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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/622b2e92ff7f9c46a68987ec/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">第<span class="_ _0"> </span><span class="ff2 sc1">4<span class="_"> </span></span>章<span class="ff2 sc1 ls1"> </span><span class="ls2">卡尔曼（<span class="ff2 sc1 ls3">Kalman</span>）滤波</span><span class="ff2 sc1"> </span></div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc1 ls4 ws0">卡尔曼滤波的思想是把动态系统表示成状态空间形式，<span class="_ _1"></span><span class="ls0">是一种连</span></div><div class="t m0 x3 h2 y3 ff1 fs0 fc0 sc1 ls5 ws0">续修正系统的线性投影算法。<span class="ff2 ls0"> </span></div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 ls2 ws0">功能<span class="ff2 sc1 ls0"> </span></div><div class="t m0 x4 h3 y5 ff3 fs0 fc0 sc1 ls0 ws0">1<span class="ff1">）<span class="ff4"> <span class="_ _2"> </span></span><span class="ls4">连续修正系统的线性投影算法。</span></span> </div><div class="t m0 x4 h3 y6 ff3 fs0 fc0 sc1 ls0 ws0">2<span class="ff1">）<span class="ff4"> <span class="_ _2"> </span></span><span class="ls6">用于计算高斯<span class="_ _3"> </span></span></span><span class="ls5">ARMA<span class="_ _3"> </span><span class="ff1 ls7">过程的精确有限样本预测和精确的</span></span></div><div class="t m0 x5 h3 y7 ff1 fs0 fc0 sc1 ls5 ws0">似然函数。<span class="ff3 ls0"> </span></div><div class="t m0 x4 h3 y8 ff3 fs0 fc0 sc1 ls0 ws0">3<span class="ff1">）<span class="ff4"> <span class="_ _2"> </span></span><span class="ls5">分解矩阵自协方差生成函数或谱密度。</span></span> </div><div class="t m0 x4 h3 y9 ff3 fs0 fc0 sc1 ls0 ws0">4<span class="ff1">）<span class="ff4"> <span class="_ _2"> </span></span><span class="ls8">估计系数随时间变化的向量自回归。</span></span> </div><div class="t m0 x6 h3 ya ff1 fs0 fc0 sc1 ls0 ws0">第一节<span class="ff3 ls9"> </span><span class="ls8">动态系统的状态空间表示</span><span class="ff3"> </span></div><div class="t m0 x3 h2 yb ff1 fs0 fc0 sc0 lsa ws0">一．假设条件<span class="ff2 sc1 ls0"> </span></div><div class="t m0 x2 h2 yc ff1 fs0 fc0 sc1 ls0 ws0">令</div><div class="t m0 x7 h4 yd ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="c x8 ye w2 h5"><div class="t m0 x0 h6 yf ff2 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="t m0 x9 h2 y10 ff1 fs0 fc0 sc1 lsb ws0">表示时期<span class="_ _4"></span><span class="ff5 fs2 ls0">t<span class="_ _5"> </span></span>观察到变量的一个</div><div class="c xa y11 w3 h7"><div class="t m1 x0 h8 y12 ff6 fs3 fc0 sc1 ls0 ws0">(</div></div><div class="t m1 xb h8 y13 ff6 fs3 fc0 sc1 ls0 ws0">)</div><div class="t m0 xc h9 y10 ff3 fs4 fc0 sc1 ls0 ws0">1<span class="_ _6"></span><span class="ff5">n</span></div><div class="c xd y14 w4 ha"><div class="t m0 x0 hb y15 ff6 fs4 fc0 sc1 ls0 ws0">×</div></div><div class="t m0 xe h2 y10 ff1 fs0 fc0 sc1 lsb ws0">向量。则</div><div class="t m0 xf h4 yd ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="c x10 ye w5 h5"><div class="t m0 x0 h6 yf ff2 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="t m0 x11 h2 y10 ff1 fs0 fc0 sc1 lsc ws0">的动态可以用</div><div class="t m0 x3 h2 y16 ff1 fs0 fc0 sc1 ls5 ws0">不可观测的</div><div class="t m2 x12 h8 y17 ff6 fs3 fc0 sc1 lsd ws0">()</div><div class="t m0 x13 h2 y18 ff3 fs4 fc0 sc1 ls0 ws0">1<span class="_ _7"></span><span class="ff5">r<span class="_ _8"></span><span class="ff6">×<span class="_ _9"> </span><span class="ff1 fs0">向量</span></span></span></div><div class="t m0 x14 h4 y19 ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="c x15 y1a w6 h5"><div class="t m0 x0 hc yf ff7 fs2 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x16 h2 y18 ff1 fs0 fc0 sc1 ls0 ws0">来表示，</div><div class="t m0 x17 h4 y19 ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="c x18 y1a w6 h5"><div class="t m0 x0 hc yf ff7 fs2 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x19 h2 y18 ff1 fs0 fc0 sc1 lse ws0">为状态向量。</div><div class="t m0 x1a h4 y19 ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="c x1b y1a w5 h5"><div class="t m0 x0 h6 yf ff2 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="t m0 x1c h2 y18 ff1 fs0 fc0 sc1 lsf ws0">的动态系统可以表</div><div class="t m0 x3 h3 y1b ff1 fs0 fc0 sc1 ls10 ws0">示为如下的状态空间模型：<span class="ff3 ls0"> </span></div><div class="t m0 x1d hd y1c ff3 fs1 fc0 sc1 ls11 ws0">11<span class="_ _a"></span><span class="ff5 ls12">tt<span class="_ _b"></span>t</span></div><div class="t m0 x1e he y1d ff5 fs2 fc0 sc1 ls13 ws0">Fv</div><div class="c x1f y1e w7 hf"><div class="t m3 x0 h10 y15 ff6 fs5 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m3 x20 h10 y1d ff6 fs5 fc0 sc1 ls0 ws0">ξ</div><div class="t m0 x21 h11 y1c ff6 fs1 fc0 sc1 ls14 ws0">++</div><div class="t m0 x22 h3 y1d ff6 fs2 fc0 sc1 ls15 ws0">=+<span class="_ _c"></span><span class="ff3 fs0 ls16 ws1"> <span class="ls17 ws0"> <span class="ff1 ls0">（<span class="ff3">1</span>）<span class="ff3"> </span></span></span></span></div><div class="t m0 x23 h4 y1f ff5 fs1 fc0 sc1 ls18 ws0">tt<span class="_ _4"> </span>t<span class="_ _d"></span>t</div><div class="t m0 x6 he y20 ff5 fs2 fc0 sc1 ls19 ws0">yA<span class="_ _e"></span>x<span class="_ _f"></span>H<span class="_ _10"> </span>w</div><div class="c x24 y21 w8 hf"><div class="t m3 x0 h10 y22 ff6 fs5 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x25 h12 y23 ff6 fs2 fc0 sc1 ls1a ws0">′′</div><div class="t m0 x26 h12 y24 ff6 fs2 fc0 sc1 ls1b ws0">=+<span class="_ _5"> </span>+</div><div class="t m0 x27 h3 y20 ff3 fs0 fc0 sc1 ls1c ws2"> <span class="ws3"> <span class="ff1 ls0 ws0">（<span class="ff3">2</span>）<span class="ff3"> </span></span></span></div><div class="t m0 x3 h2 y25 ff1 fs0 fc0 sc1 ls1d ws0">其中</div><div class="t m0 x7 h13 y26 ff6 fs6 fc0 sc1 ls1e ws0">′′</div><div class="t m0 x28 h14 y27 ff2 fs6 fc0 sc1 ls1f ws0">F,<span class="_ _4"> </span>A<span class="_ _11"> </span>,<span class="_ _4"> </span>H</div><div class="t m0 x29 h2 y28 ff1 fs0 fc0 sc1 ls20 ws0">分别为</div><div class="t m4 x22 h8 y29 ff6 fs3 fc0 sc1 ls21 ws0">()</div><div class="t m0 x2a h2 y28 ff5 fs4 fc0 sc1 ls22 ws0">rr<span class="_ _12"></span><span class="ff6 ls0">×<span class="_ _13"> </span><span class="ff1 fs0">，</span></span></div><div class="c x2b y2a w3 h7"><div class="t m5 x0 h8 y12 ff6 fs3 fc0 sc1 ls0 ws0">(</div></div><div class="t m5 x2c h8 y29 ff6 fs3 fc0 sc1 ls0 ws0">)</div><div class="t m0 x2d h15 y28 ff5 fs4 fc0 sc1 ls23 ws0">nk</div><div class="c x2e y2b w9 ha"><div class="t m0 x0 hb y15 ff6 fs4 fc0 sc1 ls0 ws0">×</div></div><div class="t m0 x18 h2 y28 ff1 fs0 fc0 sc1 ls0 ws0">和</div><div class="c x2f y2a w3 h7"><div class="t m6 x0 h8 y12 ff6 fs3 fc0 sc1 ls0 ws0">(</div></div><div class="t m6 x30 h8 y29 ff6 fs3 fc0 sc1 ls0 ws0">)</div><div class="t m0 x31 h15 y28 ff5 fs4 fc0 sc1 ls24 ws0">nr</div><div class="c x32 y2b wa ha"><div class="t m0 x0 hb y15 ff6 fs4 fc0 sc1 ls0 ws0">×</div></div><div class="t m0 x33 h2 y28 ff1 fs0 fc0 sc1 ls20 ws0">矩阵，</div><div class="t m0 x34 h4 y2c ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="t m0 x35 h2 y28 ff2 fs2 fc0 sc1 ls0 ws0">x<span class="_ _14"> </span><span class="ff1 fs0 ls25">是外生变量或前定</span></div><div class="t m0 x3 h2 y2d ff1 fs0 fc0 sc1 ls20 ws0">变量的</div><div class="t m7 x8 h16 y2e ff6 fs7 fc0 sc1 ls26 ws0">()</div><div class="t m0 x36 h17 y2f ff3 fs8 fc0 sc1 ls0 ws0">1<span class="_ _6"></span><span class="ff5">k<span class="_ _8"></span><span class="ff6">×</span></span></div><div class="t m0 x37 h3 y30 ff1 fs0 fc0 sc1 ls27 ws0">向量。方程（<span class="ff3 ls0">1</span><span class="ls28">）称为状态方程，方程（<span class="ff3 ls0">2<span class="_ _15"></span></span><span class="ls29">）称为观察方</span></span></div><div class="t m0 x3 h2 y31 ff1 fs0 fc0 sc1 ls0 ws0">程。其中</div><div class="t m8 x38 h8 y32 ff6 fs3 fc0 sc1 ls2a ws0">()</div><div class="t m0 x39 h2 y33 ff3 fs8 fc0 sc1 ls0 ws0">1<span class="_ _7"></span><span class="ff5">r<span class="_ _8"></span><span class="ff6">×<span class="_ _9"> </span><span class="ff1 fs0">向量</span></span></span></div><div class="t m0 x3a h4 y34 ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="t m0 x3b h2 y33 ff2 fs2 fc0 sc1 ls0 ws0">v<span class="_ _16"> </span><span class="ff1 fs0">和</span></div><div class="t m9 x3c h8 y32 ff6 fs3 fc0 sc1 ls2b ws0">()</div><div class="t m0 x3d h2 y33 ff3 fs8 fc0 sc1 ls0 ws0">1<span class="_ _6"></span><span class="ff5">n<span class="_ _4"></span><span class="ff6">×<span class="_ _9"> </span><span class="ff1 fs0">向量</span></span></span></div><div class="t m0 x2f h4 y34 ff5 fs1 fc0 sc1 ls0 ws0">t</div><div class="t m0 x3e h3 y33 ff2 fs2 fc0 sc1 ls0 ws0">w<span class="_ _14"> </span><span class="ff1 fs0 ls2c">为向量白噪声：<span class="ff3 ls0"> </span></span></div><div class="t ma x3f h18 y35 ff6 fs9 fc0 sc1 ls2d ws0">()</div><div class="t ma x3f h18 y36 ff6 fs9 fc0 sc1 ls2e ws0">()</div><div class="t m0 x40 h19 y37 ff3 fsa fc0 sc1 ls0 ws0">0</div><div class="t m0 x2b h19 y38 ff3 fsa fc0 sc1 ls0 ws0">0</div><div class="t m0 x2a h1a y39 ff5 fsb fc0 sc1 ls0 ws0">t</div><div class="t m0 x41 h1a y3a ff5 fsb fc0 sc1 ls0 ws0">t</div><div class="t m0 x42 h1b y3b ff5 fsa fc0 sc1 ls2f ws0">Qt</div><div class="t m0 x6 h1b y3c ff5 fsa fc0 sc1 ls30 ws0">Ev<span class="_ _1"></span>v</div><div class="t m0 x2e h1b y3d ff5 fsa fc0 sc1 ls0 ws0">t</div><div class="t m0 x3d h1b y3e ff5 fsa fc0 sc1 ls31 ws0">Rt</div><div class="t m0 x6 h1b y3f ff5 fsa fc0 sc1 ls32 ws0">Ew<span class="_ _17"></span>w</div><div class="t m0 x43 h1b y40 ff5 fsa fc0 sc1 ls0 ws0">t</div><div class="t mb x44 h1c y39 ff6 fsc fc0 sc1 ls0 ws0">τ</div><div class="t mb x45 h1c y3a ff6 fsc fc0 sc1 ls0 ws0">τ</div><div class="c