SequentialMonteCarlofilteringtechniquesappliedtoin

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序列蒙特卡罗滤波技术应用到综合导航系统--前沿论文
SequentialMonteCarlofilteringtechniquesappliedtoin
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<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://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/625baaf0be9ad24cfa25366c/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/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://static.pudn.com/prod/directory_preview_static/625baaf0be9ad24cfa25366c/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Proceedings <span class="_ _0"></span><span class="ls1">of <span class="_ _1"> </span><span class="ls0">the <span class="ls2">American <span class="_ _2"></span>Control <span class="_ _3"></span>Conference </span></span></span></div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls2 ws0">Arlington, </div><div class="t m1 x2 h3 y3 ff1 fs1 fc0 sc0 ls3 ws0">VA </div><div class="t m0 x3 h2 y3 ff1 fs0 fc0 sc0 ls2 ws0">June </div><div class="t m2 x4 h3 y3 ff1 fs1 fc0 sc0 ls4 ws0">25-27, </div><div class="t m3 x5 h4 y3 ff1 fs2 fc0 sc0 ls5 ws0">2001 </div><div class="t m4 x6 h5 y4 ff2 fs3 fc0 sc0 ls6 ws0">Sequential <span class="_ _4"></span>Monte <span class="_ _4"></span><span class="ls7">Carlo <span class="_ _5"></span><span class="ls8">filtering <span class="_ _2"></span>techniques <span class="_ _5"></span>applied <span class="_ _2"></span><span class="ls9">to </span></span></span></div><div class="t m5 x7 h5 y5 ff2 fs3 fc0 sc0 lsa ws0">integrated <span class="_ _3"></span>navigation <span class="_ _3"></span><span class="lsb">systems </span></div><div class="t m6 x8 h6 y6 ff3 fs4 fc0 sc0 lsc ws0">Per-Johan <span class="_ _4"></span>Nordlund <span class="_ _4"></span><span class="lsd">and <span class="_ _2"></span><span class="lsb">Fredrik <span class="_ _4"></span></span></span>Gustafsson </div><div class="t m6 x9 h6 y7 ff3 fs4 fc0 sc0 lse ws0">Department <span class="_ _5"></span><span class="lsf">of <span class="_ _6"> </span><span class="lsc">Electrical <span class="_ _7"></span><span class="lsb">Engineering </span></span></span></div><div class="t m6 xa h6 y8 ff3 fs4 fc0 sc0 lsb ws0">Linkoping <span class="_ _5"></span>University </div><div class="t m7 xb h7 y9 ff3 fs5 fc0 sc0 ls10 ws0">SE-58183 </div><div class="t m6 xc h6 y9 ff3 fs4 fc0 sc0 lsb ws0">Linkoping, <span class="_ _5"></span><span class="ls11">Sweden </span></div><div class="t m8 xd h8 ya ff4 fs6 fc0 sc0 ls12 ws0">perno@isy.liu.se, <span class="_ _8"></span><span class="lsb">fredrik@isy.liu.se </span></div><div class="t m9 xe h9 yb ff3 fs7 fc0 sc0 ls13 ws0">Abstract </div><div class="t m9 xf h9 yc ff3 fs7 fc0 sc0 ls14 ws0">This paper addresses <span class="_ _9"></span><span class="ls15">the <span class="_ _a"></span><span class="ls16">problem <span class="_ _2"></span><span class="ls17">of <span class="_ _1"> </span><span class="ls14">integrated <span class="lsb">aircraft </span></span></span></span></span></div><div class="t m9 xf h9 yd ff3 fs7 fc0 sc0 ls14 ws0">navigation, <span class="_ _a"></span><span class="ls18">and <span class="ls14">more <span class="_ _a"></span><span class="ls19">specifically <span class="_ _3"></span><span class="ls1a">how <span class="_ _b"></span><span class="ls15">to <span class="_ _3"></span><span class="ls18">integrate <span class="_ _9"></span><span class="lsb">iner- </span></span></span></span></span></span></span></div><div class="t m9 xf h9 ye ff3 fs7 fc0 sc0 ls18 ws0">tial <span class="_ _3"></span><span class="ls14">navigation <span class="_ _3"></span>with <span class="lsb">terrain <span class="_ _2"></span><span class="ls16">aided <span class="_ _7"></span></span>positioning. <span class="_ _7"></span><span class="ls18">This <span class="_ _a"></span><span class="ls16">is <span class="_ _2"></span><span class="ls14">a </span></span></span></span></span></div><div class="t m9 xf h9 yf ff3 fs7 fc0 sc0 ls16 ws0">highly <span class="_ _7"></span><span class="ls14">nonlinear <span class="_ _7"></span><span class="ls18">and <span class="_ _7"></span></span></span>non-Gaussian <span class="_ _5"></span>recursive <span class="_ _b"></span><span class="ls1b">state <span class="ls1c">es- </span></span></div><div class="t m9 xf h9 y10 ff3 fs7 fc0 sc0 ls14 ws0">timation <span class="_ _2"></span>problem <span class="_ _3"></span><span class="ls1c">which <span class="_ _7"></span><span class="ls16">requires <span class="ls1b">state <span class="_ _a"></span><span class="ls17">of <span class="_ _c"> </span><span class="ls15">the <span class="ls1d">art <span class="_ _a"></span><span class="ls14">meth- </span></span></span></span></span></span></span></div><div class="t m9 xf h9 y11 ff3 fs7 fc0 sc0 ls16 ws0">ods. </div><div class="t m9 xf h9 y12 ff3 fs7 fc0 sc0 ls17 ws0">We <span class="_ _d"> </span><span class="ls14">propose <span class="_ _1"> </span><span class="ls18">an <span class="_ _1"> </span></span>algorithm <span class="_ _5"></span><span class="ls19">based <span class="_ _6"> </span>on <span class="_ _c"> </span><span class="ls15">the <span class="_ _1"> </span><span class="lsb">particle <span class="_ _6"> </span><span class="ls1e">fil- </span></span></span></span></span></div><div class="t m9 xf h9 y13 ff3 fs7 fc0 sc0 ls15 ws0">ter <span class="_ _7"></span><span class="ls14">with <span class="_ _7"></span><span class="ls18">particular <span class="_ _5"></span>attention <span class="ls1d">to </span>the <span class="_ _7"></span><span class="ls16">complexity <span class="_ _7"></span><span class="ls17">of <span class="_ _e"> </span></span></span></span></span>the </div><div class="t m9 xf h9 y14 ff3 fs7 fc0 sc0 ls16 ws0">problem. <span class="_ _f"> </span><span class="ls1f">The <span class="ls14">proposed algorithm <span class="_ _3"></span>takes <span class="_ _7"></span>advantage <span class="_ _2"></span><span class="ls17">of </span></span></span></div><div class="t m9 xf h9 y15 ff3 fs7 fc0 sc0 lsb ws0">linear <span class="_ _5"></span><span class="ls18">and <span class="_ _4"> </span><span class="ls14">Gaussian <span class="_ _2"></span></span>structure <span class="_ _5"></span><span class="ls16">within <span class="_ _b"> </span><span class="ls15">the <span class="_ _5"></span><span class="ls14">system <span class="_ _b"></span>and </span></span></span></span></div><div class="t m9 xf h9 y16 ff3 fs7 fc0 sc0 ls19 ws0">solves <span class="_ _b"></span><span class="ls14">these <span class="_ _4"> </span><span class="ls1b">parts <span class="_ _b"> </span><span class="ls16">using <span class="_ _4"> </span><span class="ls18">the <span class="_ _1"> </span></span>Kalman <span class="_"> </span><span class="lsb">filter. <span class="_ _10"> </span><span class="ls1f">The </span></span></span></span></span></div><div class="t ma x10 ha y17 ff4 fs8 fc0 sc0 lsb ws0">re- </div><div class="t m9 xf h9 y18 ff3 fs7 fc0 sc0 ls16 ws0">maining <span class="_ _4"> </span><span class="ls1b">parts <span class="_ _7"></span></span>suffering <span class="_ _2"></span>from <span class="_ _5"></span>severe <span class="_ _7"></span><span class="ls14">nonlinear <span class="_ _2"></span><span class="ls15">and/or </span></span></div><div class="t m9 xf h9 y19 ff3 fs7 fc0 sc0 ls14 ws0">non-Gaussian <span class="_ _3"></span><span class="ls15">structure </span></div><div class="t mb x11 hb y1a ff3 fs9 fc0 sc0 ls20 ws0">is </div><div class="t m9 x12 h9 y1a ff3 fs7 fc0 sc0 ls19 ws0">solved <span class="_ _7"></span><span class="ls16">using <span class="ls15">the <span class="_ _2"></span><span class="lsb">particle </span></span></span></div><div class="t mc x10 hc y1a ff4 fsa fc0 sc0 ls21 ws0">fil- </div><div class="t m9 xf h9 y1b ff3 fs7 fc0 sc0 ls15 ws0">ter. <span class="_ _7"></span>The <span class="ls14">proposed <span class="_ _3"></span><span class="lsb">filter <span class="ls16">is <span class="ls14">applied <span class="_ _3"></span><span class="ls19">on <span class="_ _2"></span><span class="ls14">a <span class="_ _2"></span><span class="ls16">simplified <span class="lsb">inte- </span></span></span></span></span></span></span></span></div><div class="t m9 xf h9 y1c ff3 fs7 fc0 sc0 ls18 ws0">grated <span class="ls14">navigation <span class="_ _7"></span>system. <span class="_ _5"></span></span>The <span class="_ _2"></span><span class="lsb">result <span class="_ _7"></span><span class="ls19">shows <span class="_ _7"></span><span class="ls1d">that <span class="ls16">very </span></span></span></span></div><div class="t m9 xf h9 y1d ff3 fs7 fc0 sc0 ls16 ws0">good <span class="_ _2"></span><span class="ls14">performance <span class="_ _3"></span><span class="ls16">is <span class="ls19">achieved <span class="_ _2"></span>for <span class="_ _2"></span><span class="ls14">a <span class="_ _2"></span><span class="ls18">tractable <span class="_ _3"></span><span class="ls14">computa- </span></span></span></span></span></span></div><div class="t m9 xf h9 y1e ff3 fs7 fc0 sc0 lsb ws0">tional <span class="_ _7"></span>load. </div><div class="t md x13 hd y1f ff4 fs7 fc0 sc0 lsb ws0">1 </div><div class="t m9 x14 h9 y1f ff3 fs7 fc0 sc0 ls13 ws0">Introduction </div><div class="t m9 xf h9 y20 ff3 fs7 fc0 sc0 ls18 ws0">The <span class="ls16">classical <span class="_ _7"></span><span class="ls14">approach <span class="_ _3"></span><span class="ls22">to <span class="_ _0"></span><span class="ls16">recursive <span class="_ _2"></span><span class="ls15">state <span class="ls14">estimation <span class="ls17">of </span></span></span></span></span></span></span></div><div class="t m9 xf h9 y21 ff3 fs7 fc0 sc0 ls14 ws0">nonlinear <span class="_ _9"></span><span class="ls15">and <span class="_ _a"></span><span class="ls16">non-Gaussian <span class="_ _7"></span><span class="ls14">systems <span class="_ _0"></span><span class="ls1c">is <span class="ls16">based <span class="ls18">on <span class="_ _a"></span><span class="ls1b">the <span class="_ _a"></span><span class="ls19">ex- </span></span></span></span></span></span></span></span></div><div class="t m9 xf h9 y22 ff3 fs7 fc0 sc0 ls14 ws0">tended <span class="_ _2"></span>Kalman <span class="_ _2"></span><span class="lsb">filter <span class="_ _7"></span></span>(EKF) </div><div class="t me x15 he y23 ff2 fsb fc0 sc0 lsb ws0">[l]. </div><div class="t m9 xd h9 y23 ff3 fs7 fc0 sc0 ls16 ws0">Depending <span class="ls18">on <span class="ls1b">the <span class="ls19">ex- </span></span></span></div><div class="t m9 xf h9 y24 ff3 fs7 fc0 sc0 ls15 ws0">tent </div><div class="t mf x6 hf y25 ff3 fsc fc0 sc0 ls23 ws0">of </div><div class="t m9 x16 h9 y25 ff3 fs7 fc0 sc0 ls14 ws0">nonlinearities <span class="_ _a"></span><span class="ls18">and <span class="ls16">non-Gaussian <span class="_ _2"></span><span class="ls19">noise <span class="_ _7"></span><span class="ls1b">the <span class="_ _3"></span><span class="ls15">EKF </span></span></span></span></span></div><div class="t m9 xf h9 y26 ff3 fs7 fc0 sc0 ls14 ws0">often provides </div><div class="t m10 x17 h10 y27 ff3 fsd fc0 sc0 lsb ws0">a </div><div class="t m9 x18 h9 y27 ff3 fs7 fc0 sc0 ls14 ws0">solution <span class="_ _a"></span><span class="lsb">far <span class="ls16">from <span class="_ _2"></span><span class="ls14">acceptable. Another </span></span></span></div><div class="t m9 xf h9 y28 ff3 fs7 fc0 sc0 ls16 ws0">possible <span class="_ _2"></span><span class="ls14">technique <span class="_ _3"></span><span class="lsb">for <span class="_ _3"></span><span class="ls16">recursive <span class="ls14">estimation <span class="_ _a"></span><span class="lsb">is <span class="ls22">to <span class="_ _9"></span><span class="ls16">use <span class="_ _2"></span><span class="ls19">se- </span></span></span></span></span></span></span></span></div><div class="t m9 xf h9 y29 ff3 fs7 fc0 sc0 ls14 ws0">quential <span class="_ _7"></span>Monte <span class="_ _b"></span>Carlo <span class="_ _7"></span>methods, </div><div class="t m11 x19 h11 y2a ff2 fse fc0 sc0 ls24 ws0">or </div><div class="t m9 x1a h9 y2a ff3 fs7 fc0 sc0 lsb ws0">particle <span class="_ _b"> </span>filters </div><div class="t m12 x1b h12 y2a ff2 fs7 fc0 sc0 ls1c ws0">[7], </div><div class="t m2 xf h13 y2b ff2 fs9 fc0 sc0 ls25 ws0">[5]. </div><div class="t m9 x1c h9 y2b ff3 fs7 fc0 sc0 ls18 ws0">Particle <span class="_ _3"></span><span class="lsb">filters <span class="_ _7"></span><span class="ls16">provide </span></span></div><div class="t m13 x1d h14 y2b ff3 fs8 fc0 sc0 lsb ws0">a </div><div class="t m9 x15 h9 y2b ff3 fs7 fc0 sc0 ls16 ws0">numerical <span class="_ _7"></span><span class="ls14">solution <span class="_ _3"></span><span class="ls26">to <span class="_ _0"></span><span class="ls15">the </span></span></span></div><div class="t m9 xf h9 y2c ff3 fs7 fc0 sc0 ls14 ws0">general <span class="_ _3"></span>nonlinear <span class="_ _7"></span><span class="ls18">and/or <span class="_ _b"> </span><span class="ls16">non-Gaussian <span class="_ _b"></span><span class="lsb">filtering <span class="_ _2"></span></span></span></span>prob- </div><div class="t m9 xf h9 y2d ff3 fs7 fc0 sc0 ls16 ws0">lem. <span class="_ _11"> </span><span