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">估</span><span class="fc2 sc0">计</span><span class="_ _3"></span><span class="fc2 sc0">误</span><span class="_ _3"></span><span class="fc2 sc0">差</span><span class="fc2 sc0">协</span><span class="_ _3"></span><span class="fc2 sc0">方</span><span class="fc2 sc0">差</span><span class="_ _c"> </span><span class="ff9"><span class="fc2 sc0">P</span></span></div><div class="t m0 x36 h12 y8b ffc fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">−</span></div><div class="t m0 x51 h10 y8c ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 x56 hc y8a ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">越</span><span class="fc2 sc0">小</span><span class="_ _3"></span>，<span class="_ _3"></span>残余<span class="_ _3"></span>的增<span class="_ _3"></span>益<span class="_ _5"> </span><span class="ff9">K<span class="_ _0"> </span></span>越小<span class="_ _3"></span>。<span class="_ _3"></span>特别</div><div class="t m0 x14 hc y8d ff1 fs6 fc0 sc0 ls0 ws0">地，<span class="_ _b"> </span><span class="ff9">P</span></div><div class="t m0 x89 h12 y8e ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x8a h10 y8f ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x8b hc y8d ff1 fs6 fc0 sc0 ls0 ws0">趋向于零时，有：</div><div class="t m0 x7a hb y90 ff5 fs6 fc0 sc0 ls0 ws0">lim</div><div class="t m0 x54 h10 y91 ffb fs2 fc0 sc0 ls0 ws0">P</div><div class="t m0 x7f h14 y92 ffe fs4 fc0 sc0 ls0 ws0">−</div><div class="t m0 x6 h13 y93 ffd fs4 fc0 sc0 ls0 ws0">k</div><div class="t m0 x80 h4 y91 ffc fs2 fc0 sc0 ls0 ws0">→<span class="ff3">0</span></div><div class="t m0 x40 h11 y90 ff9 fs6 fc0 sc0 ls0 ws0">K</div><div class="t m0 x26 h10 y94 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x27 hb y90 ff5 fs6 fc0 sc0 ls0 ws0">=<span class="_ _5"> </span>0<span class="ff9">.</span></div><div class="t m0 x15 hc y95 ff1 fs6 fc0 sc0 ls0 ws0">增<span class="_ _3"></span>益<span class="_ _c"> </span><span class="ff9">K<span class="_ _0"> </span></span>的<span class="_ _3"></span>另<span class="_ _9"></span>一<span class="_ _3"></span>种<span class="_ _3"></span>解<span class="_ _3"></span>释<span class="_ _3"></span>是<span class="_ _9"></span>随<span class="_ _3"></span>着<span class="_ _3"></span>测<span class="_ _3"></span>量<span class="_ _3"></span>噪<span class="_ _9"></span>声<span class="_ _3"></span>协<span class="_ _3"></span>方<span class="_ _3"></span>差<span class="_ _6"> </span><span class="ff9">R<span class="_ _c"> </span></span>趋<span class="_ _3"></span>于<span class="_ _3"></span>零<span class="_ _9"></span>，<span class="_ _3"></span>测<span class="_ _3"></span>量<span class="_ _3"></span>变<span class="_ _3"></span>量<span class="_ _6"> </span><span class="ff9">z</span></div><div class="t m0 x3a h10 y96 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x14 hc y97 ff1 fs6 fc0 sc0 ls0 ws0">的<span class="_ _3"></span>权重<span class="_ _3"></span>越<span class="_ _3"></span>来<span class="_ _3"></span>越<span class="_ _3"></span>大<span class="_ _3"></span>，<span class="_ _3"></span>而<span class="_ _c"> </span><span class="ff9">z</span></div><div class="t m0 x1a h10 y98 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x22 hc y97 ff1 fs6 fc0 sc0 ls0 ws0">的<span class="_ _3"></span>预测<span class="_ _c"> </span><span class="ff9">H<span class="_ _18"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></span></div><div class="t m0 xe h12 y99 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 xe h10 y9a ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x50 hc y97 ff1 fs6 fc0 sc0 ls0 ws0">的<span class="_ _3"></span>权重<span class="_ _3"></span>越<span class="_ _3"></span>来<span class="_ _3"></span>越<span class="_ _3"></span>小<span class="_ _3"></span>。