x2c y41 wb ha"><div class="t m3 x0 h1d y15 ff6 fsd fc0 sc1 ls0 ws0">τ</div></div><div class="c x2c y42 wc ha"><div class="t m3 x0 h1d y15 ff6 fsd fc0 sc1 ls0 ws0">τ</div></div><div class="c x46 y43 wd ha"><div class="t m3 x0 h1d y15 ff6 fsd fc0 sc1 ls0 ws0">τ</div></div><div class="c x46 y44 we ha"><div class="t m3 x0 h1d y15 ff6 fsd fc0 sc1 ls0 ws0">τ</div></div><div class="c x47 y41 wf ha"><div class="t m0 x0 h1e y15 ff6 fsa fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x48 h1e y45 ff6 fsa fc0 sc1 ls0 ws0">⎧</div><div class="t m0 x15 h1e y46 ff6 fsa fc0 sc1 ls0 ws0">′</div><div class="t m0 x49 h1e y47 ff6 fsa fc0 sc1 ls0 ws0">=</div><div class="t m0 x48 h1e y48 ff6 fsa fc0 sc1 ls0 ws0">⎨</div><div class="c x47 y42 w10 ha"><div class="t m0 x0 h1e y15 ff6 fsa fc0 sc1 ls0 ws0">≠</div></div><div class="t m0 x48 h1e y49 ff6 fsa fc0 sc1 ls0 ws0">⎩</div><div class="c x4a y43 w11 ha"><div class="t m0 x0 h1e y15 ff6 fsa fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x42 h1e y4a ff6 fsa fc0 sc1 ls0 ws0">⎧</div><div class="t m0 x4b h1e y4b ff6 fsa fc0 sc1 ls0 ws0">′</div><div class="t m0 x4c h1e y4c ff6 fsa fc0 sc1 ls0 ws0">=</div><div class="t m0 x42 h1e y4d ff6 fsa fc0 sc1 ls0 ws0">⎨</div><div class="c x4a y44 w12 ha"><div class="t m0 x0 h1e y15 ff6 fsa fc0 sc1 ls0 ws0">≠</div></div><div class="t m0 x42 h1e y4e ff6 fsa fc0 sc1 ls0 ws0">⎩</div><div class="t m0 x4d h3 y4f ff3 fs0 fc0 sc1 ls1c ws2"> <span class="ls17 ws3"> <span class="ff1 ls0 ws0">（<span class="ff3">3</span>）<span class="ff3"> </span></span></span></div><div class="t m0 x3 h2 y50 ff1 fs0 fc0 sc1 ls2 ws0">其中</div><div class="t m0 x5 h2 y51 ff3 fs6 fc0 sc1 ls0 ws0">,<span class="_ _18"></span><span class="ff5 ls33">QR<span class="_ _19"></span><span class="ff1 fs0 ls0">为</span></span></div><div class="t mc x4e h16 y52 ff6 fs7 fc0 sc1 ls34 ws0">()<span class="_ _1a"></span>(<span class="_ _8"></span>)</div><div class="t m0 x4f h2 y51 ff3 fsa fc0 sc1 ls0 ws0">,<span class="_ _1b"></span><span class="ff5 ls35">rr<span class="_ _14"> </span>n<span class="_ _1c"></span>n<span class="_ _1d"></span><span class="ff6 ls36">××<span class="_ _1e"></span><span class="ff1 fs0 ls37">矩阵。假定扰动项</span></span></span></div><div class="t m0 xb h1a y53 ff5 fsb fc0 sc1 ls0 ws0">t</div><div class="t m0 xc h2 y51 ff5 fs2 fc0 sc1 ls0 ws0">v<span class="_ _1f"> </span><span class="ff1 fs0">和</span></div><div class="t m0 x50 h1a y53 ff5 fsb fc0 sc1 ls0 ws0">t</div><div class="t m0 x51 h2 y51 ff5 fs2 fc0 sc1 ls0 ws0">w<span class="_ _1f"> </span><span class="ff1 fs0 ls38">在所有阶滞后都不相</span></div><div class="t m0 x3 h3 y54 ff1 fs0 fc0 sc1 ls0 ws0">关：<span class="ff3"> </span></div><div class="t ma x52 h18 y55 ff6 fs9 fc0 sc1 ls39 ws0">()</div><div class="t m0 x53 h19 y56 ff3 fsa fc0 sc1 ls0 ws0">0</div><div class="t m0 x54 h1f y57 ff5 fse fc0 sc1 ls3a ws0">tt</div><div class="t m0 x55 h1b y56 ff5 fsa fc0 sc1 ls30 ws0">Ev<span class="_ _c"></span>w</div><div class="t m0 x56 h1e y58 ff6 fsa fc0 sc1 ls0 ws0">′</div><div class="t m0 x57 h3 y56 ff6 fsa fc0 sc1 ls0 ws0">=<span class="_ _20"> </span><span class="ff3 fs0 ls16"> <span class="ff1 ls5">对所有的<span class="_ _4"></span></span></span><span class="ff5 fs2">t<span class="_ _5"> </span><span class="ff1 fs0">和</span></span></div><div class="c x58 y59 w13 h20"><div class="t md x0 h21 yf ff6 fsf fc0 sc1 ls0 ws0">τ</div></div><div class="t m0 x59 h3 y56 ff3 fs0 fc0 sc1 ls1c ws3"> <span class="ff1 ls0 ws0">（<span class="ff3">4</span>）<span class="ff3"> </span></span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
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<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://static.pudn.com/prod/directory_preview_static/622b2e92ff7f9c46a68987ec/bg2.jpg"><div class="t m0 x5a h1f y5a ff5 fse fc0 sc1 ls0 ws0">t</div><div class="c x5b y5b w14 h22"><div class="t m0 x0 he y15 ff5 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="t m0 x5c h2 y5c ff1 fs0 fc0 sc1 ls1d ws0">为前定或外生变量，意味着对<span class="_ _21"> </span><span class="ff3 fs6 ls3b">0,1<span class="_ _22"></span>,<span class="_ _4"></span>2,<span class="_ _23"></span>....,<span class="_ _24"></span><span class="ff5 ls0">s</span></span></div><div class="c x5d y5b w15 h23"><div class="t m0 x0 h13 y15 ff6 fs6 fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x5e h2 y5c ff1 fs0 fc0 sc1 ls1d ws0">除包含在</div><div class="t m0 x5f hd y5a ff3 fs1 fc0 sc1 ls3c ws0">12<span class="_ _25"> </span>1</div><div class="t m0 x60 h24 y5c ff3 fs2 fc0 sc1 ls0 ws0">,<span class="_ _26"> </span>,<span class="_ _23"></span>...,</div><div class="t m0 x61 h1f y5a ff5 fse fc0 sc1 ls3d ws0">tt</div><div class="t m0 x62 he y5c ff5 fs2 fc0 sc1 ls3e ws0">yy<span class="_ _27"> </span>y</div><div class="t m0 x63 h11 y5a ff6 fs1 fc0 sc1 ls3f ws0">−−</div><div class="t m0 x64 h2 y5c ff1 fs0 fc0 sc1 ls1d ws0">之内</div><div class="t m0 x3 h2 y5d ff1 fs0 fc0 sc1 ls5 ws0">的信息外，</div><div class="t m0 x29 h1f y5e ff5 fse fc0 sc1 ls0 ws0">t</div><div class="c x65 y5f w14 h22"><div class="t m0 x0 he y15 ff5 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="t m0 x66 h2 y60 ff1 fs0 fc0 sc1 ls2c ws0">不再能提供关于</div><div class="t m0 x67 h1f y5e ff5 fse fc0 sc1 ls40 ws0">ts</div><div class="c x2e y5f w16 hf"><div class="t m3 x0 h10 y15 ff6 fs5 fc0 sc1 ls0 ws0">ξ</div></div><div class="c x68 y61 w17 h25"><div class="t m0 x0 h11 y62 ff6 fs1 fc0 sc1 ls0 ws0">+</div></div><div class="t m0 x69 h2 y60 ff1 fs0 fc0 sc1 ls0 ws0">以及</div><div class="t m0 xa h1f y5e ff5 fse fc0 sc1 ls40 ws0">ts</div><div class="t m0 x6a he y60 ff5 fs2 fc0 sc1 ls0 ws0">w</div><div class="c x6b y61 w17 h25"><div class="t m0 x0 h11 y62 ff6 fs1 fc0 sc1 ls0 ws0">+</div></div><div class="t m0 x6c h2 y60 ff1 fs0 fc0 sc1 ls0 ws0">的任何信息。<span class="_ _17"></span>即</div><div class="t m0 x6d h1f y5e ff5 fse fc0 sc1 ls0 ws0">t</div><div class="c x6e y5f w14 h22"><div class="t m0 x0 he y15 ff5 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="t m0 x6f h2 y60 ff1 fs0 fc0 sc1 ls0 ws0">可能包含</div><div class="t m0 x70 h26 y63 ff5 fs10 fc0 sc1 ls0 ws0">y</div><div class="t m0 x3 h2 y64 ff1 fs0 fc0 sc1 ls41 ws0">的滞后值或所有与</div><div class="c x3f y65 w13 h27"><div class="t m3 x0 h28 y15 ff6 fs11 fc0 sc1 ls0 ws0">τ</div></div><div class="t m0 x2a h2 y64 ff1 fs0 fc0 sc1 ls0 ws0">、</div><div class="c x71 y66 w18 h25"><div class="t me x0 h29 y62 ff6 fs12 fc0 sc1 ls0 ws0">τ</div></div><div class="c x72 y65 w19 hf"><div class="t m3 x0 h10 y15 ff6 fs5 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x73 h2 y64 ff1 fs0 fc0 sc1 ls0 ws0">和<span class="_ _8"></span><span class="ff5 fs2">w</span></div><div class="c x74 y66 w18 h25"><div class="t me x0 h29 y62 ff6 fs12 fc0 sc1 ls0 ws0">τ</div></div><div class="t m0 x75 h3 y64 ff1 fs0 fc0 sc1 ls0 ws0">不相关变量。<span class="ff3"> </span></div><div class="t m0 x2 h2 y67 ff1 fs0 fc0 sc1 ls4 ws0">状态空间系统描述有限观察值序列</div><div class="c x76 y68 w1a h2a"><div class="t mf x0 h16 y69 ff6 fs7 fc0 sc1 ls0 ws0">{</div></div><div class="c x77 y68 w1a h2a"><div class="t mf x0 h16 y69 ff6 fs7 fc0 sc1 ls0 ws0">}</div></div><div class="t m0 x78 h2b y6a ff3 fs13 fc0 sc1 ls0 ws0">1</div><div class="t m0 x79 h19 y6b ff3 fsa fc0 sc1 ls42 ws0">,<span class="_ _23"></span>...,</div><div class="t m0 x7a h2c y6a ff5 fs13 fc0 sc1 ls0 ws0">T</div><div class="t m0 x7b h1b y6b ff5 fsa fc0 sc1 ls43 ws0">yy</div><div class="t m0 x35 h2 y6c ff1 fs0 fc0 sc1 ls41 ws0">，<span class="_ _22"></span>需要知道状态向量</div><div class="t m0 x3 h2 y6d ff1 fs0 fc0 sc1 ls0 ws0">的初始值</div><div class="t m0 x7c h2b y6e ff3 fs13 fc0 sc1 ls0 ws0">1</div><div class="c x38 y6f w1b hf"><div class="t m3 x0 h10 y15 ff6 fs5 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x7d h3 y70 ff1 fs0 fc0 sc1 ls41 ws0">，根据状态方程（<span class="ff3 ls0">1<span class="ff1">）<span class="_ _28"></span>，</span></span></div><div class="t m0 x7e h2c y6e ff5 fs13 fc0 sc1 ls0 ws0">t</div><div class="c x7f y6f w1b hf"><div class="t m3 x0 h10 y15 ff6 fs5 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x80 h2 y70 ff1 fs0 fc0 sc1 ls0 ws0">可写作</div><div class="c x81 y71 w3 h7"><div class="t m10 x0 h8 y12 ff6 fs3 fc0 sc1 ls0 ws0">(</div></div><div class="t m10 x11 h8 y72 ff6 fs3 fc0 sc1 ls0 ws0">)</div><div class="t m0 x82 h2d y6e ff3 fse fc0 sc1 ls44 ws0">12<span class="_ _15"></span>3</div><div class="t m0 x51 h19 y70 ff3 fsa fc0 sc1 ls42 ws0">,<span class="_ _20"> </span>,<span class="_ _20"> </span>,<span class="_ _23"></span>...,</div><div class="t m0 xf h2c y6e ff5 fs13 fc0 sc1 ls0 ws0">t</div><div class="t m0 x83 h1b y70 ff5 fsa fc0 sc1 ls45 ws0">vv<span class="_ _29"> </span>v</div><div class="t m11 x84 h2e y70 ff6 fs14 fc0 sc1 ls0 ws0">ξ</div><div class="t m0 x85 h3 y70 ff1 fs0 fc0 sc1 lse ws0">的线性函数：<span class="_ _2a"></span><span class="ff3 ls0"> </span></div><div class="t m0 x86 h2f y73 ff3 fs15 fc0 sc1 ls46 ws0">22<span class="_ _1b"></span>1</div><div class="t m0 x87 h2f y74 ff3 fs15 fc0 sc1 ls47 ws0">12<span class="_ _2b"> </span>2<span class="_ _22"></span>1</div><div class="t m0 x3c h30 y75 ff3 fs16 fc0 sc1 ls48 ws0">....