class="ls1f">The <span class="_ _2"></span><span class="ls14">more <span class="_ _4"> </span></span></span>nonlinear <span class="_"> </span><span class="ls14">system, </span></div><div class="t m14 x1e h10 y2e ff3 fsd fc0 sc0 ls27 ws0">or </div><div class="t m9 x1f h9 y2e ff3 fs7 fc0 sc0 ls18 ws0">the <span class="_ _4"> </span><span class="ls14">more <span class="_ _7"></span><span class="ls16">non- </span></span></div><div class="t m9 xf h9 y2f ff3 fs7 fc0 sc0 ls14 ws0">Gaussian <span class="ls16">noise, <span class="_ _b"></span><span class="ls1b">the <span class="_ _2"></span></span>more <span class="_ _7"></span></span>potential <span class="_ _7"></span><span class="ls18">the <span class="_ _2"></span><span class="lsb">particle <span class="_ _4"> </span>filters </span></span></div><div class="t m9 xf h9 y30 ff3 fs7 fc0 sc0 ls19 ws0">have. </div><div class="t m9 xf h9 y31 ff3 fs7 fc0 sc0 ls14 ws0">Integrated <span class="_ _6"> </span>navigation <span class="_ _1"> </span><span class="ls16">is <span class="_ _c"> </span><span class="ls18">an <span class="_"> </span></span>example <span class="_"> </span><span class="ls17">of <span class="_ _11"> </span></span></span>a <span class="_ _6"> </span>recursive </div><div class="t m9 xf h9 y32 ff3 fs7 fc0 sc0 ls14 ws0">nonlinear <span class="ls15">and <span class="_ _2"></span><span class="ls16">non-Gaussian <span class="_ _4"> </span></span>state <span class="_ _2"></span></span>estimation problem </div><div class="t m9 xf h9 y33 ff3 fs7 fc0 sc0 ls19 ws0">where <span class="ls14">two </span></div><div class="t m15 x20 h9 y34 ff3 fs7 fc0 sc0 ls16 ws0">or </div><div class="t m9 x21 h9 y34 ff3 fs7 fc0 sc0 ls14 ws0">more <span class="_ _3"></span>separate <span class="_ _3"></span><span class="ls16">navigation <span class="_ _2"></span><span class="ls14">system <span class="_ _3"></span><span class="ls15">outputs </span></span></span></div><div class="t m9 xf h9 y35 ff3 fs7 fc0 sc0 ls18 ws0">are <span class="_ _3"></span><span class="ls16">blended <span class="_ _5"></span><span class="ls14">together <span class="_ _7"></span><span class="ls1d">to <span class="_ _9"></span><span class="ls14">obtain <span class="ls18">better <span class="_ _2"></span></span>accuracy <span class="_ _a"></span><span class="ls18">and </span></span></span></span></span></div><div class="t m16 x1b h15 y36 ff4 fsf fc0 sc0 lsb ws0">re- </div><div class="t m9 x22 h9 y37 ff3 fs7 fc0 sc0 ls16 ws0">liability. <span class="_ _11"> </span><span class="ls1f">The <span class="ls14">primary <span class="_ _4"> </span></span></span>source <span class="_ _b"></span><span class="ls17">of <span class="_ _e"> </span><span class="ls14">navigational <span class="_ _7"></span><span class="ls1d">data </span></span></span>is </div><div class="t m9 x22 h9 y38 ff3 fs7 fc0 sc0 ls14 ws0">often <span class="ls1b">the <span class="_ _2"></span><span class="ls18">inertial <span class="_ _7"></span></span></span>navigation <span class="_ _3"></span>system (INS), <span class="ls19">which <span class="_ _4"> </span><span class="lsb">uti- </span></span></div><div class="t m9 x23 h9 y39 ff3 fs7 fc0 sc0 ls16 ws0">lizes <span class="_ _5"></span><span class="ls14">an <span class="_ _7"></span>accurate <span class="_ _7"></span>nonlinear <span class="_ _2"></span>motion <span class="_ _7"></span></span>model <span class="_ _b"> </span><span class="ls1d">to <span class="ls14">calculate </span></span></div><div class="t m9 x23 h9 y3a ff3 fs7 fc0 sc0 ls15 ws0">the <span class="_ _5"></span><span class="ls19">vehicle's <span class="_ _c"> </span></span>attitude, <span class="_ _b"></span><span class="ls14">heading, <span class="_ _5"></span><span class="ls16">velocity, <span class="_ _b"></span></span>position <span class="_ _5"></span><span class="ls18">and </span></span></div><div class="t m9 x23 h9 y3b ff3 fs7 fc0 sc0 ls18 ws0">altitude. <span class="_ _12"> </span><span class="ls16">Due <span class="_ _4"> </span><span class="ls22">to <span class="_ _2"></span><span class="ls14">sensor <span class="_ _7"></span><span class="ls15">and <span class="_ _b"> </span><span class="lsb">initialization <span class="_ _13"> </span></span></span></span></span></span>errors <span class="_ _7"></span><span class="ls1b">the </span></div><div class="t m9 x23 h9 y3c ff3 fs7 fc0 sc0 ls16 ws0">INS <span class="_"> </span><span class="ls14">computed <span class="_ _7"></span><span class="ls18">quantities <span class="_ _7"></span>drift, <span class="_ _1"> </span>and <span class="_ _b"></span></span>one <span class="_ _b"></span><span class="ls17">of <span class="_ _d"> </span><span class="ls15">the <span class="_ _5"></span></span></span>main </span></div><div class="t m9 x23 h9 y3d ff3 fs7 fc0 sc0 ls14 ws0">purposes <span class="ls17">of <span class="_ _e"> </span><span class="ls18">an <span class="_ _2"></span>integrated </span></span>navigation <span class="_ _7"></span>system <span class="lsb">is <span class="_ _2"></span><span class="ls22">to <span class="_ _3"></span><span class="ls15">sta- </span></span></span></div><div class="t m9 x23 h9 y3e ff3 fs7 fc0 sc0 ls16 ws0">bilize <span class="_ _7"></span><span class="ls18">the <span class="_ _b"></span><span class="lsb">drift <span class="_ _4"> </span><span class="ls1c">by <span class="_"> </span></span></span>estimating <span class="ls1d">it <span class="_ _2"></span></span>and <span class="_ _7"></span>then <span class="_ _b"> </span><span class="ls14">compensate </span></span></div><div class="t m9 x23 h9 y3f ff3 fs7 fc0 sc0 ls16 ws0">for <span class="_ _2"></span><span class="ls1b">it. <span class="_ _b"></span><span class="ls19">Here <span class="_ _5"></span><span class="ls28">we <span class="_ _c"> </span></span>use <span class="_ _7"></span><span class="ls18">terrain <span class="_ _7"></span><span class="ls14">aided positioning <span class="_ _2"></span></span>(TAP) <span class="_ _2"></span><span class="ls15">as </span></span></span></span></div><div class="t m9 x23 h9 y40 ff3 fs7 fc0 sc0 ls14 ws0">a <span class="_ _b"> </span>redundant <span class="_ _1"> </span>component <span class="_ _2"></span><span class="lsb">for <span class="_ _5"></span><span class="ls18">estimating <span class="_ _2"></span><span class="ls15">the <span class="_ _5"></span><span class="ls19">INS <span class="_"> </span></span></span>drift. </span></span></div><div class="t m9 x23 h9 y41 ff3 fs7 fc0 sc0 ls18 ws0">Other <span class="_ _3"></span><span class="ls14">applications <span class="_ _0"></span><span class="ls29">of <span class="_ _5"></span><span class="ls18">integrated <span class="_ _a"></span><span class="ls14">navigation <span class="_ _a"></span>systems <span class="_ _a"></span>use </span></span></span></span></div><div class="t m9 x23 h9 y42 ff3 fs7 fc0 sc0 lsb ws0">for <span class="ls14">example <span class="_ _9"></span><span class="ls18">the <span class="_ _2"></span><span class="ls14">Global <span class="_ _a"></span>Positioning <span class="_ _3"></span>System <span class="ls18">(GPS) </span></span></span></span></div><div class="t m17 x24 h16 y43 ff2 fs8 fc0 sc0 ls2a ws0">[ll]. </div><div class="t m9 x23 h9 y44 ff3 fs7 fc0 sc0 ls14 ws0">One <span class="_ _2"></span><span class="ls18">important <span class="_ _b"></span></span>aspect <span class="_ _b"> </span><span class="ls16">is <span class="_ _5"></span><span class="ls1d">that <span class="_ _7"></span><span class="ls18">in <span class="_ _7"></span></span></span>case <span class="_ _5"></span><span class="ls29">of <span class="_ _e"> </span><span class="ls18">an <span class="_ _7"></span>outage </span></span></span></div><div class="t m18 x25 h14 y44 ff3 fs8 fc0 sc0 ls2b ws0">of </div><div class="t m19 x26 h17 y44 ff5 fs10 fc0 sc0 lsb ws0">' </div><div class="t m9 x23 h9 y45 ff3 fs7 fc0 sc0 ls1b ws0">the <span class="_ _5"></span><span class="ls18">supporting <span class="_ _7"></span><span class="ls14">component <span class="_ _7"></span>one <span class="_ _b"></span><span class="lsb">still <span class="_ _14"> </span></span>wants <span class="_ _4"> </span>a <span class="_ _14"> </span>solution </span></span></div><div class="t m9 x23 h9 y46 ff3 fs7 fc0 sc0 ls19 ws0">which <span class="_ _2"></span><span class="lsb">is </span></div><div class="t m1a x27 ha y47 ff4 fs8 fc0 sc0 ls2b ws0">as </div><div class="t m9 x28 h9 y47 ff3 fs7 fc0 sc0 ls14 ws0">accurate </div><div class="t m1b x29 ha y47 ff4 fs8 fc0 sc0 ls2c ws0">as </div><div class="t m9 x2a h9 y47 ff3 fs7 fc0 sc0 ls14 ws0">possible <span class="_ _3"></span><span class="lsb">(graceful <span class="_ _a"></span><span class="ls18">degradation). </span></span></div><div class="t m9 x23 h9 y48 ff3 fs7 fc0 sc0 ls14 ws0">To <span class="ls16">achieve <span class="_ _2"></span>graceful <span class="ls18">degradation </span></span>one <span class="ls16">needs <span class="_ _7"></span><span class="ls22">to <span class="_ _a"></span><span class="ls18">estimate </span></span></span></div><div class="t m9 x23 h9 y49 ff3 fs7 fc0 sc0 ls14 ws0">accurately <span class="_ _3"></span>not <span class="_ _2"></span>only <span class="_ _a"></span><span class="ls1b">the <span class="_ _3"></span><span class="ls16">INS <span class="_ _2"></span><span class="lsb">position, <span class="_ _7"></span></span>velocity, <span class="ls1b">attitude </span></span></span></div><div class="t m9 x23 h9 y4a ff3 fs7 fc0 sc0 ls18 ws0">and <span class="_ _7"></span><span class="ls14">heading <span class="lsb">errors <span class="_ _7"></span><span class="ls15">but <span class="_ _5"></span></span>also <span class="_ _7"></span><span class="ls15">the <span class="_ _7"></span></span></span>sensor <span class="_ _2"></span>(accelerometer </span></div><div class="t m9 x23 h9 y4b ff3 fs7 fc0 sc0 ls15 ws0">and <span class="_ _3"></span>rate </div><div class="t m1c x2b h9 y4c ff3 fs7 fc0 sc0 ls16 ws0">gyro) </div><div class="t m9 x2c h9 y4c ff3 fs7 fc0 sc0 lsb ws0">errors. <span class="_ _14"> </span><span class="ls14">Until <span class="_ _3"></span><span class="ls19">now, <span class="_ _7"></span><span class="ls15">the <span class="_ _3"></span><span class="ls14">graceful <span class="_ _9"></span>degrada- </span></span></span></span></div><div class="t m9 x23 h9 y4d ff3 fs7 fc0 sc0 ls18 ws0">tion <span class="ls16">problem <span class="_ _7"></span><span class="ls14">has been tackled <span class="lsb">in </span></span></span></div><div class="t m13 x2d h14 y4e ff3 fs8 fc0 sc0 lsb ws0">a </div><div class="t m9 x2e h9 y4e ff3 fs7 fc0 sc0 ls18 ws0">suboptimal <span class="_ _a"></span><span class="ls14">manner </span></div><div class="t m9 x23 h9 y4f ff3 fs7 fc0 sc0 ls14 ws0">using <span class="_ _3"></span><span class="ls15">the <span class="ls18">EKF. </span></span></div><div class="t m9 x23 h9 y50 ff3 fs7 fc0 sc0 ls1f ws0">The <span class="_ _14"> </span><span class="ls16">complexity <span class="_ _c"> </span><span class="ls29">of <span class="_ _d"> </span><span class="ls1d">the <span class="_ _4"> </span><span class="ls14">problem <span class="_ _1"> </span>increases <span class="_ _b"> </span><span class="ls15">the <span class="_ _1"> </span></span>more </span></span></span></span></div><div class="t m9 x23 h9 y51 ff3 fs7 fc0 sc0 ls18 ws0">quantities <span class="_ _a"></span>there <span class="_ _2"></span><span class="ls15">are <span class="_ _3"></span><span class="ls22">to <span class="_ _0"></span><span class="ls18">estimate. <span class="_ _b"></span><span class="ls1f">The <span class="_ _a"></span><span class="ls16">dimension <span class="_ _7"></span><span class="ls29">of <span class="_ _c"> </span><span class="ls1b">the </span></span></span></span></span></span></span></div><div class="t m9 x23 h9 y52 ff3 fs7 fc0 sc0 ls1b ws0">state <span class="ls16">vector <span class="_ _b"></span><span class="ls14">representing </span></span></div><div class="t m1d x2f h18 y53 ff3 fs11 fc0 sc0 lsb ws0">a </div><div class="t m9 x30 h9 y53 ff3 fs7 fc0 sc0 ls14 ws0">complete <span class="ls18">set <span class="_ _2"></span><span class="ls17">of <span class="_ _e"> </span><span class="ls19">INS <span class="_ _5"></span></span></span>errors </span></div><div class="t m9 x23 h9 y54 ff3 fs7 fc0 sc0 ls16 ws0">is <span class="_ _5"></span><span class="ls18">quite </span>high </div><div class="t m1e x31 h19 y55 ff5 fs7 fc0 sc0 ls19 ws0">(&gt; </div><div class="t m2 x32 h13 y55 ff2 fs9 fc0 sc0 ls2d ws0">15). </div><div class="t m9 x33 h9 y55 ff3 fs7 fc0 sc0 ls14 ws0">A <span class="_ _2"></span><span class="lsb">direct <span class="_ _14"> </span></span>application <span class="_ _7"></span><span class="ls17">of <span class="_ _e"> </span><span class="ls1b">the <span class="_ _2"></span></span></span>par- </div><div class="t m9 x23 h9 y56 ff3 fs7 fc0 sc0 lsb ws0">ticle <span class="_ _4"> </span>filter <span class="_ _b"> </span><span class="ls19">shows <span class="_ _b"> </span><span class="ls1b">that </span></span></div><div class="t m13 x2a h14 y57 ff3 fs8 fc0 sc0 lsb ws0">a </div><div class="t m9 x34 h9 y57 ff3 fs7 fc0 sc0 ls14 ws0">vast <span class="_ _b"></span>number <span class="_ _b"></span><span class="ls29">of <span class="_ _e"> </span><span class="lsb">particles <span class="_"> </span><span class="ls15">are </span></span></span></div><div class="t m9 x23 h9 y58 ff3 fs7 fc0 sc0 ls16 ws0">needed <span class="_ _7"></span>for <span class="_ _2"></span><span class="ls15">the <span class="lsb">particle <span class="_ _7"></span>filter <span class="_ _7"></span><span class="ls1d">to <span class="_ _a"></span><span class="ls14">perform <span class="ls1c">well. <span class="_"> </span></span>One <span class="ls1c">way </span></span></span></span></span></div><div class="t m9 x23 h9 y59 ff3 fs7 fc0 sc0 ls17 ws0">of <span class="_ _6"> </span><span class="ls14">dealing <span class="_ _3"></span>with <span class="_ _2"></span><span class="ls18">this <span class="lsb">is <span class="_ _2"></span><span class="ls22">to <span class="_ _3"></span><span class="ls18">estimate </span></span></span></span></span></div><div class="t m1f x35 ha y5a ff4 fs8 fc0 sc0 ls2e ws0">as </div><div class="t m9 x36 h9 y5a ff3 fs7 fc0 sc0 ls14 ws0">much </div><div class="t m1a x37 ha y5a ff4 fs8 fc0 sc0 ls2f ws0">as </div><div class="t m9 x38 h9 y5a ff3 fs7 fc0 sc0 ls14 ws0">possible </div><div class="t m9 x23 h9 y5b ff3 fs7 fc0 sc0 lsb ws0">analytically, <span class="_ _3"></span><span class="ls16">using <span class="_ _3"></span><span class="ls15">the <span class="_ _3"></span><span class="ls14">Kalman <span class="_ _3"></span><span class="lsb">filter, <span class="ls18">and the <span class="_ _a"></span><span class="ls14">remaining </span></span></span></span></span></span></div><div class="t m9 x23 h9 y5c ff3 fs7 fc0 sc0 ls1b ws0">part <span class="ls29">of <span class="_"> </span><span class="ls16">reduced <span class="_ _7"></span>dimension <span class="_ _7"></span><span class="ls14">can <span class="ls15">then <span class="_ _3"></span><span class="ls18">be estimated <span class="_ _a"></span><span class="ls14">using </span></span></span></span></span></span></div><div class="t m9 x23 h9 y5d ff3 fs7 fc0 sc0 lsb ws0">particle <span class="_ _2"></span>filtering. <span class="_ _7"></span><span class="ls18">This <span class="_ _a"></span><span class="lsb">is <span class="_ _3"></span><span class="ls14">a <span class="_ _3"></span><span class="ls15">type <span class="_ _a"></span><span class="ls17">of <span class="_ _1"> </span><span class="ls16">Rao-Blackwellisation </span></span></span></span></span></span></div><div class="t m9 x23 h9 y5e ff3 fs7 fc0 sc0 ls14 ws0">where <span class="_ _3"></span><span class="ls15">the <span class="_ _2"></span><span class="ls14">purpose <span class="ls18">in </span>general <span class="_ _3"></span><span class="ls16">is <span class="_ _2"></span><span class="ls22">to <span class="_ _a"></span><span class="ls14">reduce <span class="ls1b">the <span class="_ _3"></span><span class="ls14">variance </span></span></span></span></span></span></span></div><div class="t m20 x23 hb y5f ff3 fs9 fc0 sc0 ls30 ws0">of </div><div class="t m9 x39 h9 y5f ff3 fs7 fc0 sc0 ls1b ws0">the <span class="ls14">estimator </span></div><div class="t m21 x3a h1a y5f ff2 fs12 fc0 sc0 ls31 ws0">[lo]. </div><div class="t m9 x3b h9 y5f ff3 fs7 fc0 sc0 ls1d ws0">The <span class="_ _a"></span><span class="ls14">aim <span class="_ _2"></span><span class="ls29">of <span class="_ _c"> </span><span class="ls18">this <span class="_ _2"></span>paper <span class="_ _2"></span><span class="lsb">is <span class="_ _2"></span><span class="ls26">to <span class="_ _9"></span><span class="ls14">pro- </span></span></span></span></span></span></div><div class="t m9 x23 h9 y60 ff3 fs7 fc0 sc0 ls16 ws0">pose <span class="_ _4"> </span><span class="ls14">a <span class="_ _5"></span></span>combined <span class="_ _5"></span><span class="ls14">Kalman <span class="_ _b"></span><span class="ls15">and <span class="_ _2"></span><span class="lsb">particle <span class="_"> </span>filter, <span class="_ _b"></span><span class="ls19">which <span class="_ _4"> </span></span>is </span></span></span></div><div class="t m9 x23 h9 y61 ff3 fs7 fc0 sc0 ls14 ws0">applied <span class="_ _a"></span><span class="ls22">to </span></div><div class="t m10 x3c h10 y62 ff3 fsd fc0 sc0 lsb ws0">a </div><div class="t m9 x3d h9 y62 ff3 fs7 fc0 sc0 ls19 ws0">simplified <span class="ls18">integrated <span class="_ _3"></span><span class="ls14">navigation <span class="_ _a"></span>system. </span></span></div><div