<span class="_ _3"></span>另<span class="_ _3"></span>一<span class="_ _3"></span>方面<span class="_ _3"></span>，<span class="_ _3"></span>随<span class="_ _3"></span>着</div><div class="t m1 x6d he y97 ff1 fs8 fc0 sc0 ls0 ws0">先</div><div class="t m1 x14 he y9b ff1 fs8 fc0 sc0 ls0 ws0">验</div><div class="t m0 x6e hc y9b ff1 fs6 fc0 sc0 ls0 ws0">估计误差协方差<span class="_ _5"> </span><span class="ff9">P</span></div><div class="t m0 x8c h12 y9c ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x8d h10 y9d ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1a hc y9b ff1 fs6 fc0 sc0 ls0 ws0">趋于零，测量变量<span class="_ _5"> </span><span class="ff9">z</span></div><div class="t m0 x8e h10 y9e ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1f hc y9b ff1 fs6 fc0 sc0 ls0 ws0">的权重越来越小，而<span class="_ _5"> </span><span class="ff9">z</span></div><div class="t m0 x8f h10 y9e ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x90 hc y9b ff1 fs6 fc0 sc0 ls0 ws0">的预测</div><div class="t m0 x14 hb y9f ff9 fs6 fc0 sc0 ls0 ws0">H<span class="_ _18"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x12 h12 ya0 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x12 h10 ya1 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x91 hc y9f ff1 fs6 fc0 sc0 ls0 ws0">的权重越来越大。</div><div class="t m0 x1d hb ya2 ff5 fs6 fc1 sc0 ls0 ws0">UNC-Chap<span class="_ _3"></span>el<span class="_ _6"> </span>Hill,<span class="_ _0"> </span>TR<span class="_ _6"> </span>95-041,<span class="_ _0"> </span>July<span class="_ _6"> </span>24,<span class="_ _0"> </span>2006</div></div><div class="pi" data-data='{"ctm":[1.611984,0.000000,0.000000,1.611984,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/4852278/bg4.jpg"><div class="t m0 x14 hc y1e ff5 fs6 fc1 sc0 ls0 ws0">W<span class="_ _1"></span>elch<span class="_ _6"> </span>&<span class="_ _6"> </span>Bishop,<span class="ff1">卡尔曼滤波器介绍<span class="_ _7"> </span></span>4</div><div class="t m0 x14 hf ya3 ff4 fs1 fc0 sc0 ls0 ws0">滤波器的概率原型解释</div><div class="t m0 x15 hc ya4 ff5 fs6 fc0 sc0 ls0 ws0">1.7<span class="ff1">式的解释来源于贝叶斯规则：<span class="_ _0"> </span></span>ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 x92 h10 ya5 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x62 hc ya4 ff1 fs6 fc0 sc0 ls0 ws0">的更新取决于在已知先前的<span class="_ _3"></span>测量变</div><div class="t m0 x14 hc ya6 ff1 fs6 fc0 sc0 ls0 ws0">量<span class="_ _5"> </span><span class="ff9">z</span></div><div class="t m0 x93 h10 ya7 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x10 hc ya6 ff1 fs6 fc0 sc0 ls0 ws0">的情况下<span class="_ _5"> </span><span class="ff9">x</span></div><div class="t m0 x94 h10 ya7 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x31 hc ya6 ff1 fs6 fc0 sc0 ls0 ws0">的先验估计<span class="_ _0"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x7a h12 ya8 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 x7a h10 ya9 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4a hc ya6 ff1 fs6 fc0 sc0 ls0 ws0">的概率分布<span class="_ _3"></span>。卡尔曼滤波<span class="_ _3"></span>器表达式中包<span class="_ _3"></span>含</div><div class="t m0 x14 hc yaa ff1 fs6 fc0 sc0 ls0 ws0">了状态分布的前二阶矩。</div><div class="t m0 x7f hb yab ff9 fs6 fc0 sc0 ls0 ws0">E<span class="_ _9"></span><span class="ff5">[</span>x</div><div class="t m0 x95 h10 yac ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x13 hb yab ff5 fs6 fc0 sc0 ls0 ws0">]<span class="_ _5"> </span>=<span class="_ _0"> </span>ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 x69 h10 yac ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1a hb yad ff9 fs6 fc0 sc0 ls0 ws0">E<span class="_ _9"></span><span class="ff5">[(</span>x</div><div class="t m0 x96 h10 yae ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x97 hb yad ffa fs6 fc0 sc0 ls0 ws0">−<span class="_ _5"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x25 h10 yae ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4a hb yad ff5 fs6 fc0 sc0 ls0 ws0">)(<span class="ff9">x</span></div><div class="t m0 x13 h10 yae ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x26 hb yad ffa fs6 fc0 sc0 ls0 ws0">−<span class="_ _5"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></div><div class="t m0 x98 h10 yae ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x57 hb yad ff5 fs6 fc0 sc0 ls0 ws0">)</div><div class="t m0 x42 h10 yaf ffb fs2 fc0 sc0 ls0 ws0">T</div><div class="t m0 x63 hb yad ff5 fs6 fc0 sc0 ls0 ws0">]<span class="_ _5"> </span>=<span class="_ _c"> </span><span class="ff9">P</span></div><div class="t m0 x99 h10 yae ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x21 h11 yad ff9 fs6 fc0 sc0 ls0 ws0">.