</div><div class="t m0 x88 h31 y73 ff5 fs15 fc0 sc1 ls49 ws0">tt</div><div class="t m0 x89 h31 y74 ff5 fs15 fc0 sc1 ls4a ws0">tt<span class="_ _2c"> </span>t<span class="_"> </span>t</div><div class="t m0 x7 h32 y75 ff5 fs16 fc0 sc1 ls4b ws0">vF<span class="_ _1e"></span>v<span class="_ _3"> </span>F<span class="_ _2d"></span>v<span class="_ _2e"> </span>F<span class="_ _19"></span>v<span class="_ _4"></span>F</div><div class="c x8a y76 w1c ha"><div class="t m12 x0 h33 y15 ff6 fs17 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m12 x6a h33 y75 ff6 fs17 fc0 sc1 ls0 ws0">ξ</div><div class="t m0 x75 h34 y73 ff6 fs15 fc0 sc1 ls4c ws0">−−</div><div class="t m0 x8b h34 y74 ff6 fs15 fc0 sc1 ls4d ws0">−−</div><div class="t m0 x8c h3 y75 ff6 fs16 fc0 sc1 ls4e ws0">=<span class="_ _2f"></span>+<span class="_ _28"></span>++<span class="_ _30"></span>++<span class="_ _31"></span><span class="ff3 fs0 ls16"> </span></div><div class="t m0 x8d h26 y77 ff3 fs6 fc0 sc1 ls3b ws0">2,<span class="_ _32"></span>3<span class="_ _1c"></span>,<span class="_ _23"></span>...,<span class="_ _33"></span><span class="ff5 fs10 ls4f">tT</span></div><div class="c x8e y78 w8 h23"><div class="t m0 x0 h13 y15 ff6 fs6 fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x60 h3 y75 ff3 fs0 fc0 sc1 ls50 ws0"> <span class="ff1 ls0">（<span class="ff3">5</span>）<span class="_ _34"></span><span class="ff3"> </span></span></div><div class="t m0 x3 h2 y79 ff1 fs0 fc0 sc1 ls0 ws0">这里假定</div><div class="t m0 x7c h2f y7a ff3 fs15 fc0 sc1 ls0 ws0">1</div><div class="c x38 y7b w1b hf"><div class="t m12 x0 h33 y15 ff6 fs17 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x7d h2 y7c ff1 fs0 fc0 sc1 ls0 ws0">与</div><div class="t m0 x87 h31 y7a ff5 fs15 fc0 sc1 ls0 ws0">t</div><div class="t m0 x8f h2 y7c ff5 fs16 fc0 sc1 ls0 ws0">v<span class="_ _1f"> </span><span class="ff1 fs0">和</span></div><div class="t m0 x22 h31 y7a ff5 fs15 fc0 sc1 ls0 ws0">t</div><div class="t m0 x1d h3 y7c ff5 fs16 fc0 sc1 ls0 ws0">w<span class="_ _1f"> </span><span class="ff1 fs0 ls51">的任何实现都不相关：<span class="ff3 ls0"> </span></span></div><div class="t m13 x37 h35 y7d ff6 fs18 fc0 sc1 ls0 ws0">(</div><div class="t m13 x4f h35 y7e ff6 fs18 fc0 sc1 ls0 ws0">)</div><div class="t m13 x29 h35 y7f ff6 fs18 fc0 sc1 ls0 ws0">(</div><div class="t m13 x57 h35 y80 ff6 fs18 fc0 sc1 ls0 ws0">)</div><div class="t m0 x90 h36 y81 ff3 fs19 fc0 sc1 ls0 ws0">1</div><div class="t m0 x91 h36 y82 ff3 fs19 fc0 sc1 ls0 ws0">1</div><div class="t m0 x92 h37 y83 ff3 fs1a fc0 sc1 ls52 ws0">0<span class="_ _35"> </span>1<span class="_ _22"></span>,<span class="_ _4"></span>2,<span class="_ _23"></span>...,</div><div class="t m0 x22 h37 y84 ff3 fs1a fc0 sc1 ls52 ws0">0<span class="_ _36"> </span>1<span class="_ _22"></span>,<span class="_ _4"></span>2,<span class="_ _23"></span>...,</div><div class="t m0 x8f h38 y81 ff5 fs19 fc0 sc1 ls0 ws0">t</div><div class="t m0 x8b h38 y82 ff5 fs19 fc0 sc1 ls0 ws0">t</div><div class="t m0 x93 h39 y83 ff5 fs1a fc0 sc1 ls53 ws0">Ev<span class="_ _37"> </span>T</div><div class="t m0 x36 h39 y84 ff5 fs1a fc0 sc1 ls54 ws0">Ew<span class="_ _38"> </span>T</div><div class="t mb x94 h3a y83 ff6 fs1b fc0 sc1 ls55 ws0">ξτ</div><div class="t mb x95 h3a y84 ff6 fs1b fc0 sc1 ls56 ws0">ξτ</div><div class="t m0 x96 h3b y85 ff6 fs1a fc0 sc1 ls0 ws0">′</div><div class="t m0 x21 h3b y86 ff6 fs1a fc0 sc1 ls57 ws0">==</div><div class="t m0 x97 h3b y87 ff6 fs1a fc0 sc1 ls0 ws0">′</div><div class="t m0 x23 h3b y88 ff6 fs1a fc0 sc1 ls58 ws0">==</div><div class="t m0 x2c h3 y89 ff3 fs0 fc0 sc1 ls17 ws2"> <span class="ls16 ws3"> <span class="ff1 ls0 ws0">（<span class="ff3">6</span>）<span class="ff3"> </span></span></span></div><div class="t m0 x3 h3 y8a ff1 fs0 fc0 sc1 ls0 ws0">根据（<span class="ff3">3</span>）和（<span class="ff3">6</span>）<span class="_ _28"></span>，得</div><div class="t m0 x98 h38 y8b ff5 fs19 fc0 sc1 ls0 ws0">t</div><div class="t m0 x45 h2 y8c ff5 fs16 fc0 sc1 ls0 ws0">v<span class="_ _1f"> </span><span class="ff1 fs0">和</span></div><div class="c x40 y8d w1d h23"><div class="t m12 x0 h3c y15 ff6 fs1c fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x99 h3 y8c ff1 fs0 fc0 sc1 ls41 ws0">的滞后值不相关：<span class="ff3 ls0"> </span></div><div class="t m14 x29 h16 y8e ff6 fs7 fc0 sc1 ls59 ws0">()</div><div class="t m0 x3f h37 y8f ff3 fs1a fc0 sc1 ls0 ws0">0</div><div class="t m0 x9a h38 y90 ff5 fs19 fc0 sc1 ls0 ws0">t</div><div class="t m0 x36 h39 y8f ff5 fs1a fc0 sc1 ls53 ws0">Ev</div><div class="t m15 x56 h3d y90 ff6 fs1d fc0 sc1 ls0 ws0">τ</div><div class="t m16 x8b h3e y8f ff6 fs1e fc0 sc1 ls0 ws0">ξ</div><div class="t m0 x90 h3b y91 ff6 fs1a fc0 sc1 ls0 ws0">′</div><div class="t m0 x6 h3b y92 ff6 fs1a fc0 sc1 ls0 ws0">=</div><div class="t m0 x9b h3 y8f ff3 fs0 fc0 sc1 ls16 ws0"> <span class="_ _39"> </span><span class="fs6 ls3b">1<span class="_ _22"></span>,<span class="_ _3a"> </span>2,<span class="_ _23"></span>...,1<span class="_ _3b"></span><span class="ff5 fs10 ls5a">tt</span></span></div><div class="c x9c y93 w15 h23"><div class="t me x0 h3f y15 ff6 fs1f fc0 sc1 ls0 ws0">τ</div></div><div class="c x6c y93 w1e h23"><div class="t m0 x0 h13 y15 ff6 fs6 fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x9d h3 y8f ff6 fs6 fc0 sc1 ls5b ws0">−−<span class="_ _3c"> </span><span class="ff3 fs0 ls1c"> <span class="ff1 ls0">（<span class="ff3">7</span>）<span class="ff3"> </span></span></span></div><div class="t m17 x7d h8 y94 ff6 fs3 fc0 sc1 ls5c ws0">()</div><div class="t m0 x53 h37 y95 ff3 fs1a fc0 sc1 ls0 ws0">0</div><div class="t m0 x54 h38 y96 ff5 fs19 fc0 sc1 ls0 ws0">t</div><div class="t m0 x9e h39 y95 ff5 fs1a fc0 sc1 ls5d ws0">Ew</div><div class="t m18 x9f h40 y96 ff6 fs20 fc0 sc1 ls0 ws0">τ</div><div class="t m16 x9a h3e y95 ff6 fs1e fc0 sc1 ls0 ws0">ξ</div><div class="t m0 x13 h3b y97 ff6 fs1a fc0 sc1 ls0 ws0">′</div><div class="t m0 x57 h3b y98 ff6 fs1a fc0 sc1 ls0 ws0">=</div><div class="t m0 x3b h3 y95 ff3 fs0 fc0 sc1 ls1c ws0"> <span class="_ _3d"> </span><span class="fs21 ls5e">1<span class="_ _22"></span>,<span class="_ _4"></span>2,<span class="_ _23"></span>...,<span class="_ _23"></span><span class="ff5 ls0">T</span></span></div><div class="c xa0 y99 w8 h23"><div class="t m12 x0 h3c y15 ff6 fs1c fc0 sc1 ls0 ws0">τ</div></div><div class="c xa1 y99 w8 h23"><div class="t m0 x0 h41 y15 ff6 fs21 fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x34 h3 y95 ff3 fs0 fc0 sc1 ls5f ws3"> <span class="ff1 ls0 ws0">（<span class="ff3">8</span>）<span class="ff3"> </span></span></div><div class="t m19 x93 h8 y9a ff6 fs3 fc0 sc1 ls60 ws0">()<span class="_ _3e"> </span>(<span class="_ _3f"> </span>)</div><div class="t m1a x3b h42 y9b ff6 fs22 fc0 sc1 ls61 ws0">()</div><div class="t m0 x76 h37 y9c ff3 fs1a fc0 sc1 ls0 ws0">0</div><div class="t m0 x66 h38 y9d ff5 fs19 fc0 sc1 ls62 ws0">tt</div><div class="t m0 xa2 h39 y9c ff5 fs1a fc0 sc1 ls5d ws0">Ew<span class="_ _c"></span>y<span class="_ _3c"> </span>E<span class="_ _40"></span>w<span class="_ _41"> </span>A<span class="_ _1"></span>x<span class="_ _42"> </span>H<span class="_ _3d"> </span>w</div><div class="t m18 x8b h40 y9d ff6 fs20 fc0 sc1 ls63 ws0">ττ<span class="_ _43"></span>τ<span class="_ _44"></span>τ</div><div class="t m16 x47 h3e y9c ff6 fs1e fc0 sc1 ls0 ws0">ξ</div><div class="t m0 x95 h3b y9e ff6 fs1a fc0 sc1 ls64 ws0">′′<span class="_ _45"></span>′</div><div class="t m0 xa3 h3b y9f ff6 fs1a fc0 sc1 ls65 ws0">=+<span class="_ _46"></span>+<span class="_ _47"></span>=</div><div class="t m0 x33 h3 y9c ff3 fs0 fc0 sc1 ls50 ws0"> </div><div class="t m0 xa4 h26 ya0 ff3 fs6 fc0 sc1 ls3b ws0">1<span class="_ _22"></span>,<span class="_ _3a"> </span>2,<span class="_ _23"></span>...,1<span class="_ _3b"></span><span class="ff5 fs10 ls5a">tt</span></div><div class="c x83 ya1 w15 h23"><div class="t me x0 h3f y15 ff6 fs1f fc0 sc1 ls0 ws0">τ</div></div><div class="c x1b ya1 w1e h23"><div class="t m0 x0 h13 y15 ff6 fs6 fc0 sc1 ls0 ws0">=</div></div><div class="t m0 xa5 h13 ya0 ff6 fs6 fc0 sc1 ls5b ws0">−−</div><div class="t m0 xa6 h3 y9c ff3 fs0 fc0 sc1 ls1 ws0"> <span class="ff1 ls0">（<span class="ff3">9</span>）<span class="ff3"> </span></span></div><div class="t m1b xa7 h16 ya2 ff6 fs7 fc0 sc1 ls66 ws0">()</div><div class="t m0 xa8 h37 ya3 ff3 fs1a fc0 sc1 ls0 ws0">0</div><div class="t m0 x9f h38 ya4 ff5 fs19 fc0 sc1 ls0 ws0">t</div><div class="t m0 x52 h39 ya3 ff5 fs1a fc0 sc1 ls53 ws0">Ev<span class="_ _48"></span>y</div><div class="t m18 xa9 h40 ya4 ff6 fs20 fc0 sc1 ls0 ws0">τ</div><div class="t m0 xa3 h3b ya5 ff6 fs1a fc0 sc1 ls0 ws0">′</div><div class="t m0 x53 h3b ya6 ff6 fs1a fc0 sc1 ls0 ws0">=</div><div class="t m0 xaa h3 ya7 ff3 fs0 fc0 sc1 ls17 ws0"> <span class="_ _39"> </span><span class="fs21 ls5e">1<span class="_ _22"></span>,<span class="_ _3a"> </span>2,<span class="_ _15"></span>...,<span class="_ _15"></span>1<span class="_ _3b"></span><span class="ff5 ls67">tt</span></span></div><div class="c x9c ya8 w15 h23"><div class="t m12 x0 h3c y15 ff6 fs1c fc0 sc1 ls0 ws0">τ</div></div><div class="c x6c ya8 w1e h23"><div class="t m0 x0 h41 y15 ff6 fs21 fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x9d h3 ya7 ff6 fs21 fc0 sc1 ls68 ws0">−−<span class="_ _3c"> </span><span class="ff3 fs0 ls69"> <span class="ff1 ls0">（</span><span class="ls6a">10<span class="ff1 ls0">）<span class="ff3"> </span></span></span></span></div><div class="t m0 x3 h2 ya9 ff1 fs0 fc0 sc0 ls6b ws0">二．