class="t m22 x3e h1b y62 ff2 fs13 fc0 sc0 lsb ws0">A </div><div class="t m9 x23 h9 y63 ff3 fs7 fc0 sc0 ls15 ws0">standard <span class="_ _2"></span><span class="lsb">particle <span class="_ _5"></span>filter <span class="_ _7"></span>is <span class="_ _7"></span>also <span class="_ _7"></span><span class="ls14">applied </span>for <span class="_ _7"></span><span class="ls14">comparison. </span></span></div><div class="t m9 x23 h9 y64 ff3 fs7 fc0 sc0 ls14 ws0">Simulations <span class="ls19">show <span class="_ _5"></span><span class="ls1d">that <span class="_ _2"></span><span class="ls1b">the <span class="_ _5"></span><span class="ls16">combined <span class="_ _4"> </span><span class="lsb">filter <span class="_ _b"></span></span>makes <span class="_ _4"> </span></span>the </span></span></span></div><div class="t m9 x23 h9 y65 ff3 fs7 fc0 sc0 ls14 ws0">problem <span class="_ _3"></span><span class="ls18">tractable <span class="_ _2"></span><span class="ls1c">by <span class="_ _b"></span><span class="ls14">reducing <span class="ls15">the <span class="_ _2"></span></span>number <span class="_ _2"></span><span class="ls17">of <span class="_ _6"> </span></span>required </span></span></span></div><div class="t m9 x23 h9 y66 ff3 fs7 fc0 sc0 lsb ws0">particles <span class="_ _7"></span><span class="ls16">significantly. </span></div><div class="t m9 x23 h9 y67 ff3 fs7 fc0 sc0 ls14 ws0">Section </div><div class="t m23 x3f h1c y68 ff2 fsc fc0 sc0 lsb ws0">2 </div><div class="t m9 x3c h9 y68 ff3 fs7 fc0 sc0 ls19 ws0">gives <span class="_ _b"></span><span class="ls14">a <span class="_ _b"></span></span>brief <span class="_"> </span><span class="ls18">introduction <span class="_ _7"></span><span class="ls1d">to <span class="_ _2"></span><span class="ls14">p&amp;ticle <span class="_ _b"></span><span class="lsb">filter- </span></span></span></span></div><div class="t m9 x23 h9 y69 ff3 fs7 fc0 sc0 lsb ws0">ing, <span class="_ _7"></span><span class="ls1c">followed <span class="_ _7"></span><span class="ls1a">by </span></span></div><div class="t m10 x40 h10 y6a ff3 fsd fc0 sc0 lsb ws0">a </div><div class="t m9 x41 h9 y6a ff3 fs7 fc0 sc0 ls14 ws0">derivation <span class="ls29">of <span class="_ _c"> </span><span class="ls1b">the <span class="ls16">combined <span class="_ _5"></span></span></span></span>Kalman </div><div class="t m9 x23 h9 y6b ff3 fs7 fc0 sc0 ls15 ws0">and <span class="_ _7"></span><span class="lsb">particle <span class="_ _4"> </span>filter <span class="_ _b"></span><span class="ls19">in <span class="_"> </span><span class="ls14">Section </span></span></span></div><div class="t m24 x42 h13 y6c ff2 fs9 fc0 sc0 ls32 ws0">3. </div><div class="t m9 x43 h9 y6c ff3 fs7 fc0 sc0 ls14 ws0">Section </div><div class="t m25 x44 h1d y6c ff1 fs14 fc0 sc0 lsb ws0">4 </div><div class="t m9 x45 h9 y6c ff3 fs7 fc0 sc0 ls14 ws0">introduces </div><div class="t m9 x23 h9 y6d ff3 fs7 fc0 sc0 ls15 ws0">the <span class="_ _b"></span><span class="ls14">reader <span class="_ _5"></span><span class="ls1d">to <span class="_ _2"></span></span>integrated <span class="_ _1"> </span>navigation <span class="_ _5"></span></span>and <span class="_ _5"></span><span class="lsb">in <span class="_"> </span><span class="ls14">Section </span></span></div><div class="t m26 x46 h1e y6e ff6 fs15 fc0 sc0 lsb ws0">5 </div><div class="t m9 x23 h9 y6f ff3 fs7 fc0 sc0 ls29 ws0">we <span class="_ _1"> </span><span class="ls14">apply <span class="_ _2"></span><span class="ls15">the <span class="_ _2"></span></span>proposed <span class="_ _3"></span><span class="lsb">filter <span class="_ _7"></span><span class="ls22">to </span></span></span></div><div class="t m13 x47 h14 y6f ff3 fs8 fc0 sc0 lsb ws0">a </div><div class="t m9 x48 h9 y6f ff3 fs7 fc0 sc0 ls16 ws0">simplified <span class="_ _2"></span><span class="ls18">integrated </span></div><div class="t m27 x1 h1f y70 ff1 fs8 fc0 sc0 ls33 ws0">0-7803-6495-3/01/$10.00 </div><div class="t m28 x49 h20 y70 ff7 fs5 fc0 sc0 lsb ws0">0 </div><div class="t m29 x1d h21 y70 ff1 fs7 fc0 sc0 ls1a ws0">2001 </div><div class="t m21 x19 h22 y70 ff1 fs12 fc0 sc0 ls34 ws0">AACC </div><div class="t m2a x4a h23 y70 ff1 fs16 fc0 sc0 ls35 ws0">4375 </div></div><div class="pi" data-data='{"ctm":[1.559456,0.000000,0.000000,1.559456,0.000000,0.000000]}'></div></div> </body> </html>
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