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基于粒子滤波的雷达检测前跟踪算法,建立新的目标模型和观测模型,提出了线性扩展目标。能够检测1db的弱小目标。
radar-target-detect.rar
  • radar target detect.pdf
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内容介绍
<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/622b5d8015da9b288b09ba43/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/622b5d8015da9b288b09ba43/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Radar Target Detect using Particle Filter<span class="ff2 ls1 ws1"> </span></div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws2">Zhaoping Wu, Ta<span class="_ _0"></span>o Su </div><div class="t m0 x3 h4 y3 ff1 fs2 fc0 sc0 ls2 ws3">National key lab of radar signa<span class="_ _1"></span>l processing, Xidian Univ. </div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls3 ws4">Xi&#8217;an, China </div><div class="t m0 x5 h4 y5 ff1 fs2 fc0 sc0 ls4 ws1">zpwu@mail.xidian.edu.cn </div><div class="t m0 x6 h5 y6 ff2 fs2 fc0 sc0 ls5 ws1"> </div><div class="t m0 x7 h6 y7 ff3 fs3 fc0 sc0 ls6 ws1">Abstract<span class="ff4 ls7 ws5">&#8212;A radar targ<span class="_ _1"></span>et track-before-d<span class="_ _1"></span>etect (TBD) algorithm </span></div><div class="t m0 x7 h6 y8 ff4 fs3 fc0 sc0 ls8 ws6">using particle<span class="_ _1"></span> filter (PF)<span class="_ _1"></span> is present<span class="_ _1"></span>ed in t<span class="_ _1"></span>his paper. S<span class="_ _1"></span>ystem </div><div class="t m0 x7 h6 y9 ff4 fs3 fc0 sc0 ls9 ws7">dynamic model and measurement model are established based </div><div class="t m0 x7 h6 ya ff4 fs3 fc0 sc0 lsa ws8">on a sequence of radar range-Doppler measuremen<span class="_ _1"></span>ts using the </div><div class="t m0 x7 h6 yb ff4 fs3 fc0 sc0 ls8 ws9">new algorithm. Furthermo<span class="_ _1"></span>re, a linear extend<span class="_ _1"></span>ed target model is </div><div class="t m0 x7 h6 yc ff4 fs3 fc0 sc0 lsb wsa">proposed, whic<span class="_ _1"></span>h is more <span class="_ _1"></span>capable of d<span class="_ _1"></span>escribing a<span class="_ _1"></span> maneuvering </div><div class="t m0 x7 h6 yd ff4 fs3 fc0 sc0 lsc wsb">target than the conventional p<span class="_ _1"></span>oint target<span class="_ _1"></span> model. The lik<span class="_ _1"></span>elihood </div><div class="t m0 x7 h6 ye ff4 fs3 fc0 sc0 lsd wsc">ratio function of the new model is a<span class="_ _1"></span>lso derived in this paper. Due </div><div class="t m0 x7 h6 yf ff4 fs3 fc0 sc0 ls8 wsd">to the accumu<span class="_ _1"></span>lation of the PF-TBD <span class="_ _1"></span>over time and<span class="_ _1"></span> the </div><div class="t m0 x7 h6 y10 ff4 fs3 fc0 sc0 lse wse">effectiveness of<span class="_ _1"></span> the proposed target model, an improv<span class="_ _1"></span>ed </div><div class="t m0 x7 h6 y11 ff4 fs3 fc0 sc0 lsa wsf">probability of det<span class="_ _1"></span>ection for dim target<span class="_ _1"></span> is obtained. Th<span class="_ _1"></span>e </div><div class="t m0 x7 h6 y12 ff4 fs3 fc0 sc0 lsf ws10">experimental simulations demonstrate th<span class="_ _1"></span>at the proposed method </div><div class="t m0 x7 h6 y13 ff4 fs3 fc0 sc0 ls10 ws11">is capable of detecting and tracki<span class="ls11 ws12">ng a targ<span class="_ _1"></span>et with SNR of 1 dB </span></div><div class="t m0 x7 h6 y14 ff4 fs3 fc0 sc0 ls12 ws1">robustly. </div><div class="t m0 x8 h7 y15 ff2 fs2 fc0 sc0 ls13 ws1">I.