状态空间系统的例子<span class="ff2 sc1 ls0"> </span></div><div class="t m0 x2 h3 yaa ff1 fs0 fc0 sc1 ls0 ws0">例<span class="_ _0"> </span><span class="ff3 ls6a ws4">1 </span></div><div class="t m1c xa3 h8 yab ff6 fs3 fc0 sc1 ls6c ws0">()</div><div class="t m0 x9a h3 yac ff5 fs1a fc0 sc1 ls0 ws0">AR<span class="_ _49"> </span>p<span class="_ _2c"> </span><span class="ff1 fs0">过程，<span class="ff3"> </span></span></div><div class="t m1d xab h43 yad ff6 fs23 fc0 sc1 ls6d ws0">()</div><div class="c x2b yae w3 h44"><div class="t m1d x0 h43 y12 ff6 fs23 fc0 sc1 ls0 ws0">(</div></div><div class="t m1d x4d h43 yad ff6 fs23 fc0 sc1 ls0 ws0">)</div><div class="c x78 yaf w3 h45"><div class="t m1e x0 h46 yb0 ff6 fs24 fc0 sc1 ls0 ws0">(</div></div><div class="t m1e xac h46 yb1 ff6 fs24 fc0 sc1 ls0 ws0">)</div><div class="t m0 xad h47 yb2 ff3 fs25 fc0 sc1 ls6e ws0">11<span class="_ _4a"> </span>2<span class="_ _4b"></span>1<span class="_ _4c"> </span>1<span class="_ _4d"> </span>1</div><div class="t m0 xae h48 yb3 ff3 fs26 fc0 sc1 ls6f ws0">...</div><div class="t m0 xaf h49 yb2 ff5 fs25 fc0 sc1 ls70 ws0">tt<span class="_ _19"></span>t<span class="_ _2c"> </span>p<span class="_ _4e"></span>t<span class="_ _4f"></span>p<span class="_ _50"></span>t</div><div class="t m0 xb0 h4a yb3 ff5 fs26 fc0 sc1 ls71 ws0">yy<span class="_ _19"></span>y<span class="_ _51"> </span>y</div><div class="c x37 yb4 w1f ha"><div class="t m15 x0 h4b y15 ff6 fs27 fc0 sc1 ls0 ws0">µ</div></div><div class="t m15 x91 h4b yb3 ff6 fs27 fc0 sc1 ls72 ws0">φµ<span class="_ _4b"></span>φ<span class="_ _42"> </span>µ<span class="_ _0"> </span>φ<span class="_ _26"> </span>µ<span class="_ _52"></span>ε</div><div class="t m0 xa2 h4c yb2 ff6 fs25 fc0 sc1 ls73 ws0">+−<span class="_ _53"></span>−<span class="_ _54"></span>+<span class="_ _55"></span>+</div><div class="t m0 x93 h3 yb3 ff6 fs26 fc0 sc1 ls74 ws0">−<span class="_ _c"></span>=<span class="_ _56"> </span>−+<span class="_ _3e"> </span>−+<span class="_ _57"></span>+<span class="_ _58"> </span>−+<span class="_ _11"> </span><span class="ff3 fs0 ls16"> <span class="ff1 ls0">（</span><span class="ls75">11<span class="_ _23"></span><span class="ff1 ls0">）<span class="ff3"> </span></span></span></span></div><div class="t m1f x9a h4d yb5 ff6 fs28 fc0 sc1 ls76 ws0">()</div><div class="t m0 xb1 h4e yb6 ff3 fs29 fc0 sc1 ls0 ws0">2</div><div class="t m0 x20 h4f yb7 ff3 fs2a fc0 sc1 ls0 ws0">0</div><div class="t m0 x91 h50 yb8 ff5 fs29 fc0 sc1 ls0 ws0">t</div><div class="t m0 xb2 h51 yb9 ff5 fs2a fc0 sc1 ls0 ws0">t</div><div class="t m0 xb3 h51 yba ff5 fs2a fc0 sc1 ls0 ws0">E</div><div class="t m0 xb2 h51 ybb ff5 fs2a fc0 sc1 ls0 ws0">t</div><div class="t mb x57 h52 yb8 ff6 fs2b fc0 sc1 ls0 ws0">τ</div><div class="c x44 ybc w20 ha"><div class="t m16 x0 h53 y22 ff6 fs2c fc0 sc1 ls0 ws0">σ</div></div><div class="t m16 x2d h53 yb9 ff6 fs2c fc0 sc1 ls0 ws0">τ</div><div class="t m16 x95 h53 yba ff6 fs2c fc0 sc1 ls77 ws0">εε</div><div class="c x2d ybd w21 ha"><div class="t m16 x0 h53 y15 ff6 fs2c fc0 sc1 ls0 ws0">τ</div></div><div class="t m0 x3a h54 ybe ff6 fs2a fc0 sc1 ls0 ws0">⎧</div><div class="c xb4 ybc w22 ha"><div class="t m0 x0 h54 y22 ff6 fs2a fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x26 h54 ybf ff6 fs2a fc0 sc1 ls0 ws0">=</div><div class="t m0 x3a h54 yc0 ff6 fs2a fc0 sc1 ls0 ws0">⎨</div><div class="c xb4 ybd w23 ha"><div class="t m0 x0 h54 y15 ff6 fs2a fc0 sc1 ls0 ws0">≠</div></div><div class="t m0 x3a h54 yc1 ff6 fs2a fc0 sc1 ls0 ws0">⎩</div><div class="t m0 x75 h3 ybf ff3 fs0 fc0 sc1 ls17 ws2"> <span class="ls1c ws3"> <span class="ff1 ls0 ws0">（<span class="ff3 ls6a">12</span>）<span class="ff3"> </span></span></span></div><div class="t m0 x3 h2 yc2 ff1 fs0 fc0 sc1 ls4 ws0">可以写作状态空间形式。状态方程</div><div class="c xb5 yc3 w3 h2a"><div class="t m20 x0 h16 y69 ff6 fs7 fc0 sc1 ls0 ws0">(</div></div><div class="t m20 xb6 h16 yc4 ff6 fs7 fc0 sc1 ls0 ws0">)</div><div class="t m0 xb7 h51 yc5 ff5 fs2a fc0 sc1 ls78 ws0">rp</div><div class="c x6a yc6 w24 h55"><div class="t m0 x0 h54 yf ff6 fs2a fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x59 h3 yc7 ff1 fs0 fc0 sc1 ls0 ws0">：<span class="ff3"> </span></div><div class="t m0 x1f h4e yc8 ff3 fs29 fc0 sc1 ls79 ws0">12<span class="_ _59"> </span>1</div><div class="t m0 x8c h4e yc9 ff3 fs29 fc0 sc1 ls0 ws0">1</div><div class="t m0 x8e h4e yca ff3 fs29 fc0 sc1 ls0 ws0">1</div><div class="t m0 x6a h4e ycb ff3 fs29 fc0 sc1 ls0 ws0">1</div><div class="t m0 xb8 h4e ycc ff3 fs29 fc0 sc1 ls7a ws0">21</div><div class="t m0 x91 h48 ycd ff3 fs26 fc0 sc1 ls7b ws0">10<span class="_ _5a"> </span>0<span class="_ _16"> </span>0</div><div class="t m0 xb9 h48 yce ff3 fs26 fc0 sc1 ls0 ws0">0</div><div class="t m0 x91 h48 ycf ff3 fs26 fc0 sc1 ls7c ws0">01<span class="_ _5a"> </span>0<span class="_ _14"> </span>0</div><div class="t m0 xb9 h48 yd0 ff3 fs26 fc0 sc1 ls0 ws0">0</div><div class="t m0 x91 h48 yd1 ff3 fs26 fc0 sc1 ls7d ws0">00<span class="_ _5a"> </span>1<span class="_ _5b"> </span>0</div><div class="t m0 xb4 h50 yc8 ff5 fs29 fc0 sc1 ls7e ws0">pp</div><div class="t m0 x89 h50 yc9 ff5 fs29 fc0 sc1 ls7f ws0">tt</div><div class="t m0 xb9 h50 yca ff5 fs29 fc0 sc1 ls0 ws0">t</div><div class="t m0 x5 h50 ycb ff5 fs29 fc0 sc1 ls80 ws0">tt</div><div class="t m0 x28 h50 ycc ff5 fs29 fc0 sc1 ls81 ws0">tp<span class="_ _5c"> </span>tp</div><div class="t m0 x28 h4a yd2 ff5 fs26 fc0 sc1 ls82 ws0">yy</div><div class="t m0 xba h4a yd3 ff5 fs26 fc0 sc1 ls83 ws0">yy</div><div class="t m0 xbb h4a yd4 ff5 fs26 fc0 sc1 ls84 ws0">yy</div><div class="t m15 xbc h4b yd5 ff6 fs27 fc0 sc1 ls85 ws0">φφ<span class="_ _51"> </span>φ<span class="_ _5d"> </span>φ</div><div class="t m15 xbd h4b yd6 ff6 fs27 fc0 sc1 ls86 ws0">µµ</div><div class="c x82 yd7 w24 ha"><div class="t m15 x0 h4b y15 ff6 fs27 fc0 sc1 ls0 ws0">ε</div></div><div class="t m15 xaf h4b yd8 ff6 fs27 fc0 sc1 ls87 ws0">µµ</div><div class="t m15 xbe h4b yd9 ff6 fs27 fc0 sc1 ls88 ws0">µµ</div><div class="t m0 xbf h4c yc8 ff6 fs25 fc0 sc1 ls0 ws0">−</div><div class="t m0 xc0 h4c yda ff6 fs25 fc0 sc1 ls0 ws0">+</div><div class="t m0 x83 h4c ydb ff6 fs25 fc0 sc1 ls0 ws0">+</div><div class="t m0 xc1 h4c ydc ff6 fs25 fc0 sc1 ls0 ws0">−</div><div class="t m0 xc2 h4c ydd ff6 fs25 fc0 sc1 ls89 ws0">−+<span class="_ _5e"> </span>−+</div><div class="t m0 x95 h56 yde ff6 fs26 fc0 sc1 ls8a ws0">⎡⎤</div><div class="t m0 xb0 h56 ydf ff6 fs26 fc0 sc1 ls8b ws0">−−</div><div class="t m0 xc3 h56 ye0 ff6 fs26 fc0 sc1 ls8c ws0">⎡⎤<span class="_ _5f"> </span>⎡<span class="_ _22"></span>⎤</div><div class="c xc4 ye1 w25 ha"><div class="t m0 x0 h56 y22 ff6 fs26 fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 x35 h56 ye2 ff6 fs26 fc0 sc1 ls0 ws0">⎤</div><div class="t m0 x95 h56 ye3 ff6 fs26 fc0 sc1 ls8a ws0">⎢⎥</div><div class="t m0 xc3 h56 ye4 ff6 fs26 fc0 sc1 ls8c ws0">⎢⎥<span class="_ _5f"> </span>⎢<span class="_ _22"></span>⎥</div><div class="c xc4 ye5 w25 ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x35 h56 ye6 ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x95 h56 ye7 ff6 fs26 fc0 sc1 ls8a ws0">⎢⎥</div><div class="t m0 x8 h56 ye8 ff6 fs26 fc0 sc1 ls8d ws0">−−</div><div class="t m0 xc3 h56 ye9 ff6 fs26 fc0 sc1 ls8c ws0">⎢⎥<span class="_ _5f"> </span>⎢<span class="_ _22"></span>⎥</div><div class="c xc4 yea w25 ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x35 h56 yeb ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x95 h56 yec ff6 fs26 fc0 sc1 ls8a ws0">⎢⎥</div><div class="t m0 x66 h56 yed ff6 fs26 fc0 sc1 ls8e ws0">=+</div><div class="t m0 xc3 h56 yee ff6 fs26 fc0 sc1 ls8c ws0">⎢⎥<span class="_ _5f"> </span>⎢<span class="_ _22"></span>⎥</div><div class="c xc4 yef w25 ha"><div class="t m0 x0 h56 y22 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x35 h56 yf0 ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x95 h56 yf1 ff6 fs26 fc0 sc1 ls8a ws0">⎢⎥</div><div class="t m0 xc3 h56 yf2 ff6 fs26 fc0 sc1 ls8c ws0">⎢⎥<span class="_ _5f"> </span>⎢<span class="_ _22"></span>⎥</div><div class="c xc4 yf3 w25 ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x35 h56 yf4 ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x95 h56 yf5 ff6 fs26 fc0 sc1 ls8a ws0">⎢⎥</div><div class="t m0 xaf h56 yf6 ff6 fs26 fc0 sc1 ls8f ws0">−−</div><div class="t m0 xc3 h56 yf7 ff6 fs26 fc0 sc1 ls8c ws0">⎢⎥<span class="_ _5f"> </span>⎢<span class="_ _22"></span>⎥</div><div class="c xc4 yf8 w25 ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 x35 h56 yf9 ff6 fs26 fc0 sc1 ls0 ws0">⎦</div><div class="t m0 xc3 h56 yfa ff6 fs26 fc0 sc1 ls8c ws0">⎣⎦<span class="_ _5f"> </span>⎣<span class="_ _22"></span>⎦</div><div class="t m0 x95 h56 yfb ff6 fs26 fc0 sc1 ls8a ws0">⎢⎥</div><div class="t m0 x95 h56 yfc ff6 fs26 fc0 sc1 ls8a ws0">⎣⎦</div><div class="t m0 xc5 h57 yd5 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 xc5 h57 ycd ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 xc5 h57 yfd ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x8 h57 yfe ff8 fs2 fc0 sc1 ls90 ws0"></div><div class="t m0 xc6 h57 yff ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x96 h57 y100 ff8 fs2 fc0 sc1 ls91 ws0"><span class="_ _31"></span><span class="_ _15"></span><span class="_ _5b"> </span></div><div class="t m0 xc5 h57 y101 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x34 h3 y102 ff3 fs0 fc0 sc1 ls16 ws0"> <span class="ff1 ls0">（</span><span class="ls6a">13<span class="ff1 ls0">）<span class="ff3"> </span></span></span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></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://static.pudn.com/prod/directory_preview_static/622b2e92ff7f9c46a68987ec/bg3.jpg"><div class="t m0 x2 h2 y5c ff1 fs0 fc0 sc1 ls0 ws0">观察方程</div><div class="c x8b y103 w3 h2a"><div class="t m21 x0 h16 y69 ff6 fs7 fc0 sc1 ls0 ws0">(</div></div><div class="t m21 x86 h16 y104 ff6 fs7 fc0 sc1 ls0 ws0">)</div><div class="t m0 x23 h3 y5c ff3 fs2a fc0 sc1 ls0 ws0">1<span class="_ _60"></span><span class="ff5">n<span