</div><div class="t m1 x15 he yb0 ff1 fs8 fc0 sc0 ls0 ws0">后<span class="_ _9"></span>验</div><div class="t m0 x71 hc yb0 ff1 fs6 fc0 sc0 ls0 ws0">状<span class="_ _9"></span>态<span class="_ _9"></span>估<span class="_ _a"></span>计<span class="ff5">1.7</span>式<span class="_ _9"></span>反<span class="_ _9"></span>应<span class="_ _9"></span>了<span class="_ _a"></span>状<span class="_ _9"></span>态<span class="_ _9"></span>分<span class="_ _a"></span>布<span class="_ _9"></span>的<span class="_ _9"></span>均<span class="_ _a"></span>值<span class="_ _9"></span>（<span class="_ _9"></span>一<span class="_ _9"></span>阶<span class="_ _a"></span>矩<span class="_ _9"></span>）<span class="_ _9"></span>—<span class="_ _a"></span>—<span class="_ _9"></span>如<span class="_ _9"></span>果<span class="_ _a"></span>条<span class="_ _9"></span>件</div><div class="t m0 x14 hc yb1 ff1 fs6 fc0 sc0 ls0 ws0">式<span class="ff5">1.3</span>和<span class="ff5">1.4</span>成立，均值的估计便是正态分布的。</div><div class="t m1 x9a he yb1 ff1 fs8 fc0 sc0 ls0 ws0">后验</div><div class="t m0 x21 hc yb1 ff1 fs6 fc0 sc0 ls0 ws0">估计误差协方差<span class="ff5">1.6</span>式反</div><div class="t m0 x14 hc yb2 ff1 fs6 fc0 sc0 ls0 ws0">映了状态分布<span class="_ _3"></span>的方差（二阶非中<span class="_ _3"></span>心矩）。在已知<span class="_ _c"> </span><span class="ff9">z</span></div><div class="t m0 x9b h10 yb3 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x9c hc yb2 ff1 fs6 fc0 sc0 ls0 ws0">的情况下，<span class="_ _5"> </span><span class="ff9">x</span></div><div class="t m0 x9d h10 yb3 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x6c hc yb2 ff1 fs6 fc0 sc0 ls0 ws0">的分布可</div><div class="t m0 x14 hc yb4 ff1 fs6 fc0 sc0 ls0 ws0">写为：</div><div class="t m0 x9e hb yb5 ff9 fs6 fc0 sc0 ls0 ws0">p<span class="ff5">(</span>x</div><div class="t m0 xc h10 yb6 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x7 hb yb5 ffa fs6 fc0 sc0 ls0 ws0">|<span class="ff9"><span class="fc2 sc0">z</span></span></div><div class="t m0 x9f h10 yb6 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 x77 hb yb5 ff5 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">)</span><span class="_ _5"> </span><span class="ffa"><span class="fc2 sc0">∼</span><span class="_ _c"> </span><span class="ff9"><span class="fc2 sc0">N</span><span class="_ _f"></span></span></span><span class="fc2 sc0">(</span><span class="ff9"><span class="fc2 sc0">E</span><span class="_ _9"></span></span><span class="fc2 sc0">[</span><span class="ff9"><span class="fc2 sc0">x</span></span></div><div class="t m0 x55 h10 yb6 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 x3 hb yb5 ff5 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">]</span><span class="ff9"><span class="fc2 sc0">,</span><span class="_ _10"> </span><span class="fc2 sc0">E</span><span class="_ _9"></span></span><span class="fc2 sc0">[(</span><span class="ff9"><span class="fc2 sc0">x</span></span></div><div class="t m0 x1e h10 yb6 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 x98 hb yb5 ffa fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">−</span><span class="_ _5"> </span><span class="ff5"><span class="fc2 sc0">ˆ</span><span class="_ _14"></span><span class="ff9"><span class="fc2 sc0">x</span></span></span></div><div class="t m0 x47 h10 yb6 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 xa0 hb yb5 ff5 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">)(</span><span class="ff9"><span class="fc2 sc0">x</span></span></div><div class="t m0 x9b h10 yb6 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 xa1 hb yb5 ffa fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">−</span><span class="_ _5"> </span><span class="ff5"><span class="fc2 sc0">ˆ</span><span class="_ _14"></span><span class="ff9"><span class="fc2 sc0">x</span></span></span></div><div class="t m0 xa2 h10 yb6 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 xa3 hb yb5 ff5 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">)</span></div><div class="t m0 xa4 h10 yb7 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">T</span></div><div class="t m0 x65 hb yb5 ff5 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">])</span></div><div class="t m0 xa5 hb yb8 ff5 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">=</span><span class="_ _5"> </span><span class="ff9"><span class="fc2 sc0">N</span><span class="_ _f"> </span></span><span class="fc2 sc0">(</span><span class="_ _a"></span><span class="fc2 sc0">ˆ</span><span class="_ _14"></span><span class="ff9"><span class="fc2 sc0">x</span></span></div><div class="t m0 x54 h10 yb9 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 x7a h11 yb8 ff9 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">,</span><span class="_ _10"> </span><span class="fc2 sc0">P</span></div><div class="t m0 x3 h10 yb9 ffb fs2 fc0 sc0 ls0 ws0"><span class="fc2 sc0">k</span></div><div class="t m0 x7c hb yb8 ff5 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">)</span><span class="ff9"><span class="fc2 sc0">.