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<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://static.pudn.com/prod/directory_preview_static/62869954b305d84a4f781f7f/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">实验一 卡尔曼滤波</div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls0 ws0">一、<span class="_ _0"> </span>实验目的</div><div class="t m0 x3 h5 y4 ff2 fs2 fc0 sc0 ls0 ws0">1<span class="ff1">、了解卡尔曼滤波的准则和信号模型，以及卡尔曼滤波的应用。</span></div><div class="t m0 x3 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">2<span class="ff1">、熟练掌握卡尔曼滤波的递推过程，提高对信号进行处理的能力。</span></div><div class="t m0 x3 h5 y6 ff2 fs2 fc0 sc0 ls0 ws0">3<span class="ff1">、分析讨论实际状态值和估计值的误差。</span></div><div class="t m0 x2 h4 y7 ff1 fs1 fc0 sc0 ls0 ws0">二、实验原理</div><div class="t m0 x3 h5 y8 ff2 fs2 fc0 sc0 ls0 ws0">1<span class="ff1">、卡尔曼滤波简介</span></div><div class="t m0 x3 h5 y9 ff1 fs2 fc0 sc0 ls0 ws0">卡尔<span class="_ _1"></span>曼滤<span class="_ _1"></span>波是<span class="_ _1"></span>解决<span class="_ _1"></span>以均<span class="_ _1"></span>方误<span class="_ _1"></span>差最<span class="_ _1"></span>小为<span class="_ _1"></span>准则<span class="_ _1"></span>的最<span class="_ _1"></span>佳线<span class="_ _1"></span>性滤<span class="_ _1"></span>波问<span class="_ _1"></span>题，<span class="_ _1"></span>它根<span class="_ _1"></span>据<span class="_ _2"> </span><span class="fc1">前</span></div><div class="t m0 x2 h5 ya ff1 fs2 fc1 sc0 ls0 ws0">一个<span class="_ _1"></span>估计<span class="_ _1"></span>值和<span class="_ _1"></span>最近<span class="_ _1"></span>一个<span class="_ _1"></span>观察<span class="_ _1"></span>数据<span class="_ _1"></span>来估<span class="_ _1"></span>计信<span class="_ _1"></span>号的<span class="_ _1"></span>当前<span class="_ _1"></span>值。<span class="_ _3"></span><span class="fc0">它是<span class="_ _1"></span>用状<span class="_ _1"></span>态方<span class="_ _1"></span>程和<span class="_ _1"></span>递推</span></div><div class="t m0 x2 h5 yb ff1 fs2 fc0 sc0 ls0 ws0">方法<span class="_ _1"></span>进行<span class="_ _1"></span>估计<span class="_ _1"></span>的，<span class="_ _1"></span>而它<span class="_ _1"></span>的解<span class="_ _1"></span>是以<span class="_ _1"></span>估计<span class="_ _1"></span>值（<span class="_ _1"></span>常常<span class="_ _1"></span>是状<span class="_ _1"></span>态变<span class="_ _1"></span>量的<span class="_ _1"></span>估计<span class="_ _1"></span>值）<span class="_ _1"></span>的形<span class="_ _1"></span>式给</div><div class="t m0 x2 h5 yc ff1 fs2 fc0 sc0 ls0 ws0">出其信号模型是从状态方程和量测方程得到的。</div><div class="t m0 x3 h5 yd ff1 fs2 fc0 sc0 ls0 ws0">卡尔<span class="_ _1"></span>曼过<span class="_ _1"></span>滤中<span class="_ _1"></span>信号<span class="_ _1"></span>和噪<span class="_ _1"></span>声是<span class="_ _1"></span>用状<span class="_ _1"></span>态方<span class="_ _1"></span>程和<span class="_ _1"></span>测量<span class="_ _1"></span>方程<span class="_ _1"></span>来表<span class="_ _1"></span>示的<span class="_ _1"></span>。<span class="_ _2"></span><span class="fc1">因此<span class="_ _1"></span>设计<span class="_ _1"></span>卡</span></div><div class="t m0 x2 h5 ye ff1 fs2 fc1 sc0 ls0 ws0">尔曼<span class="_ _1"></span>滤波<span class="_ _1"></span>器要<span class="_ _1"></span>求已<span class="_ _1"></span>知状<span class="_ _1"></span>态方<span class="_ _1"></span>程和<span class="_ _1"></span>测量<span class="_ _1"></span>方程<span class="_ _1"></span>。