<span class="ff5 ls1"> <span class="_ _2"> </span><span class="ff2">I<span class="fs4 ls14">NTRODUCTION<span class="_ _0"></span></span> </span></span></div><div class="t m0 x9 h5 y16 ff2 fs2 fc0 sc0 ls15 ws13">Increasing coherent in<span class="_ _0"></span>tegration period is<span class="_ _0"></span> a common way to </div><div class="t m0 x7 h5 y17 ff2 fs2 fc0 sc0 ls15 ws14">improve radar <span class="_ _0"></span>detection per<span class="_ _0"></span>formance, but the <span class="_ _0"></span>two basic </div><div class="t m0 x7 h5 y18 ff2 fs2 fc0 sc0 ls16 ws15">problem, range migration and Doppler spread[1], restrict the </div><div class="t m0 x7 h5 y19 ff2 fs2 fc0 sc0 ls17 ws16">integration period within a superior limit time beyond which </div><div class="t m0 x7 h5 y1a ff2 fs2 fc0 sc0 ls18 ws17">either range migration or Doppler spread <span class="_ _0"></span>occur. TBD </div><div class="t m0 x7 h5 y1b ff2 fs2 fc0 sc0 ls19 ws18">algorithms can significantly prolong the inte<span class="_ _0"></span>gration time </div><div class="t m0 x7 h5 y1c ff2 fs2 fc0 sc0 ls19 ws19">without any restrict. It <span class="_ _0"></span>makes use of all the information </div><div class="t m0 x7 h5 y1d ff2 fs2 fc0 sc0 ls19 ws1a">underlying the raw measured data to ultimately integrate the </div><div class="t m0 x7 h5 y1e ff2 fs2 fc0 sc0 ls1a ws1b">target energy, which can considerab<span class="_ _0"></span>ly improve the detection<span class="_ _0"></span> </div><div class="t m0 x7 h5 y1f ff2 fs2 fc0 sc0 ls1b ws1">performance[2]. </div><div class="t m0 x9 h5 y20 ff2 fs2 fc0 sc0 ls17 ws1c">The particle filter based TBD (PF-TBD) algori<span class="_ _0"></span>thm </div><div class="t m0 x7 h5 y21 ff2 fs2 fc0 sc0 ls1c ws1d">performs sequential Monte Carlo (MC) estimation to fulfill a </div><div class="t m0 x7 h5 y22 ff2 fs2 fc0 sc0 ls18 ws1e">recursive Bayesian detector. It is convenient <span class="_ _0"></span>for handling the </div><div class="t m0 x7 h5 y23 ff2 fs2 fc0 sc0 ls19 ws1f">problem of nonlinear or non-Gaussia<span class="_ _0"></span>n dynamic system, and </div><div class="t m0 x7 h5 y24 ff2 fs2 fc0 sc0 ls19 ws20">the target buried in a sequence of range-Doppler data happ<span class="_ _0"></span>ens </div><div class="t m0 x7 h5 y25 ff2 fs2 fc0 sc0 ls19 ws21">to be case of nonlinear and non-Gaussian pr<span class="_ _0"></span>ocess. The first </div><div class="t m0 x7 h5 y26 ff2 fs2 fc0 sc0 ls1d ws22">relatively systematic PF-TBD algorithm was proposed by D.<span class="_ _0"></span> J. </div><div class="t m0 x7 h5 y27 ff2 fs2 fc0 sc0 ls17 ws23">Salmond in 2001[3]. Since the<span class="_ _0"></span>n, research in detec<span class="_ _0"></span>ting and </div><div class="t m0 x7 h5 y28 ff2 fs2 fc0 sc0 ls18 ws24">tracking using PF-TBD has dramatically increas<span class="_ _0"></span>ed, resulting </div><div class="t m0 x7 h5 y29 ff2 fs2 fc0 sc0 ls19 ws25">in many improvements of PF-TBD algorithms with better </div><div class="t m0 x7 h5 y2a ff2 fs2 fc0 sc0 ls1e ws26">performances[4,5,6,7,8,9,10]. However, among the current </div><div class="t m0 x7 h5 y2b ff2 fs2 fc0 sc0 ls18 