</span></span></div><div class="t m0 x15 hc yba ff1 fs6 fc0 sc0 ls0 ws0">有<span class="_ _f"> </span>关<span class="_ _18"> </span>卡<span class="_ _f"></span>尔<span class="_ _18"> </span>曼<span class="_ _f"></span>滤<span class="_ _f"> </span>波<span class="_ _18"> </span>器<span class="_ _f"> </span>的<span class="_ _18"> </span>概<span class="_ _f"></span>率<span class="_ _18"> </span>原<span class="_ _f"></span>型<span class="_ _f"> </span>的<span class="_ _18"> </span>更<span class="_ _f"> </span>多<span class="_ _18"> </span>讨<span class="_ _f"></span>论<span class="_ _18"> </span>，<span class="_ _f"></span>请<span class="_ _f"> </span>参<span class="_ _18"> </span>考<span class="_ _1a"> </span><span class="ff5">[Ma<span class="_ _2"></span>yb<span class="_ _3"></span>ec<span class="_ _2"></span>k79,</span></div><div class="t m0 x14 hc ybb ff5 fs6 fc0 sc0 ls0 ws0">Bro<span class="_ _2"></span>wn92,<span class="_ _0"> </span>Jacobs93]<span class="ff1">。</span></div><div class="t m0 x14 hf ybc ff4 fs1 fc0 sc0 ls0 ws0">离散卡尔曼滤波器算法</div><div class="t m0 x15 hc ybd ff1 fs6 fc0 sc0 ls0 ws0">我<span class="_ _3"></span>们<span class="_ _3"></span>先<span class="_ _3"></span>给<span class="_ _3"></span>出<span class="_ _3"></span>卡<span class="_ _3"></span>尔<span class="_ _3"></span>曼<span class="_ _3"></span>滤<span class="_ _3"></span>波<span class="_ _3"></span>器<span class="_ _3"></span>的<span class="_ _3"></span>总<span class="_ _3"></span>体<span class="_ _3"></span>性<span class="_ _3"></span>概<span class="_ _3"></span>述<span class="_ _3"></span>，<span class="_ _3"></span>然<span class="_ _3"></span>后<span class="_ _3"></span>讨<span class="_ _3"></span>论<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>式<span class="_ _3"></span>的<span class="_ _3"></span>具<span class="_ _3"></span>体<span class="_ _3"></span>细<span class="_ _3"></span>节</div><div class="t m0 x14 hc ybe ff1 fs6 fc0 sc0 ls0 ws0">及其作用。</div><div class="t m0 x15 hc ybf ff1 fs6 fc0 sc0 ls0 ws0">卡<span class="_ _3"></span>尔<span class="_ _3"></span>曼<span class="_ _3"></span>滤<span class="_ _3"></span>波<span class="_ _3"></span>器<span class="_ _3"></span>用<span class="_ _3"></span>反<span class="_ _3"></span>馈<span class="_ _3"></span>控<span class="_ _3"></span>制<span class="_ _3"></span>的<span class="_ _3"></span>方<span class="_ _3"></span>法<span class="_ _3"></span>估<span class="_ _3"></span>计<span class="_ _3"></span>过<span class="_ _3"></span>程<span class="_ _3"></span>状<span class="_ _3"></span>态<span class="_ _3"></span>：<span class="_ _3"></span>滤<span class="_ _3"></span>波<span class="_ _3"></span>器<span class="_ _3"></span>估<span class="_ _3"></span>计<span class="_ _3"></span>过<span class="_ _3"></span>程<span class="_ _3"></span>某<span class="_ _3"></span>一</div><div class="t m0 x14 hc yc0 ff1 fs6 fc0 sc0 ls0 ws0">时<span class="_ _3"></span>刻<span class="_ _3"></span>的<span class="_ _3"></span>状<span class="_ _3"></span>态，<span class="_ _3"></span>然<span class="_ _3"></span>后<span class="_ _3"></span>以<span class="_ _3"></span>（<span class="_ _3"></span>含<span class="_ _3"></span>噪<span class="_ _3"></span>声<span class="_ _3"></span>的<span class="_ _3"></span>）<span class="_ _3"></span>测<span class="_ _3"></span>量<span class="_ _3"></span>变<span class="_ _3"></span>量<span class="_ _3"></span>的<span class="_ _3"></span>方<span class="_ _3"></span>式<span class="_ _3"></span>获得<span class="_ _3"></span>反<span class="_ _3"></span>馈<span class="_ _3"></span>。