<span class="_ _4"></span><span class="fc0">它不<span class="_ _1"></span>需要<span class="_ _1"></span>知道<span class="_ _1"></span>全部<span class="_ _1"></span>过去<span class="_ _1"></span>的数<span class="_ _1"></span>据，<span class="_ _1"></span>采</span></div><div class="t m0 x2 h5 yf ff1 fs2 fc0 sc0 ls0 ws0">用递<span class="_ _1"></span>推的<span class="_ _1"></span>方法<span class="_ _1"></span>计算<span class="_ _1"></span>，它<span class="_ _1"></span>既可<span class="_ _1"></span>以用<span class="_ _1"></span>于平<span class="_ _1"></span>稳和<span class="_ _1"></span>不平<span class="_ _1"></span>稳的<span class="_ _1"></span>随机<span class="_ _1"></span>过程<span class="_ _1"></span>，同<span class="_ _1"></span>时也<span class="_ _1"></span>可以<span class="_ _1"></span>应用</div><div class="t m0 x2 h5 y10 ff1 fs2 fc0 sc0 ls0 ws0">解决非时变和时变系统，因而它比维纳过滤有更广泛的应用。</div><div class="t m0 x3 h5 y11 ff2 fs2 fc0 sc0 ls0 ws0">2<span class="ff1">、卡尔曼滤波的递推公式</span></div><div class="t m0 x4 h6 y12 ff2 fs2 fc0 sc0 ls0 ws0">………(1) </div><div class="t m0 x5 h6 y13 ff2 fs2 fc0 sc0 ls0 ws0">………(2)</div><div class="t m0 x6 h6 y14 ff2 fs2 fc0 sc0 ls0 ws0">………(3)</div><div class="t m0 x7 h6 y15 ff2 fs2 fc0 sc0 ls0 ws0">………(4)</div><div class="t m0 x3 h5 y16 ff2 fs2 fc0 sc0 ls0 ws0">3<span class="ff1">、递推过程的实现</span></div><div class="t m0 x3 h5 y17 ff1 fs2 fc0 sc0 ls0 ws0">如果初始状态<span class="_ _5"> </span>的统计特性<span class="_ _6"> </span>及<span class="_ _7"> </span>已知，并</div><div class="t m0 x3 h5 y18 ff1 fs2 fc0 sc0 ls0 ws0">令 </div><div class="t m0 x3 h5 y19 ff1 fs2 fc0 sc0 ls0 ws0">又 </div><div class="t m0 x3 h5 y1a ff1 fs2 fc0 sc0 ls0 ws0">将<span class="_ _8"> </span>代<span class="_ _1"></span>入<span class="_ _1"></span>式<span class="_ _1"></span>（<span class="_ _4"></span><span class="ff2">3<span class="_ _1"></span></span>）<span class="_ _1"></span>可<span class="_ _1"></span>求<span class="_ _4"></span>得<span class="_ _8"> </span>，<span class="_ _1"></span>将<span class="_ _8"> </span>代入<span class="_ _4"></span>式<span class="_ _1"></span>（<span class="_ _1"></span><span class="ff2">2<span class="_ _4"></span></span>）<span class="_ _1"></span>可<span class="_ _1"></span>求<span class="_ _1"></span>得<span class="_ _9"> </span>，<span class="_ _1"></span>将<span class="_ _1"></span>此</div><div class="t m0 x2 h5 y1b ff1 fs2 fc0 sc0 ls0 ws0">代入式<span class="_ _1"></span>（<span class="ff2">1</span>）<span class="_ _1"></span>可求得在最<span class="_ _1"></span>小均方误<span class="_ _1"></span>差条件下的<span class="_ _a"> </span>，同时<span class="_ _1"></span>将<span class="_ _b"> </span>代入式<span class="_ _1"></span>（<span class="ff2">4</span>）<span class="_ _1"></span>又可</div><div class="t m0 x2 h5 y1c ff1 fs2 fc0 sc0 ls0 ws0">求得<span class="_ _b"> </span>；<span class="_ _1"></span>由<span class="_ _b"> </span>又可求<span class="_ _c"> </span>，由<span class="_ _b"> </span>又<span class="_ _1"></span>可求得<span class="_ _d"> </span>，由<span class="_ _d"> </span>又可求得<span class="_ _5"> </span>，同时由</div><div class="t m0 x8 h5 y1d ff1 fs2 fc0 sc0 ls0 ws0">与<span class="_ _c"> </span>又可<span class="_ _1"></span>求<span class="_ _1"></span>得<span class="_ _c"> </span>…<span class="_ _1"></span>…；<span class="_ _1"></span>以此<span class="_ _1"></span>类<span class="_ _1"></span>推，<span class="_ _1"></span>这<span class="_ _1"></span>种递<span class="_ _1"></span>推计<span class="_ _1"></span>算<span class="_ _1"></span>方法<span class="_ _1"></span>用<span class="_ _1"></span>计算<span class="_ _1"></span>机计<span class="_ _1"></span>算<span class="_ _1"></span>十分</div><div class="t m0 x2 h5 y1e ff1 fs2 fc0 sc0 ls0 ws0">方便。</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
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matlab实现
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