class="_ _11"> </span><span class="ff6">=<span class="_ _61"> </span><span class="ff1 fs0">：<span class="ff3"> </span></span></span></span></div><div class="t m22 xc7 h58 y105 ff6 fs2d fc0 sc1 ls92 ws0">[]</div><div class="t m0 x2c h59 y106 ff3 fs2e fc0 sc1 ls0 ws0">1</div><div class="t m0 x46 h59 y107 ff3 fs2e fc0 sc1 ls0 ws0">1</div><div class="t m0 xab h5a y108 ff3 fs2f fc0 sc1 ls93 ws0">10<span class="_ _62"> </span>0</div><div class="t m0 xc8 h5b y109 ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 xc9 h5b y10a ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x65 h5b y10b ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x43 h5b y10c ff5 fs2e fc0 sc1 ls94 ws0">tp</div><div class="t m0 x47 h5c y10d ff5 fs2f fc0 sc1 ls0 ws0">y</div><div class="t m0 xca h5c y10e ff5 fs2f fc0 sc1 ls0 ws0">y</div><div class="t m0 xbe h5c y10f ff5 fs2f fc0 sc1 ls0 ws0">y</div><div class="t m0 x2e h5c y110 ff5 fs2f fc0 sc1 ls0 ws0">y</div><div class="c x17 y111 w26 ha"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">µ</div></div><div class="c x5d y112 w27 ha"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">µ</div></div><div class="t m12 x9a h5d y108 ff6 fs30 fc0 sc1 ls0 ws0">µ</div><div class="c xb5 y113 w28 ha"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">µ</div></div><div class="t m0 x4a h5e y106 ff6 fs2e fc0 sc1 ls0 ws0">−</div><div class="t m0 x47 h5e y107 ff6 fs2e fc0 sc1 ls95 ws0">−+</div><div class="t m0 x69 h5f y10d ff6 fs2f fc0 sc1 ls0 ws0">−</div><div class="c xcb y114 w29 ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 x80 h5f y115 ff6 fs2f fc0 sc1 ls0 ws0">⎤</div><div class="c xcb y116 w29 ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x80 h5f y117 ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x27 h5f y118 ff6 fs2f fc0 sc1 ls0 ws0">−</div><div class="c xcb y119 w29 ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x80 h5f y11a ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x29 h5f y11b ff6 fs2f fc0 sc1 ls96 ws0">=+</div><div class="c xcb y11c w29 ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x80 h5f y11d ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="c xcb y11e w29 ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x80 h5f y11f ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="c x17 y113 w2a ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">−</div></div><div class="c xcb y120 w29 ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x80 h5f y121 ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="c xcb y122 w29 ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 x80 h5f y123 ff6 fs2f fc0 sc1 ls0 ws0">⎦</div><div class="t m0 x4b h60 y124 ff8 fs2f fc0 sc1 ls0 ws0"></div><div class="t m0 x69 h60 y125 ff8 fs2f fc0 sc1 ls0 ws0"></div><div class="t m0 xcc h3 y126 ff3 fs0 fc0 sc1 ls17 ws2"> <span class="ls5f ws0"> <span class="ff1 ls0">（</span><span class="ls6a">14<span class="ff1 ls0">）<span class="ff3"> </span></span></span></span></div><div class="t m0 x3 h3 y127 ff1 fs0 fc0 sc1 ls0 ws0">此时，<span class="ff3"> </span></div><div class="t m0 xa8 h61 y128 ff3 fsb fc0 sc1 ls0 ws0">1</div><div class="t m0 x3a h61 y129 ff3 fsb fc0 sc1 ls0 ws0">1</div><div class="t m0 x22 h5b y12a ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x86 h5b y12b ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 xcd h5b y12c ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x23 h5b y12d ff5 fs2e fc0 sc1 ls94 ws0">tp</div><div class="t m0 xce h5c y12e ff5 fs2f fc0 sc1 ls0 ws0">y</div><div class="t m0 x23 h5c y12f ff5 fs2f fc0 sc1 ls0 ws0">y</div><div class="t m0 x6 h5c y130 ff5 fs2f fc0 sc1 ls0 ws0">y</div><div class="c x15 y131 w26 ha"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">µ</div></div><div class="c x20 y132 w27 ha"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">µ</div></div><div class="t m12 x37 h5d y133 ff6 fs30 fc0 sc1 ls0 ws0">ξ</div><div class="c xb1 y134 w28 ha"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">µ</div></div><div class="t m0 x92 h62 y128 ff6 fsb fc0 sc1 ls0 ws0">−</div><div class="t m0 xce h62 y129 ff6 fsb fc0 sc1 ls97 ws0">−+</div><div class="t m0 x2a h5f y12e ff6 fs2f fc0 sc1 ls0 ws0">−</div><div class="t m0 x1f h5f y135 ff6 fs2f fc0 sc1 ls98 ws0">⎡⎤</div><div class="t m0 x1f h5f y136 ff6 fs2f fc0 sc1 ls98 ws0">⎢⎥</div><div class="t m0 x1e h5f y12f ff6 fs2f fc0 sc1 ls0 ws0">−</div><div class="t m0 x1f h5f y137 ff6 fs2f fc0 sc1 ls98 ws0">⎢⎥</div><div class="t m0 x95 h5f y138 ff6 fs2f fc0 sc1 ls0 ws0">=</div><div class="t m0 x1f h5f y139 ff6 fs2f fc0 sc1 ls98 ws0">⎢⎥</div><div class="t m0 x1f h5f y13a ff6 fs2f fc0 sc1 ls98 ws0">⎢⎥</div><div class="t m0 x15 h5f y13b ff6 fs2f fc0 sc1 ls0 ws0">−</div><div class="t m0 x1f h5f y13c ff6 fs2f fc0 sc1 ls98 ws0">⎢⎥</div><div class="t m0 x1f h5f y13d ff6 fs2f fc0 sc1 ls98 ws0">⎣⎦</div><div class="t m0 x2a h63 y13e ff8 fsa fc0 sc1 ls0 ws0"></div><div class="t m0 xb2 h3 y13f ff3 fs0 fc0 sc1 ls99 ws0"> </div><div class="t m0 xcf h61 y140 ff3 fsb fc0 sc1 ls9a ws0">12<span class="_ _59"> </span>1</div><div class="t m0 xa h48 y141 ff3 fs26 fc0 sc1 ls9b ws0">10<span class="_ _5a"> </span>0<span class="_ _16"> </span>0</div><div class="t m0 xa h48 y142 ff3 fs26 fc0 sc1 ls9c ws0">01<span class="_ _63"> </span>0<span class="_ _5b"> </span>0</div><div class="t m0 xa h48 y143 ff3 fs26 fc0 sc1 ls7d ws0">00<span class="_ _5a"> </span>1<span class="_ _5b"> </span>0</div><div class="t m0 xd0 h5b y140 ff5 fs2e fc0 sc1 ls9d ws0">pp</div><div class="t m0 xd1 h4a y13f ff5 fs26 fc0 sc1 ls0 ws0">F</div><div class="c xd2 y144 w2b ha"><div class="t m15 x0 h4b y15 ff6 fs27 fc0 sc1 ls0 ws0">φ</div></div><div class="t m15 x78 h4b y145 ff6 fs27 fc0 sc1 ls9e ws0">φφ<span class="_ _1e"></span>φ</div><div class="t m0 x1c h62 y140 ff6 fsb fc0 sc1 ls0 ws0">−</div><div class="c x32 y146 w2c ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 xd3 h56 y147 ff6 fs26 fc0 sc1 ls0 ws0">⎤</div><div class="c x32 y148 w2c ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xd3 h56 y149 ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="c x32 y14a w2c ha"><div class="t m0 x0 h56 y22 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xd3 h56 y14b ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="c x32 y14c w2c ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xd3 h56 y14d ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="t m0 xb7 h56 y14e ff6 fs26 fc0 sc1 ls0 ws0">=</div><div class="c x32 y14f w2c ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xd3 h56 y150 ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="c x32 y151 w2c ha"><div class="t m0 x0 h56 y22 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xd3 h56 y152 ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="c x32 y153 w2c ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xd3 h56 y154 ff6 fs26 fc0 sc1 ls0 ws0">⎥</div><div class="c x32 y155 w2c ha"><div class="t m0 x0 h56 y15 ff6 fs26 fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 xd3 h56 y156 ff6 fs26 fc0 sc1 ls0 ws0">⎦</div><div class="t m0 xd4 h57 y145 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 xd4 h57 y141 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 xd4 h57 y157 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x9c h57 y158 ff8 fs2 fc0 sc1 ls91 ws0"><span class="_ _31"></span><span class="_ _15"></span><span class="_ _5b"> </span></div><div class="t m0 xd4 h57 y159 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 xd5 h3 y13f ff3 fs0 fc0 sc1 ls0 ws0"> </div><div class="t m0 xaa h61 y15a ff3 fsb fc0 sc1 ls0 ws0">1</div><div class="t m0 x96 h61 y15b ff3 fsb fc0 sc1 ls0 ws0">1</div><div class="t m0 x9b h48 y15c ff3 fs26 fc0 sc1 ls0 ws0">0</div><div class="t m0 x9b h48 y15d ff3 fs26 fc0 sc1 ls0 ws0">0</div><div class="t m0 x9b h5b y15a ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x95 h5b y15e ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x9a h4a y15f ff5 fs26 fc0 sc1 ls0 ws0">v</div><div class="t m15 x92 h4b y160 ff6 fs27 fc0 sc1 ls0 ws0">ε</div><div class="t m0 x3a h62 y15a ff6 fsb fc0 sc1 ls0 ws0">+</div><div class="t m0 x56 h62 y15b ff6 fsb fc0 sc1 ls0 ws0">+</div><div class="t m0 x53 h56 y161 ff6 fs26 fc0 sc1 ls9f ws0">⎡⎤</div><div class="t m0 x53 h56 y162 ff6 fs26 fc0 sc1 ls9f ws0">⎢⎥</div><div class="t m0 x53 h56 y163 ff6 fs26 fc0 sc1 ls9f ws0">⎢⎥</div><div class="t m0 xc7 h56 y164 ff6 fs26 fc0 sc1 ls0 ws0">=</div><div class="t m0 x53 h56 y165 ff6 fs26 fc0 sc1 ls9f ws0">⎢⎥</div><div class="t m0 x53 h56 y166 ff6 fs26 fc0 sc1 ls9f ws0">⎢⎥</div><div class="t m0 x53 h56 y167 ff6 fs26 fc0 sc1 ls9f ws0">⎣⎦</div><div class="t m0 x2a h57 y168 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x98 h3 y15f ff3 fs0 fc0 sc1 ls16 ws3"> </div><div class="t m0 xd6 h61 y169 ff3 fsb fc0 sc1 ls0 ws0">2</div><div class="t m0 xd7 h5a y16a ff3 fs2f fc0 sc1 lsa0 ws0">00</div><div class="t m0 x5e h5a y16b ff3 fs2f fc0 sc1 lsa1 ws0">00<span class="_"> </span>0</div><div class="t m0 x5e h5a y16c ff3 fs2f fc0 sc1 lsa1 ws0">00<span class="_"> </span>0</div><div class="t m0 xa h5c y16d ff5 fs2f fc0 sc1 ls0 ws0">Q</div><div class="t m12 xb h5d y16a ff6 fs30 fc0 sc1 ls0 ws0">σ</div><div class="c xd8 y16e w2d ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 xf h5f y16f ff6 fs2f fc0 sc1 ls0 ws0">⎤</div><div class="c xd8 y170 w2d ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf h5f y171 ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="c xd8 y172 w2d ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf h5f y173 ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x6c h5f y174 ff6 fs2f fc0 sc1 ls0 ws0">=</div><div class="c xd8 y175 w2d ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf h5f y176 ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="c xd8 y177 w2d ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf h5f y178 ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="c xd8 y179 w2d ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf h5f y17a ff6 fs2f fc0 sc1 ls0 ws0">⎥</div><div class="c xd8 y17b w2d ha"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 xf h5f y17c ff6 fs2f fc0 sc1 ls0 ws0">⎦</div><div class="t m0 xd9 h63 y16a ff8 fsa fc0 sc1 ls0 ws0"></div><div class="t m0 xd9 h63 y17d ff8 fsa fc0 sc1 ls0 ws0"></div><div class="t m0 xe h63 y17e ff8 fsa fc0 sc1 lsa2 ws0"><span class="_ _64"></span><span class="_ _64"></span></div><div class="t m0 xd9 h63 y17f ff8 fsa fc0 sc1 ls0 ws0"></div><div class="t m0 xd3 h3 y15f ff3 fs0 fc0 sc1 ls0 ws0"> </div><div class="t m23 x4b h64 y180 ff6 fs31 fc0 sc1 lsa3 ws0">[]</div><div class="t m0 x3c h5a y181 ff3 fs2f fc0 sc1 lsa4 ws0"> <span class="_ _59"> </span> <span class="_ _26"> </span>1</div><div class="t m0 xb1 h5a y182 ff3 fs2f fc0 sc1 lsa4 ws0">1<span class="_ _65"> </span>0<span class="_ _39"> </span>0<span class="_ _5b"> </span> <span class="_ _66"> </span>0<span class="_ _15"></span> <span class="_ _26"> </span>0</div><div class="t m0 x3b h5b y183 ff5 fs2e fc0 sc1 lsa5 ws0">tt<span class="_ _67"> </span>t</div><div class="t m0 xd2 h5b y184 ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x45 h5c y181 ff5 fs2f fc0 sc1 lsa6 ws0">yA<span class="_ _68"></span>x</div><div class="t m0 xce h5c y182 ff5 fs2f fc0 sc1 lsa7 ws0">Hw<span class="_ _4f"></span>R</div><div class="c x33 y185 w15 h65"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">µ</div></div><div class="c xa y186 w8 h66"><div class="t m0 x0 h5f y15 ff6 fs2f fc0 sc1 ls0 ws0">′</div></div><div class="t m0 x3a h5f y181 ff6 fs2f fc0 sc1 lsa8 ws0">==<span class="_ _1d"></span>=</div><div class="t m0 x2a h5f y187 ff6 fs2f fc0 sc1 ls0 ws0">′</div><div class="t m0 xaa h5f y182 ff6 fs2f fc0 sc1 lsa9 ws0">==<span class="_ _69"></span>=</div><div class="t m0 xce h67 y181 ff2 fs2a fc0 sc1 ls0 ws0">y</div><div class="t m0 xda h68 y188 ff8 fs2a fc0 sc1 ls0 ws0"></div><div class="t m0 xa5 h3 y189 ff3 fs0 fc0 sc1 ls0 ws0"> </div><div class="t m0 x3 h2 y18a ff1 fs0 fc0 sc1 ls5 ws0">这里的状态方程为一阶向量差分方程；</div><div class="t m0 x58 h2 y18b ff5 fs10 fc0 sc1 ls0 ws0">F<span class="_ _0"> </span><span class="ff1 fs0 ls4">为矩阵。<span class="_ _f"></span>观察方程为平凡<span class="_ _15"></span>恒</span></div><div class="t m0 x3 h3 y18c ff1 fs0 fc0 sc1 ls0 ws0">等式。因此表达式（<span class="ff3 ls6a">13</span><span class="lsaa">）和（<span class="ff3 ls6a">14</span><span class="lsab">）是</span></span></div><div class="c xb6 y18d w3 h2a"><div class="t m21 x0 h16 y69 ff6 fs7 fc0 sc1 ls0 ws0">(</div></div><div class="t m21 xdb h16 y18e ff6 fs7 fc0 sc1 ls0 ws0">)</div><div class="c x32 y18f w2e h69"><div class="t m0 x0 h5c y15 ff5 fs2f fc0 sc1 ls0 ws0">A</div></div><div class="t m0 x6b h3 y190 ff5 fs2f fc0 sc1 lsac ws0">Rp<span class="_ _22"></span><span class="ff1 fs0 lsaa">过程（<span class="ff3 ls6a">12</span><span class="ls0">）的另一种表达</span></span></div><div class="t m0 x3 h3 y191 ff1 fs0 fc0 sc1 ls4 ws0">式。利用状态空间表示能够系统的研究其动态性质。<span class="ff3 ls0"> </span></div><div class="t m0 x2 h3 y192 ff1 fs0 fc0 sc1 ls0 ws0">例<span class="_ _0"> </span><span class="ff3 ls6a ws5">2 </span></div><div class="t m24 x23 h8 y193 ff6 fs3 fc0 sc1 lsad ws0">()</div><div class="t m0 xce h5a y194 ff3 fs2f fc0 sc1 ls0 ws0">1</div><div class="c x87 y195 w2f h22"><div class="t m0 x0 h5c y22 ff5 fs2f fc0 sc1 ls0 ws0">M</div></div><div class="t m0 x4f h3 y194 ff5 fs2f fc0 sc1 ls0 ws0">A<span class="_ _3a"> </span><span class="ff1 fs0">过程<span class="ff3"> </span></span></div><div class="t m0 xdc h61 y196 ff3 fsb fc0 sc1 ls0 ws0">1<span class="_ _6a"></span><span class="ff5 fs2e lsae">tt<span class="_ _1e"></span>t</span></div><div class="t m0 x6 h4a y197 ff5 fs26 fc0 sc1 ls0 ws0">y</div><div class="c x3a y198 w30 hf"><div class="t m15 x0 h4b y15 ff6 fs27 fc0 sc1 ls0 ws0">µ</div></div><div class="t m15 x49 h4b y197 ff6 fs27 fc0 sc1 lsaf ws0">εθ<span class="_ _6b"></span>ε</div><div class="c x2e y199 w21 h25"><div class="t m0 x0 h62 y62 ff6 fsb fc0 sc1 ls0 ws0">−</div></div><div class="t m0 x26 h3 y197 ff6 fs26 fc0 sc1 lsb0 ws0">=+<span class="_ _23"></span>+<span class="_ _6c"> </span><span class="ff3 fs0 ls17 ws2"> <span class="ls16 ws3"> <span class="ff1 ls0 ws0">（<span class="ff3 ls6a">15</span>）<span class="ff3"> </span></span></span></span></div><div class="t m0 x3 h3 y19a ff1 fs0 fc0 sc1 ls5 ws0">写成状态空间形式：<span class="ff3 ls0"> </span></div><div class="t m0 x2 h2 y19b ff1 fs0 fc0 sc1 ls0 ws0">状态方程</div><div class="c x8b y19c w3 h2a"><div class="t m1b x0 h16 y69 ff6 fs7 fc0 sc1 ls0 ws0">(</div></div><div class="t m1b x26 h16 y19d ff6 fs7 fc0 sc1 ls0 ws0">)</div><div class="t m0 x23 h3 y19e ff3 fs2f fc0 sc1 ls0 ws0">2<span class="_ _6d"></span><span class="ff5">r<span class="_ _0"> </span><span class="ff6">=<span class="_ _6e"> </span><span class="ff3 fs0"> </span></span></span></div><div class="t m0 x97 h61 y19f ff3 fsb fc0 sc1 ls0 ws0">1</div><div class="t m0 x19 h61 y1a0 ff3 fsb fc0 sc1 ls0 ws0">1</div><div class="t m0 xcb h61 y1a1 ff3 fsb fc0 sc1 ls0 ws0">1</div><div class="t m0 x3a h5a y1a2 ff3 fs2f fc0 sc1 lsb1 ws0">00</div><div class="t m0 x3a h5a y1a3 ff3 fs2f fc0 sc1 lsb2 ws0">10<span class="_ _6f"> </span>0</div><div class="t m0 x13 h5b y19f ff5 fs2e fc0 sc1 lsb3 ws0">tt</div><div class="t m0 xdd h5b y1a4 ff5 fs2e fc0 sc1 ls0 ws0">t</div><div class="t m0 x91 h5b y1a5 ff5 fs2e fc0 sc1 lsb4 ws0">tt</div><div class="t m12 x8f h5d y1a6 ff6 fs30 fc0 sc1 lsb5 ws0">εε</div><div class="c xde y1a7 w8 ha"><div class="t m12 x0 h5d y15 ff6 fs30 fc0 sc1 ls0 ws0">ε</div></div><div class="t m12 x95 h5d y1a8 ff6 fs30 fc0 sc1 lsb6 ws0">εε</div><div class="t m0 x91 h6a y19f ff6 fs29 fc0 sc1 ls0 ws0">+</div><div class="t m0 xd1 h6a y1a9 ff6 fs29 fc0 sc1 ls0 ws0">+</div><div class="t m0 xdf h6a y1aa ff6 fs29 fc0 sc1 ls0 ws0">−</div><div class="t m0 xa7 h5f y1ab ff6 fs2f fc0 sc1 lsb7 ws0">⎡⎤<span class="_ _58"> </span>⎡⎤</div><div class="t m0 xe0 h5f y1ac ff6 fs2f fc0 sc1 lsb8 ws0">⎡⎤<span class="_ _3a"> </span>⎡<span class="_ _28"></span>⎤</div><div class="t m0 x1d h5f y1ad ff6 fs2f fc0 sc1 lsb9 ws0">=+</div><div class="t m0 xa7 h5f y1ae ff6 fs2f fc0 sc1 lsb7 ws0">⎢⎥<span class="_ _58"> </span>⎢⎥</div><div class="t m0 xe0 h5f y1af ff6 fs2f fc0 sc1 lsb8 ws0">⎢⎥<span class="_ _3a"> </span>⎢<span class="_ _28"></span>⎥</div><div class="t m0 xe0 h5f y1b0 ff6 fs2f fc0 sc1 lsb8 ws0">⎣⎦<span class="_ _3a"> </span>⎣<span class="_ _28"></span>⎦</div><div class="t m0 xa7 h5f y1b1 ff6 fs2f fc0 sc1 lsb7 ws0">⎣⎦<span class="_ _58"> </span>⎣⎦</div><div class="t m0 xae h3 y1b2 ff3 fs0 fc0 sc1 ls17 ws2"> <span class="ls16 ws0"> <span class="ff1 ls0">（</span><span class="ls6a">16<span class="ff1 ls0">）<span class="ff3"> </span></span></span></span></div><div class="t m0 x2 h2 y1b3 ff1 fs0 fc0 sc1 ls0 ws0">观察方程</div><div class="c x8b y1b4 w3 h7"><div class="t m24 x0 h8 y12 ff6 fs3 fc0 sc1 ls0 ws0">(</div></div><div class="t m24 x86 h8 y1b5 ff6 fs3 fc0 sc1 ls0 ws0">)</div><div class="t m0 x23 h3 y1b6 ff3 fs2f fc0 sc1 ls0 ws0">1<span class="_ _60"></span><span class="ff5">n<span class="_ _11"> </span><span class="ff6">=<span class="_ _61"> </span><span class="ff1 fs0">：<span class="ff3"> </span></span></span></span></div><div class="t m25 xb1 h6b y1b7 ff6 fs32 fc0 sc1 lsba ws0">[]</div><div class="t m0 xe1 h6c y1b8 ff3 fs33 fc0 sc1 ls0 ws0">1</div><div class="t m0 x49 h6d y1b9 ff3 fs34 fc0 sc1 ls0 ws0">1</div><div class="t m0 x47 h6e y1ba ff5 fs33 fc0 sc1 ls0 ws0">t</div><div class="t m0 xab h6e y1bb ff5 fs33 fc0 sc1 ls0 ws0">t</div><div class="t m0 xca h6e y1bc ff5 fs33 fc0 sc1 ls0 ws0">t</div><div class="t m0 x4f h6f y1b9 ff5 fs34 fc0 sc1 ls0 ws0">y</div><div class="c x75 y1bd w31 ha"><div class="t m16 x0 h70 y15 ff6 fs35 fc0 sc1 ls0 ws0">ε</div></div><div class="t m16 x9b h70 y1b9 ff6 fs35 fc0 sc1 lsbb ws0">µθ</div><div class="c x88 y1be w32 ha"><div class="t m16 x0 h70 y15 ff6 fs35 fc0 sc1 ls0 ws0">ε</div></div><div class="t m0 x47 h71 y1b8 ff6 fs33 fc0 sc1 ls0 ws0">−</div><div class="c xcb y1bf w33 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 x2c h72 y1c0 ff6 fs34 fc0 sc1 ls0 ws0">⎤</div><div class="t m0 xce h72 y1c1 ff6 fs34 fc0 sc1 lsbc ws0">=+</div><div class="c xcb y1c2 w33 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 x2c h72 y1c3 ff6 fs34 fc0 sc1 ls0 ws0">⎥</div><div class="c xcb y1c4 w33 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 x2c h72 y1c5 ff6 fs34 fc0 sc1 ls0 ws0">⎦</div><div class="t m0 x27 h3 y1c6 ff3 fs0 fc0 sc1 ls1c ws2"> <span class="ls17 ws3"> <span class="ff1 ls0 ws0">（<span class="ff3 ls6a">17</span>）<span class="ff3"> </span></span></span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></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://static.pudn.com/prod/directory_preview_static/622b2e92ff7f9c46a68987ec/bg4.jpg"><div class="t m0 x3 h3 y1 ff1 fs0 fc0 sc1 ls0 ws0">其中<span class="ff3"> </span></div><div class="t m0 x61 h6c y1c7 ff3 fs33 fc0 sc1 ls0 ws0">1</div><div class="t m0 x1b h6c y1c8 ff3 fs33 fc0 sc1 ls0 ws0">1</div><div class="t m0 x3b h6c y1c9 ff3 fs33 fc0 sc1 ls0 ws0">1</div><div class="t m0 x17 h6d y1ca ff3 fs34 fc0 sc1 lsbd