<span class="_ _3"></span>因<span class="_ _3"></span>此<span class="_ _3"></span>卡<span class="_ _3"></span>尔<span class="_ _3"></span>曼</div><div class="t m0 x14 hc yc1 ff1 fs6 fc0 sc0 ls0 ws0">滤<span class="_ _3"></span>波<span class="_ _3"></span>器<span class="_ _3"></span>可<span class="_ _3"></span>分为<span class="_ _3"></span>两<span class="_ _3"></span>个<span class="_ _3"></span>部<span class="_ _3"></span>分<span class="_ _3"></span>：</div><div class="t m1 x1c he yc2 ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">时</span><span class="_ _3"></span><span class="fc2 sc0">间</span><span class="_ _3"></span><span class="fc2 sc0">更</span><span class="_ _3"></span><span class="fc2 sc0">新</span></div><div class="t m0 x7c hc yc2 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">方</span><span class="_ _3"></span><span class="fc2 sc0">程</span><span class="_ _3"></span><span class="fc2 sc0">和</span></div><div class="t m1 x41 he yc2 ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">测</span><span class="_ _3"></span><span class="fc2 sc0">量</span><span class="_ _3"></span><span class="fc2 sc0">更</span><span class="_ _3"></span><span class="fc2 sc0">新</span></div><div class="t m0 x21 hc yc2 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">方</span><span class="_ _3"></span><span class="fc2 sc0">程</span><span class="_ _3"></span>。<span class="_ _3"></span>时<span class="_ _3"></span>间更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>负</div><div class="t m0 x14 hc yc3 ff1 fs6 fc0 sc0 ls0 ws0">责<span class="_ _3"></span>及<span class="_ _3"></span>时<span class="_ _3"></span>向<span class="_ _3"></span>前推<span class="_ _3"></span><span class="fc2 sc0">算</span><span class="_ _3"></span><span class="fc2 sc0">当</span><span class="_ _3"></span><span class="fc2 sc0">前</span><span class="_ _3"></span><span class="fc2 sc0">状</span><span class="_ _3"></span><span class="fc2 sc0">态</span><span class="_ _3"></span><span class="fc2 sc0">变</span><span class="_ _3"></span><span class="fc2 sc0">量</span><span class="_ _3"></span><span class="fc2 sc0">和</span><span class="_ _3"></span><span class="fc2 sc0">误</span><span class="_ _3"></span><span class="fc2 sc0">差</span><span class="_ _3"></span><span class="fc2 sc0">协</span><span class="_ _3"></span><span class="fc2 sc0">方</span><span class="_ _3"></span><span class="fc2 sc0">差</span><span class="_ _3"></span><span class="fc2 sc0">估</span><span class="_ _3"></span><span class="fc2 sc0">计</span><span class="_ _3"></span><span class="fc2 sc0">的</span><span class="_ _3"></span>值，<span class="_ _3"></span>以<span class="_ _3"></span>便<span class="_ _3"></span>为<span class="_ _3"></span>下<span class="_ _3"></span>一<span class="_ _3"></span>个<span class="_ _3"></span>时<span class="_ _3"></span>间</div><div class="t m0 x14 hc yc4 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">状</span><span class="_ _3"></span><span class="fc2 sc0">态</span><span class="_ _3"></span><span class="fc2 sc0">构</span><span class="_ _3"></span><span class="fc2 sc0">造</span></div><div class="t m1 x71 he yc4 ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">先</span><span class="_ _3"></span><span class="fc2 sc0">验</span></div><div class="t m0 x8 hc yc4 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">估</span><span class="_ _3"></span><span class="fc2 sc0">计</span><span class="_ _3"></span>。<span class="_ _3"></span>测<span class="_ _3"></span>量更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>负<span class="_ _3"></span>责<span class="_ _3"></span>反<span class="_ _3"></span>馈<span class="_ _3"></span>—<span class="_ _3"></span>—<span class="_ _3"></span>也<span class="_ _3"></span>就<span class="_ _3"></span>是<span class="_ _3"></span>说<span class="_ _3"></span>，<span class="_ _3"></span><span class="fc2 sc0">它</span><span class="_ _3"></span><span class="fc2 sc0">将</span></div><div class="t m1 xa6 he yc4 ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">先</span><span class="_ _3"></span><span class="fc2 sc0">验</span></div><div class="t m0 x33 hc yc4 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">估</span><span class="_ _3"></span><span class="fc2 sc0">计</span></div><div class="t m0 x14 hc yc5 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">和新的测量变量结合以构造改进的</span></div><div class="t m1 x3 he yc5 ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">后验</span></div><div class="t m0 x4c hc yc5 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">估计</span>。