ws0">00</div><div class="t m0 x44 h6d y1cb ff3 fs34 fc0 sc1 lsbe ws0"> <span class="_ _4c"> </span> </div><div class="t m0 x17 h6d y1cc ff3 fs34 fc0 sc1 lsbf ws0">10</div><div class="t m0 xa4 h6d y1cd ff3 fs34 fc0 sc1 ls0 ws0">0</div><div class="t m0 xce h6e y1ce ff5 fs33 fc0 sc1 ls0 ws0">t</div><div class="t m0 xe2 h6e y1cf ff5 fs33 fc0 sc1 ls0 ws0">t</div><div class="t m0 x8b h6e y1d0 ff5 fs33 fc0 sc1 lsc0 ws0">tt</div><div class="t m0 xce h6e y1d1 ff5 fs33 fc0 sc1 ls0 ws0">t</div><div class="t m0 xe3 h6f y1d2 ff5 fs34 fc0 sc1 lsc1 ws0">Fv</div><div class="t m16 x21 h70 y1d3 ff6 fs35 fc0 sc1 ls0 ws0">ε</div><div class="t m16 xe4 h70 y1d4 ff6 fs35 fc0 sc1 ls0 ws0">ε</div><div class="t m16 xa7 h70 y1d5 ff6 fs35 fc0 sc1 ls0 ws0">ξ</div><div class="t m16 x21 h70 y1d6 ff6 fs35 fc0 sc1 ls0 ws0">ε</div><div class="t m0 xe5 h71 y1c7 ff6 fs33 fc0 sc1 ls0 ws0">+</div><div class="t m0 xe6 h71 y1c8 ff6 fs33 fc0 sc1 ls0 ws0">+</div><div class="t m0 x26 h71 y1c9 ff6 fs33 fc0 sc1 ls0 ws0">−</div><div class="t m0 xc7 h72 y1d7 ff6 fs34 fc0 sc1 lsc2 ws0">⎡⎤</div><div class="c xe7 y1d8 w34 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 xe8 h72 y1d9 ff6 fs34 fc0 sc1 ls0 ws0">⎤</div><div class="t m0 xe9 h72 y1da ff6 fs34 fc0 sc1 lsc3 ws0">⎡⎤</div><div class="t m0 xbc h72 y1db ff6 fs34 fc0 sc1 lsc4 ws0">==<span class="_ _13"> </span>=</div><div class="t m0 xc7 h72 y1dc ff6 fs34 fc0 sc1 lsc2 ws0">⎢⎥</div><div class="c xe7 y1dd w34 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xe8 h72 y1de ff6 fs34 fc0 sc1 ls0 ws0">⎥</div><div class="t m0 xe9 h72 y1df ff6 fs34 fc0 sc1 lsc3 ws0">⎢⎥</div><div class="t m0 xe9 h72 y1e0 ff6 fs34 fc0 sc1 lsc3 ws0">⎣⎦</div><div class="c xe7 y1e1 w34 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 xe8 h72 y1e2 ff6 fs34 fc0 sc1 ls0 ws0">⎦</div><div class="t m0 xc7 h72 y1e3 ff6 fs34 fc0 sc1 lsc2 ws0">⎣⎦</div><div class="t m0 x85 h3 y1d2 ff3 fs0 fc0 sc1 ls0 ws0"> </div><div class="t m26 x3a h73 y1e4 ff6 fs36 fc0 sc1 lsc5 ws0">[]</div><div class="t m0 x20 h74 y1e5 ff3 fs37 fc0 sc1 ls0 ws0">2</div><div class="t m0 x73 h75 y1e6 ff3 fs38 fc0 sc1 ls0 ws0">0</div><div class="t m0 xbf h75 y1e7 ff3 fs38 fc0 sc1 lsc6 ws0"> <span class="_ _39"> </span> <span class="_ _59"> </span> <span class="_ _26"> </span>1</div><div class="t m0 x44 h75 y1e8 ff3 fs38 fc0 sc1 lsc7 ws0">00</div><div class="t m0 xea h75 y1e9 ff3 fs38 fc0 sc1 lsc6 ws0">1<span class="_ _70"> </span> <span class="_ _70"> </span>0<span class="_ _23"></span> <span class="_ _26"> </span>0</div><div class="t m0 xeb h76 y1ea ff5 fs37 fc0 sc1 lsc8 ws0">tt<span class="_ _71"> </span>t</div><div class="t m0 xeb h76 y1eb ff5 fs37 fc0 sc1 ls0 ws0">t</div><div class="t m0 xa3 h77 y1ec ff5 fs38 fc0 sc1 lsc9 ws0">Qy<span class="_ _72"></span>A<span class="_ _73"></span>x</div><div class="t m0 x4f h77 y1ed ff5 fs38 fc0 sc1 lsca ws0">Hw<span class="_ _74"></span>R</div><div class="t mb x3a h78 y1e6 ff6 fs39 fc0 sc1 ls0 ws0">σ</div><div class="t mb xe h78 y1e7 ff6 fs39 fc0 sc1 ls0 ws0">µ</div><div class="t mb x49 h78 y1e9 ff6 fs39 fc0 sc1 ls0 ws0">θ</div><div class="t m0 xa8 h79 y1ee ff6 fs38 fc0 sc1 lscb ws0">⎡⎤</div><div class="t m0 xa1 h79 y1ef ff6 fs38 fc0 sc1 ls0 ws0">′</div><div class="t m0 x53 h79 y1f0 ff6 fs38 fc0 sc1 lscc ws0">==<span class="_ _53"></span>=<span class="_ _75"></span>=</div><div class="t m0 xa8 h79 y1f1 ff6 fs38 fc0 sc1 lscb ws0">⎢⎥</div><div class="t m0 xa8 h79 y1f2 ff6 fs38 fc0 sc1 lscb ws0">⎣⎦</div><div class="t m0 x1d h79 y1f3 ff6 fs38 fc0 sc1 ls0 ws0">′</div><div class="t m0 x92 h79 y1f4 ff6 fs38 fc0 sc1 lscd ws0">==<span class="_ _76"></span>=</div><div class="t m0 xe1 h7a y1f5 ff2 fs38 fc0 sc1 ls0 ws0">y</div><div class="t m0 xec h3 y1f6 ff3 fs0 fc0 sc1 ls0 ws0"> </div><div class="t m0 x3 h3 y1f7 ff1 fs0 fc0 sc1 ls5 ws0">或者写成：<span class="ff3 ls0"> </span></div><div class="t m0 x2 h2 y1f8 ff1 fs0 fc0 sc1 ls0 ws0">状态方程</div><div class="c x8b y1f9 w3 h7"><div class="t m1f x0 h4d y12 ff6 fs28 fc0 sc1 ls0 ws0">(</div></div><div class="t m1f x26 h4d y1fa ff6 fs28 fc0 sc1 ls0 ws0">)</div><div class="t m0 x23 h3 y1fb ff3 fs34 fc0 sc1 ls0 ws0">2<span class="_ _6d"></span><span class="ff5">r<span class="_ _0"> </span><span class="ff6">=<span class="_ _6e"> </span><span class="ff3 fs0"> </span></span></span></div><div class="t m0 x9f h74 y1fc ff3 fs37 fc0 sc1 lsce ws0">11<span class="_ _77"></span>1</div><div class="t m0 xab h74 y1fd ff3 fs37 fc0 sc1 lscf ws0">11</div><div class="t m0 x16 h6d y1fe ff3 fs34 fc0 sc1 lsd0 ws0">01</div><div class="t m0 x16 h6d y1ff ff3 fs34 fc0 sc1 lsbd ws0">00</div><div class="t m0 x9a h76 y1fc ff5 fs37 fc0 sc1 lsd1 ws0">tt<span class="_ _78"> </span>t<span class="_ _28"></span>t<span class="_ _10"> </span>t</div><div class="t m0 xa9 h76 y1fd ff5 fs37 fc0 sc1 lsd2 ws0">tt<span class="_ _79"></span>t</div><div class="t m16 x39 h70 y200 ff6 fs35 fc0 sc1 lsd3 ws0">εθ<span class="_ _1a"></span>ε<span class="_ _7a"> </span>ε<span class="_ _7b"></span>θ<span class="_ _1a"></span>ε<span class="_ _6e"> </span>ε</div><div class="t m16 x8b h70 y201 ff6 fs35 fc0 sc1 lsd4 ws0">θε<span class="_ _7c"> </span>θε<span class="_ _7d"> </span>θε</div><div class="t m0 x8b h71 y1fc ff6 fs33 fc0 sc1 lsd5 ws0">+−<span class="_ _77"></span>+</div><div class="t m0 xc7 h71 y202 ff6 fs33 fc0 sc1 lsd6 ws0">++</div><div class="t m0 x96 h72 y200 ff6 fs34 fc0 sc1 lsd7 ws0">++</div><div class="t m0 x12 h72 y203 ff6 fs34 fc0 sc1 lsd8 ws0">⎡⎤<span class="_ _5b"> </span>⎡⎤<span class="_ _7e"></span>⎡<span class="_ _6"></span>⎤</div><div class="t m0 x14 h72 y204 ff6 fs34 fc0 sc1 lsd9 ws0">⎡⎤</div><div class="t m0 xea h72 y205 ff6 fs34 fc0 sc1 lsda ws0">=+</div><div class="t m0 x12 h72 y206 ff6 fs34 fc0 sc1 lsd8 ws0">⎢⎥<span class="_ _5b"> </span>⎢⎥<span class="_ _7e"></span>⎢<span class="_ _6"></span>⎥</div><div class="t m0 x14 h72 y207 ff6 fs34 fc0 sc1 lsd9 ws0">⎢⎥</div><div class="t m0 x14 h72 y208 ff6 fs34 fc0 sc1 lsd9 ws0">⎣⎦</div><div class="t m0 x12 h72 y209 ff6 fs34 fc0 sc1 lsd8 ws0">⎣⎦<span class="_ _5b"> </span>⎣⎦<span class="_ _7e"></span>⎣<span class="_ _6"></span>⎦</div><div class="t m0 xc4 h3 y20a ff3 fs0 fc0 sc1 ls17 ws2"> <span class="ls50 ws0"> </span></div><div class="t m0 x2 h2 y20b ff1 fs0 fc0 sc1 ls0 ws0">观察方程</div><div class="c x8b y20c w3 h7"><div class="t m24 x0 h8 y12 ff6 fs3 fc0 sc1 ls0 ws0">(</div></div><div class="t m24 x86 h8 y20d ff6 fs3 fc0 sc1 ls0 ws0">)</div><div class="t m0 x23 h3 y20e ff3 fs34 fc0 sc1 ls0 ws0">1<span class="_ _60"></span><span class="ff5">n<span class="_ _11"> </span><span class="ff6">=<span class="_ _61"> </span><span class="ff1 fs0">：<span class="ff3"> </span></span></span></span></div><div class="t m27 xea h6b y20f ff6 fs32 fc0 sc1 lsdb ws0">[]</div><div class="t m0 xed h74 y210 ff3 fs37 fc0 sc1 ls0 ws0">1</div><div class="t m0 x15 h6d y211 ff3 fs34 fc0 sc1 lsdc ws0">10</div><div class="t m0 x2d h76 y210 ff5 fs37 fc0 sc1 lsdd ws0">tt</div><div class="t m0 x91 h76 y212 ff5 fs37 fc0 sc1 ls0 ws0">t</div><div class="t m0 x4a h76 y213 ff5 fs37 fc0 sc1 ls0 ws0">t</div><div class="t m0 x9f h6f y211 ff5 fs34 fc0 sc1 ls0 ws0">y</div><div class="t m16 x3d h70 y214 ff6 fs35 fc0 sc1 lsde ws0">εθ<span class="_ _6b"></span>ε</div><div class="t m16 x1d h70 y215 ff6 fs35 fc0 sc1 ls0 ws0">µ</div><div class="t m16 x2e h70 y216 ff6 fs35 fc0 sc1 lsdf ws0">θε</div><div class="t m0 x18 h71 y210 ff6 fs33 fc0 sc1 ls0 ws0">−</div><div class="t m0 x88 h72 y214 ff6 fs34 fc0 sc1 ls0 ws0">+</div><div class="c x40 y217 w35 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 xd1 h72 y218 ff6 fs34 fc0 sc1 ls0 ws0">⎤</div><div class="t m0 x4f h72 y219 ff6 fs34 fc0 sc1 lsbc ws0">=+</div><div class="c x40 y21a w35 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xd1 h72 y21b ff6 fs34 fc0 sc1 ls0 ws0">⎥</div><div class="c x40 y21c w35 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 xd1 h72 y21d ff6 fs34 fc0 sc1 ls0 ws0">⎦</div><div class="t m0 xee h3 y21e ff3 fs0 fc0 sc1 ls16 ws1"> <span class="ls69 ws0"> </span></div><div class="t m0 x3 h3 y21f ff1 fs0 fc0 sc1 ls3 ws0">一个动态系统可以用多种不同的状态空间来表示。<span class="ff3 ls0"> </span></div><div class="t m0 x2 h3 y220 ff1 fs0 fc0 sc1 ls0 ws0">例<span class="_ _0"> </span><span class="ff3 ls6a ws6">3 </span></div><div class="t m1f xef h4d y221 ff6 fs28 fc0 sc1 lse0 ws0">()</div><div class="t m0 x26 h3 y222 ff3 fs34 fc0 sc1 ls0 ws0">,<span class="_ _7f"></span><span class="ff5 lse1">ARMA<span class="_ _80"> </span>p<span class="_ _16"> </span>q<span class="_ _3"> </span><span class="ff1 fs0 ls0">过程<span class="ff3"> </span></span></span></div><div class="t m0 x2 h2 y223 ff1 fs0 fc0 sc1 ls0 ws0">令</div><div class="t m28 x9a h16 y224 ff6 fs7 fc0 sc1 ls0 ws0">{</div><div class="c x9b y225 w1a h2a"><div class="t m28 x0 h16 y69 ff6 fs7 fc0 sc1 ls0 ws0">}</div></div><div class="t m0 x55 h6d y226 ff3 fs34 fc0 sc1 lse2 ws0">max<span class="_ _6e"> </span>,<span class="_ _2"> </span>1<span class="_ _81"></span><span class="ff5 lse3">rp<span class="_ _43"></span>q<span class="_ _82"></span><span class="ff6 lse4">=+</span></span></div><div class="t m0 xaa h3 y227 ff1 fs0 fc0 sc1 ls0 ws0">，则<span class="ff3"> </span></div><div class="t m29 x3a h4d y228 ff6 fs28 fc0 sc1 lse5 ws0">()</div><div class="c xf0 y229 w3 h7b"><div class="t m29 x0 h4d y22a ff6 fs28 fc0 sc1 ls0 ws0">(</div></div><div class="t m29 x9c h4d y228 ff6 fs28 fc0 sc1 ls0 ws0">)</div><div class="c x51 y229 w3 h7b"><div class="t m29 x0 h4d y22a ff6 fs28 fc0 sc1 ls0 ws0">(</div></div><div class="t m29 xec h4d y228 ff6 fs28 fc0 sc1 ls0 ws0">)</div><div class="t m0 xe0 h74 y22b ff3 fs37 fc0 sc1 lse6 ws0">11<span class="_ _3e"> </span>2<span class="_ _4"> </span>2</div><div class="t m0 x73 h74 y22c ff3 fs37 fc0 sc1 lse7 ws0">11<span class="_ _14"> </span>2<span class="_ _4"> </span>2<span class="_ _83"> </span>1<span class="_ _10"> </span>1</div><div class="t m0 x33 h6d y22d ff3 fs34 fc0 sc1 lsbe ws0">...</div><div class="t m0 xb3 h6d y22e ff3 fs34 fc0 sc1 lse8 ws7"> <span class="_ _84"> </span>....</div><div class="t m0 x54 h76 y22b ff5 fs37 fc0 sc1 lse9 ws0">tt<span class="_ _85"> </span>t<span class="_ _13"> </span>r<span class="_ _86"></span>t<span class="_ _44"></span>r</div><div class="t m0 x44 h76 y22c ff5 fs37 fc0 sc1 lsea ws0">tt<span class="_ _49"> </span>t<span class="_ _87"> </span>r<span class="_ _88"></span>t<span class="_ _89"></span>r</div><div class="t m0 x37 h6f y22d ff5 fs34 fc0 sc1 lseb ws0">yy<span class="_ _85"> </span>y<span class="_ _58"> </span>y</div><div class="c xf1 y22f w36 ha"><div class="t m16 x0 h70 y15 ff6 fs35 fc0 sc1 ls0 ws0">µ</div></div><div class="t m16 x86 h70 y22d ff6 fs35 fc0 sc1 lsec ws0">φµ<span class="_ _12"></span>φ<span class="_ _41"> </span>µ<span class="_ _c"></span>φ<span class="_ _8"> </span>µ</div><div class="t m16 x3a h70 y22e ff6 fs35 fc0 sc1 lsed ws0">εθ<span class="_ _18"></span>ε<span class="_ _3"> </span>θ<span class="_ _8a"></span>ε<span class="_ _8b"> </span>θ<span class="_ _c"></span>ε</div><div class="t m0 xb1 h71 y22b ff6 fs33 fc0 sc1 lsee ws0">−−<span class="_ _26"> </span>−</div><div class="t m0 xb4 h71 y230 ff6 fs33 fc0 sc1 lsef ws0">−−<span class="_ _13"> </span>−<span class="_ _2f"></span>−<span class="_ _1b"></span>+</div><div class="c x8b y22f w37 ha"><div class="t m0 x0 h72 y15 ff6 fs34 fc0 sc1 ls0 ws0">−</div></div><div class="t m0 xab h72 y22d ff6 fs34 fc0 sc1 lsf0 ws0">=−<span class="_ _7"></span>+<span class="_ _8"> </span>−<span class="_ _8c"></span>+<span class="_ _8d"></span>+<span class="_ _4"></span>−</div><div class="t m0 x92 h72 y22e ff6 fs34 fc0 sc1 lsf1 ws0">++<span class="_ _3c"> </span>+<span class="_ _8e"> </span>+<span class="_ _4"></span>+</div><div class="t m0 xf2 h3 y231 ff3 fs0 fc0 sc1 ls99 ws0"> <span class="ff1 ls0">（</span><span class="ls6a">18<span class="ff1 ls0">）<span class="ff3"> </span></span></span></div><div class="t m0 x3 h2 y232 ff1 fs0 fc0 sc1 ls0 ws0">这里当</div><div class="t m0 x8 h2 y233 ff5 fs3a fc0 sc1 lsf2 ws0">rp<span class="_ _7e"></span><span class="ff6 ls0">><span class="_ _8f"> </span><span class="ff1 fs0">时，<span class="_ _4a"> </span><span class="ff3 fs3b">0</span></span></span></div><div class="t m0 xab h7c y234 ff5 fs3c fc0 sc1 ls0 ws0">j</div><div class="c x97 y235 w8 ha"><div class="t m2a x0 h7d y22 ff6 fs3d fc0 sc1 ls0 ws0">φ</div></div><div class="t m0 x53 h2 y233 ff6 fs3b fc0 sc1 ls0 ws0">=<span class="_ _4d"> </span><span class="ff1 fs0 lsf3">；且<span class="_ _0"> </span>当<span class="_ _5b"> </span><span class="ff5 fs3a lsf4">rq<span class="_ _90"></span><span class="ff6 fs3b ls0">><span class="_ _9"> </span><span class="ff1 fs0">时，<span class="_ _3e"> </span></span><span class="ff3">0</span></span></span></span></div><div class="t m0 x32 h76 y234 ff5 fs37 fc0 sc1 ls0 ws0">r</div><div class="c xae y235 w38 hf"><div class="t m2a x0 h7d y22 ff6 fs3d fc0 sc1 ls0 ws0">θ</div></div><div class="c x9c y235 w12 hf"><div class="t m0 x0 h7e y22 ff6 fs3b fc0 sc1 ls0 ws0">=</div></div><div class="t m0 x78 h2 y233 ff1 fs0 fc0 sc1 ls0 ws0">则状态方程</div><div class="t m2b xa6 h8 y236 ff6 fs3 fc0 sc1 ls0 ws0">{</div><div class="c xf3 y237 w1a h7"><div class="t m2b x0 h8 y12 ff6 fs3 fc0 sc1 ls0 ws0">}</div></div><div class="c xe5 y238 w3 h7f"><div class="t m2c x0 h42 y239 ff6 fs22 fc0 sc1 ls0 ws0">(</div></div><div class="t m2c xf4 h42 y23a ff6 fs22 fc0 sc1 ls0 ws0">)</div><div class="t m0 x6d h6d y233 ff3 fs34 fc0 sc1 lse2 ws0">max<span class="_ _6e"> </span>,<span class="_ _2"> </span>1<span class="_ _81"></span><span class="ff5 lse3">rp<span class="_ _43"></span>q<span class="_ _82"></span><span class="ff6 lse4">=+</span></span></div><div class="t m0 x3 h3 y23b ff1 fs0 fc0 sc1 ls0 ws0">为：<span class="ff3"> </span></div><div class="t m0 x97 h74 y23c ff3 fs37 fc0 sc1 lsf5 ws0">12<span class="_ _35"> </span>1</div><div class="t m0 xcf h74 y23d ff3 fs37 fc0 sc1 ls0 ws0">1</div><div class="t m0 x52 h74 y23e ff3 fs37 fc0 sc1 ls0 ws0">1</div><div class="t m0 x91 h80 y23f ff3 fs3b fc0 sc1 lsf6 ws0">10<span class="_ _91"> </span>0<span class="_ _0"> </span>0</div><div class="t m0 xf5 h80 y240 ff3 fs3b fc0 sc1 ls0 ws0">0</div><div class="t m0 x91 h80 y241 ff3 fs3b fc0 sc1 lsf7 ws0">01<span class="_ _91"> </span>0<span class="_ _1f"> </span>0</div><div class="t m0 xf5 h80 y242 ff3 fs3b fc0 sc1 ls0 ws0">0</div><div class="t m0 x91 h80 y243 ff3 fs3b fc0 sc1 lsf8 ws0">00<span class="_ _91"> </span>1<span class="_ _0"> </span>0</div><div class="t m0 xf6 h76 y23c ff5 fs37 fc0 sc1 lsf9 ws0">rr</div><div class="t m0 xf5 h76 y23d ff5 fs37 fc0 sc1 ls0 ws0">t</div><div class="t m0 x36 h76 y23e ff5 fs37 fc0 sc1 lsfa ws0">tt</div><div class="t m2a x56 h7d y244 ff6 fs3d fc0 sc1 lsfb ws0">φφ<span class="_ _51"> </span>φ<span class="_ _49"> </span>φ</div><div class="c x6a y245 w38 ha"><div class="t m2a x0 h7d y15 ff6 fs3d fc0 sc1 ls0 ws0">ε</div></div><div class="t m2a x38 h7d y246 ff6 fs3d fc0 sc1 lsfc ws0">εξ</div><div class="t m0 xf7 h71 y23c ff6 fs33 fc0 sc1 ls0 ws0">−</div><div class="t m0 xa h71 y247 ff6 fs33 fc0 sc1 ls0 ws0">+</div><div class="t m0 x65 h71 y248 ff6 fs33 fc0 sc1 ls0 ws0">+</div><div class="t m0 x94 h7e y249 ff6 fs3b fc0 sc1 lsfd ws0">⎡⎤</div><div class="c xae y24a w39 ha"><div class="t m0 x0 h7e y15 ff6 fs3b fc0 sc1 ls0 ws0">⎡</div></div><div class="t m0 xf8 h7e y24b ff6 fs3b fc0 sc1 ls0 ws0">⎤</div><div class="t m0 x94 h7e y24c ff6 fs3b fc0 sc1 lsfd ws0">⎢⎥</div><div class="c xae y24d w39 ha"><div class="t m0 x0 h7e y15 ff6 fs3b fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf8 h7e y24e ff6 fs3b fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x94 h7e y24f ff6 fs3b fc0 sc1 lsfd ws0">⎢⎥</div><div class="c xae y250 w39 ha"><div class="t m0 x0 h7e y15 ff6 fs3b fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf8 h7e y251 ff6 fs3b fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x94 h7e y252 ff6 fs3b fc0 sc1 lsfd ws0">⎢⎥</div><div class="t m0 x66 h7e y253 ff6 fs3b fc0 sc1 lsfe ws0">=+</div><div class="c xae y254 w39 ha"><div class="t m0 x0 h7e y15 ff6 fs3b fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf8 h7e y255 ff6 fs3b fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x94 h7e y256 ff6 fs3b fc0 sc1 lsfd ws0">⎢⎥</div><div class="c xae y257 w39 ha"><div class="t m0 x0 h7e y15 ff6 fs3b fc0 sc1 ls0 ws0">⎢</div></div><div class="t m0 xf8 h7e y258 ff6 fs3b fc0 sc1 ls0 ws0">⎥</div><div class="t m0 x94 h7e y259 ff6 fs3b fc0 sc1 lsfd ws0">⎢⎥</div><div class="c xae y25a w39 ha"><div class="t m0 x0 h7e y15 ff6 fs3b fc0 sc1 ls0 ws0">⎣</div></div><div class="t m0 xf8 h7e y25b ff6 fs3b fc0 sc1 ls0 ws0">⎦</div><div class="t m0 x94 h7e y25c ff6 fs3b fc0 sc1 lsfd ws0">⎢⎥</div><div class="t m0 x94 h7e y25d ff6 fs3b fc0 sc1 lsfd ws0">⎣⎦</div><div class="t m0 x25 h57 y244 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x25 h57 y23f ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x25 h57 y25e ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 xd2 h57 y25f ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 xf1 h57 y260 ff8 fs2 fc0 sc1 ls91 ws0"><span class="_ _31"></span><span class="_ _40"></span><span class="_ _0"> </span></div><div class="t m0 x25 h57 y261 ff8 fs2 fc0 sc1 ls0 ws0"></div><div class="t m0 x59 h3 y246 ff3 fs0 fc0 sc1 ls16 ws3"> <span class="ff1 ls0 ws0">（<span class="ff3 ls6a">19</span>）<span class="ff3"> </span></span></div><div class="t m0 x3 h2 y262 ff1 fs0 fc0 sc1 ls0 ws0">观察方程</div><div class="t m2d x38 h16 y263 ff6 fs7 fc0 sc1 lsff ws0">()</div><div class="t m0 xa7 h3 y264 ff3 fs34 fc0 sc1 ls0 ws0">1<span class="_ _12"></span><span class="ff5">n<span class="_ _41"> </span><span class="ff6">=<span class="_ _56"> </span><span class="ff1 fs0">为：<span class="ff3"> </span></span></span></span></div><div class="t m2e xc5 h81 y265 ff6 fs3e fc0 sc1 ls0 ws0">[</div><div class="c x9c y266 w3a h82"><div class="t m2e x0 h81 y267 ff6 fs3e fc0 sc1 ls0 ws0">]</div></div><div class="t m0 x42 h74 y268 ff3 fs37 fc0 sc1 ls100 ws0">12<span class="_ _35"> </span>1</div><div class="t m0 x4b h6d y269 ff3 fs34 fc0 sc1 ls0 ws0">1</div><div class="t m0 xa3 h76 y268 ff5 fs37 fc0 sc1 ls101 ws0">tr<span class="_ _92"></span>t</div><div class="t m0 x91 h6f y269 ff5 fs34 fc0 sc1 ls0 ws0">y</div><div class="c x26 y26a w3b h55"><div class="t m16 x0 h70 yf ff6 fs35 fc0 sc1 ls0 ws0">µ</div></div><div class="t m16 x48 h70 y269 ff6 fs35 fc0 sc1 ls102 ws0">θθ<span class="_ _93"> </span>θ</div><div class="c x26 y26a w3b h55"><div class="t m16 xc2 h70 yf ff6 fs35 fc0 sc1 ls0 ws0">ξ</div></div><div class="t m0 x6a h83 y268 ff6 fs13 fc0 sc1 ls0 ws0">−</div><div class="t m0 x21 h72 y269 ff6 fs34 fc0 sc1 lsbc ws0">=+<span class="_ _94"> </span><span class="ff8 fs8 ls0"></span></div><div class="t m0 x59 h3 y26b ff3 fs0 fc0 sc1 ls16 ws3"> <span class="ff1 ls0 ws0">（<span class="ff3 ls6a">20</span>）<span class="ff3"> </span></span></div><div class="t m0 x3 h2 y26c ff1 fs0 fc0 sc0 ls2 ws0">证明：<span class="ff2 sc1 ls0"> </span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
PUDN用户 2010-04-29 17:13:48我下了怎么就打不开
PUDN用户 2009-11-18 13:23:44很好