</div><div class="t m0 x15 hc yc6 ff1 fs6 fc0 sc0 ls0 ws0">时<span class="_ _3"></span>间<span class="_ _3"></span>更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>也<span class="_ _3"></span>可<span class="_ _3"></span>视<span class="_ _3"></span>为</div><div class="t m1 x75 he yc6 ff1 fs8 fc0 sc0 ls0 ws0">预<span class="_ _3"></span>估</div><div class="t m0 x25 hc yc6 ff1 fs6 fc0 sc0 ls0 ws0">方<span class="_ _3"></span>程<span class="_ _3"></span>，<span class="_ _3"></span>测<span class="_ _3"></span>量<span class="_ _3"></span>更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>可<span class="_ _3"></span>视<span class="_ _3"></span>为</div><div class="t m1 x9 he yc6 ff1 fs8 fc0 sc0 ls0 ws0">校<span class="_ _3"></span>正</div><div class="t m0 xa6 hc yc6 ff1 fs6 fc0 sc0 ls0 ws0">方<span class="_ _3"></span>程<span class="_ _3"></span>。<span class="_ _3"></span>最</div><div class="t m0 x14 hc yc7 ff1 fs6 fc0 sc0 ls0 ws0">后的估计算法成为一种具<span class="fc2 sc0">有数值解的</span></div><div class="t m1 x40 he yc7 ff1 fs8 fc0 sc0 ls0 ws0"><span class="fc2 sc0">预估－校正</span></div><div class="t m0 xa7 hc yc7 ff1 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">算法</span>，如图<span class="ff5">1-1</span>所示。</div><div class="t m0 x1d hb ya2 ff5 fs6 fc1 sc0 ls0 ws0">UNC-Chap<span class="_ _3"></span>el<span class="_ _6"> </span>Hill,<span class="_ _0"> </span>TR<span class="_ _6"> </span>95-041,<span class="_ _0"> </span>July<span class="_ _6"> </span>24,<span class="_ _0"> </span>2006</div></div><div class="pi" data-data='{"ctm":[1.611984,0.000000,0.000000,1.611984,0.000000,0.000000]}'></div></div>

<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/4852278/bg5.jpg"><div class="t m0 x14 hc y1e ff5 fs6 fc1 sc0 ls0 ws0">W<span class="_ _1"></span>elch<span class="_ _6"> </span>&<span class="_ _6"> </span>Bishop,<span class="ff1">卡尔曼滤波器介绍<span class="_ _7"> </span></span>5</div><div class="t m0 x14 hc yc8 ff1 fs6 fc1 sc0 ls0 ws0">图<span class="_ _0"> </span><span class="ff5">1-1:<span class="_ _4"> </span></span>离<span class="_ _3"></span>散卡<span class="_ _3"></span>尔曼<span class="_ _3"></span>滤波<span class="_ _3"></span>器循<span class="_ _3"></span>环更<span class="_ _3"></span>新图。</div><div class="t m1 x58 he yc8 ff1 fs8 fc1 sc0 ls0 ws0">时间<span class="_ _3"></span>更新</div><div class="t m0 xa8 hc yc8 ff1 fs6 fc1 sc0 ls0 ws0">方程<span class="_ _3"></span>将当<span class="_ _3"></span>前状<span class="_ _3"></span>态变<span class="_ _3"></span>量作为</div><div class="t m0 x14 hc yc9 ff1 fs6 fc1 sc0 ls0 ws0">先<span class="_ _3"></span>验<span class="_ _3"></span>估<span class="_ _3"></span>计及<span class="_ _3"></span>时<span class="_ _3"></span>地<span class="_ _3"></span>向<span class="_ _3"></span>前<span class="_ _3"></span>投<span class="_ _3"></span>射<span class="_ _3"></span>到<span class="_ _3"></span>测<span class="_ _3"></span>量<span class="_ _3"></span>更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>，</div><div class="t m1 x29 he yc9 ff1 fs8 fc1 sc0 ls0 ws0">测<span class="_ _3"></span>量<span class="_ _3"></span>更<span class="_ _3"></span>新</div><div class="t m0 x5c hc yc9 ff1 fs6 fc1 sc0 ls0 ws0">方<span class="_ _3"></span>程<span class="_ _3"></span>校<span class="_ _3"></span>正<span class="_ _3"></span>先验<span class="_ _3"></span>估<span class="_ _3"></span>计<span class="_ _3"></span>以</div><div class="t m0 x14 hc yca ff1 fs6 fc1 sc0 ls0 ws0">获得状态的后验估计。</div><div class="t m0 x15 hc ycb ff1 fs6 fc0 sc0 ls0 ws0">表<span class="ff5">1-1</span>和表<span class="ff5">1-2</span>分别给出了时间更新方程和测量更新方程的具体形式。</div><div class="t m0 x2b hc ycc ff1 fs6 fc1 sc0 ls0 ws0">表<span class="_ _6"> </span><span class="ff5">1-1:<span class="_ _4"> </span></span>离散卡尔曼滤波器时间更新方程</div><div class="t m0 x68 hb ycd ff5 fs6 fc1 sc0 ls0 ws0">ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 x53 h12 yce ffc fs2 fc1 sc0 ls0 ws0">−</div><div class="t m0 x53 h10 ycf ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x49 hb ycd ff5 fs6 fc1 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">A<span class="_ _a"></span></span>ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 x13 h4 yd0 ffb fs2 fc1 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x62 hb ycd ff5 fs6 fc1 sc0 ls0 ws0">+<span class="_ _13"> </span><span class="ff9">B<span class="_ _9"></span>u</span></div><div class="t m0 x6b h4 yd0 ffb fs2 fc1 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x9d hb ycd ff5 fs6 fc1 sc0 ls0 ws0">(1.9)</div><div class="t m0 xa9 h11 yd1 ff9 fs6 fc1 sc0 ls0 ws0">P</div><div class="t m0 x79 h12 yd2 ffc fs2 fc1 sc0 ls0 ws0">−</div><div class="t m0 xb h10 yd3 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 xaa hb yd1 ff5 fs6 fc1 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">AP</span></div><div class="t m0 x83 h4 yd4 ffb fs2 fc1 sc0 ls0 ws0">k<span class="ffc">−<span class="ff3">1</span></span></div><div class="t m0 x59 h11 yd1 ff9 fs6 fc1 sc0 ls0 ws0">A</div><div class="t m0 x57 h10 yd5 ffb fs2 fc1 sc0 ls0 ws0">T</div><div class="t m0 xab hb yd1 ff5 fs6 fc1 sc0 ls0 ws0">+<span class="_ _13"> </span><span class="ff9">Q<span class="_ _1b"> </span></span>(1.10)</div><div class="t m0 x15 hc yd6 ff1 fs6 fc0 sc0 ls0 ws0">请<span class="_ _3"></span>再<span class="_ _3"></span>次<span class="_ _3"></span>注<span class="_ _3"></span>意<span class="_ _3"></span>表<span class="ff5">1-1</span>中<span class="_ _3"></span>的<span class="_ _3"></span>时<span class="_ _3"></span>间<span class="_ _3"></span>更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>怎<span class="_ _3"></span>样<span class="_ _3"></span>将<span class="_ _3"></span>状<span class="_ _9"></span>态<span class="_ _3"></span>估<span class="_ _3"></span>计<span class="_ _c"> </span><span class="ff9">x</span></div><div class="t m0 xac h12 yd7 ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 xac h10 yd8 ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x9 hc yd6 ff1 fs6 fc0 sc0 ls0 ws0">和<span class="_ _3"></span>协<span class="_ _3"></span>方<span class="_ _3"></span>差<span class="_ _3"></span>估<span class="_ _3"></span>计</div><div class="t m0 x14 h11 yd9 ff9 fs6 fc0 sc0 ls0 ws0">P</div><div class="t m0 xad h12 yda ffc fs2 fc0 sc0 ls0 ws0">−</div><div class="t m0 xad h10 ydb ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x93 hc yd9 ff1 fs6 fc0 sc0 ls0 ws0">从<span class="_ _b"> </span><span class="ff9">k<span class="_ _5"> </span><span class="ffa">−<span class="_ _13"> </span><span class="ff5">1<span class="_ _5"> </span></span></span></span>时刻向前推算到<span class="_ _5"> </span><span class="ff9">k<span class="_ _5"> </span></span>时刻。<span class="_ _5"> </span><span class="ff9">A<span class="_ _b"> </span></span>和<span class="_ _5"> </span><span class="ff9">B<span class="_ _c"> </span></span>来自式<span class="ff5">1.1</span>，<span class="_ _5"> </span><span class="ff9">Q<span class="_ _b"> </span></span>来自式<span class="ff5">1.3</span>，滤</div><div class="t m0 x14 hc ydc ff1 fs6 fc0 sc0 ls0 ws0">波器的初始条件在早先的引用中讨论过。</div><div class="t m0 x2b hc ydd ff1 fs6 fc1 sc0 ls0 ws0">表<span class="_ _6"> </span><span class="ff5">1-2:<span class="_ _4"> </span></span>离散卡尔曼滤波器状态更新方程</div><div class="t m0 x3f h11 yde ff9 fs6 fc1 sc0 ls0 ws0">K</div><div class="t m0 xae h10 ydf ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 xaf hb yde ff5 fs6 fc1 sc0 ls0 ws0">=<span class="_ _5"> </span><span class="ff9">P</span></div><div class="t m0 x49 h12 ye0 ffc fs2 fc1 sc0 ls0 ws0">−</div><div class="t m0 x1d h10 ye1 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 xb0 h11 yde ff9 fs6 fc1 sc0 ls0 ws0">H</div><div class="t m0 x4 h10 ye2 ffb fs2 fc1 sc0 ls0 ws0">T</div><div class="t m0 xb1 hb yde ff5 fs6 fc1 sc0 ls0 ws0">(<span class="ff9">H<span class="_ _a"></span>P</span></div><div class="t m0 x46 h12 ye0 ffc fs2 fc1 sc0 ls0 ws0">−</div><div class="t m0 x62 h10 ye1 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x8e h11 yde ff9 fs6 fc1 sc0 ls0 ws0">H</div><div class="t m0 x6a h10 ye2 ffb fs2 fc1 sc0 ls0 ws0">T</div><div class="t m0 xa0 hb yde ff5 fs6 fc1 sc0 ls0 ws0">+<span class="_ _13"> </span><span class="ff9">R<span class="_ _3"></span></span>)</div><div class="t m0 x21 h4 ye2 ffc fs2 fc1 sc0 ls0 ws0">−<span class="ff3">1</span></div><div class="t m0 xb2 hb yde ff5 fs6 fc1 sc0 ls0 ws0">(1.11)</div><div class="t m0 x78 hb ye3 ff5 fs6 fc1 sc0 ls0 ws0">ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 xaf h10 ye4 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x97 hb ye3 ff5 fs6 fc1 sc0 ls0 ws0">=<span class="_ _0"> </span>ˆ<span class="_ _14"></span><span class="ff9">x</span></div><div class="t m0 x25 h12 ye5 ffc fs2 fc1 sc0 ls0 ws0">−</div><div class="t m0 x25 h10 ye6 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x84 hb ye3 ff5 fs6 fc1 sc0 ls0 ws0">+<span class="_ _13"> </span><span class="ff9">K</span></div><div class="t m0 x4c h10 ye4 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x27 hb ye3 ff5 fs6 fc1 sc0 ls0 ws0">(<span class="ff9">z</span></div><div class="t m0 x69 h10 ye4 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x28 hb ye3 ffa fs6 fc1 sc0 ls0 ws0">−<span class="_ _13"> </span><span class="ff9">H<span class="_ _10"> </span><span class="ff5">ˆ<span class="_ _14"></span><span class="ff9">x</span></span></span></div><div class="t m0 x32 h12 ye5 ffc fs2 fc1 sc0 ls0 ws0">−</div><div class="t m0 x32 h10 ye6 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 xb3 hb ye3 ff5 fs6 fc1 sc0 ls0 ws0">)<span class="_ _1c"> </span>(1.12)</div><div class="t m0 xb4 h11 ye7 ff9 fs6 fc1 sc0 ls0 ws0">P</div><div class="t m0 x48 h10 ye8 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x7f hb ye7 ff5 fs6 fc1 sc0 ls0 ws0">=<span class="_ _5"> </span>(<span class="ff9">I<span class="_ _6"> </span><span class="ffa">−<span class="_ _b"> </span></span>K</span></div><div class="t m0 x59 h10 ye8 ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 x5a hb ye7 ff9 fs6 fc1 sc0 ls0 ws0">H<span class="_ _a"></span><span class="ff5">)</span>P</div><div class="t m0 xb5 h12 ye9 ffc fs2 fc1 sc0 ls0 ws0">−</div><div class="t m0 xa0 h10 yea ffb fs2 fc1 sc0 ls0 ws0">k</div><div class="t m0 xb2 hb ye7 ff5 fs6 fc1 sc0 ls0 ws0">(1.13)</div><div class="t m0 x15 hc yeb ff1 fs6 fc0 sc0 ls0 ws0">测量更新方程首先做的是计算卡尔曼增益<span class="_ _5"> </span><span class="ff9">K</span></div><div class="t m0 x20 h10 yec ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x9b hc yeb ff1 fs6 fc0 sc0 ls0 ws0">。注意<span class="ff5">1.11</span>式和<span class="ff5">1.8</span>式是相</div><div class="t m0 x14 hc yed ff1 fs6 fc0 sc0 ls0 ws0">同的<span class="_ _3"></span>。其<span class="_ _3"></span>次便<span class="_ _3"></span>测量<span class="_ _3"></span>输出以<span class="_ _3"></span>获得<span class="_ _c"> </span><span class="ff9">z</span></div><div class="t m0 x7a h10 yee ffb fs2 fc0 sc0 ls0 ws0">k</div><div class="t m0 x80 hc yed ff1 fs6 fc0 sc0 ls0 ws0">，然<span class="_ _3"></span>后按<span class="ff5">1.12</span>式<span class="_ _3"></span>（与<span class="ff5">1.7</span>式<span class="_ _3"></span>相同<span class="_ _3"></span>）产<span class="_ _3"></span>生状<span class="_ _3"></span>态</div><div class="t m0 x14 hc yef ff1 fs6 fc0 sc0 ls0 ws0">的</div><div class="t m1 x6e he yef ff1 fs8 fc0 sc0 ls0 ws0">后验</div><div class="t m0 x89 hc yef ff1 fs6 fc0 sc0 ls0 ws0">估计。最后按<span class="ff5">1.13</span>式估计状态的</div><div class="t m1 x85 he yef ff1 fs8 fc0 sc0 ls0 ws0">后验</div><div class="t m0 x52 hc yef ff1 fs6 fc0 sc0 ls0 ws0">协方差。</div><div class="t m0 x15 hc yf0 ff1 fs6 fc0 sc0 ls0 ws0">计<span class="_ _3"></span>算<span class="_ _3"></span>完<span class="_ _3"></span>时<span class="_ _3"></span>间<span class="_ _3"></span>更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>和<span class="_ _3"></span>测<span class="_ _3"></span>量<span class="_ _3"></span>更<span class="_ _3"></span>新<span class="_ _3"></span>方<span class="_ _3"></span>程<span class="_ _3"></span>，<span class="_ _3"></span>整<span class="_ _3"></span>个<span class="_ _3"></span>过<span class="_ _3"></span>程<span class="_ _3"></span>再<span class="_ _3"></span>次<span class="_ _3"></span>重<span class="_ _3"></span>复<span class="_ _3"></span><span class="fc2 sc0">。</span><span class="_ _3"></span><span class="fc2 sc0">上</span><span class="_ _3"></span><span class="fc2 sc0">一</span><span class="_ _3"></span><span class="fc2 sc0">次</span><span class="_ _3"></span><span class="fc2 sc0">计</span></div><div class="t m0 x1d hb ya2 ff5 fs6 fc1 sc0 ls0 ws0">UNC-Chap<span class="_ _3"></span>el<span class="_ _6"> </span>Hill,<span class="_ _0"> </span>TR<span class="_ _6"> </span>95-041,<span class="_ _0"> </span>July<span class="_ _6"> </span>24,<span class="_ _0"> </span>2006</div></div><div class="pi" data-data='{"ctm":[1.611984,0.000000,0.000000,1.611984,0.000000,0.000000]}'></div></div>