ws27">research achievements target<span class="_ _0"></span> modeling, some of them <span class="_ _0"></span>model </div><div class="t m0 x7 h5 y2c ff2 fs2 fc0 sc0 ls17 ws28">the target as a point[6,7], while others<span class="_ _0"></span> take the target as an </div><div class="t m0 x7 h5 y2d ff2 fs2 fc0 sc0 ls18 ws29">extended model[8,10]. Although each kind of the methods </div><div class="t m0 x7 h5 y2e ff2 fs2 fc0 sc0 ls16 ws2a">above get a certain advantage <span class="_ _0"></span>over the conventional PF-<span class="_ _0"></span>TBD </div><div class="t m0 x7 h5 y2f ff2 fs2 fc0 sc0 ls16 ws15">algorithms, there are still som<span class="_ _1"></span>e places need to be improved </div><div class="t m0 x7 h5 y30 ff2 fs2 fc0 sc0 ls18 ws2b">and fused. </div><div class="t m0 x9 h5 y31 ff2 fs2 fc0 sc0 ls17 ws2c">A Doppler-dimension-extended targ<span class="_ _0"></span>et model for long-</div><div class="t m0 x7 h5 y32 ff2 fs2 fc0 sc0 ls17 ws2d">distance alert radar is proposed in this pa<span class="_ _0"></span>per, which shows </div><div class="t m0 x7 h5 y33 ff2 fs2 fc0 sc0 ls1a ws2e">better capability of describin<span class="_ _0"></span>g the actual maneuvering target<span class="_ _0"></span> </div><div class="t m0 x7 h5 y34 ff2 fs2 fc0 sc0 ls17 ws16">than the point model as pr<span class="_ _0"></span>esented in sectio<span class="_ _0"></span>n 2 of this pa<span class="_ _0"></span>per. </div><div class="t m0 x7 h5 y35 ff2 fs2 fc0 sc0 ls17 ws2f">The likelihood function of t<span class="_ _0"></span>he new model is deduced in </div><div class="t m0 x7 h5 y36 ff2 fs2 fc0 sc0 ls17 ws30">section 3. The implementation of PF-TBD algorit<span class="_ _0"></span>hm and its </div><div class="t m0 xa h5 y37 ff2 fs2 fc0 sc0 ls17 ws31">simulation analysis results are given in section 4 and 5 </div><div class="t m0 xa h5 y38 ff2 fs2 fc0 sc0 ls18 ws32">respectively. Conclusion is drawn in Sect<span class="_ _0"></span>ion 6. </div><div class="t m0 xb h7 y39 ff2 fs2 fc0 sc0 ls13 ws1">II.<span class="ff5 ls1"> <span class="_ _3"> </span><span class="ff2">T</span></span></div><div class="t m0 xc h5 y3a ff2 fs4 fc0 sc0 ls1f ws33">ARGET AND<span class="_ _0"></span> <span class="fs2 ls1 ws1">S<span class="fs4 ls20">YSTEM </span>M<span class="fs4 ls21">ODEL</span> </span></div><div class="t m0 xa h8 y3b ff1 fs2 fc0 sc0 ls22 ws1">A.<span class="ff6 ls1"> <span class="_ _4"> </span></span><span class="ls4 ws34"> System Dynamic Dodel </span></div><div class="t m0 xd h5 y3c ff2 fs2 fc0 sc0 ls4 ws35">Consider a target with <span class="_ _1"></span>a certain intensity le<span class="_ _1"></span>vel moving in </div><div class="t m0 xa h5 y3d ff2 fs2 fc0 sc0 ls4 ws36">a sequence of range-Doppler data frames according to a </div><div class="t m0 xa h5 y3e ff2 fs2 fc0 sc0 ls23 ws37">known dynamic mod<span class="_ _1"></span>el, the target state </div><div class="t m0 xe h9 y3f ff1 fs5 fc0 sc0 ls1 ws1">k</div><div class="c xf y40 w2 ha"><div class="t m0 x0 hb y41 ff1 fs6 fc0 sc0 ls1 ws1">x</div></div><div class="t m0 x10 h5 y42 ff2 fs2 fc0 sc0 ls13 ws22"> can be defin<span class="_ _1"></span>ed as </div><div class="t m0 x11 hc y43 ff2 fs7 fc0 sc0 ls24 ws1">[,<span class="_ _5"> </span>,<span class="_ _6"> </span>,<span class="_ _7"> </span>]</div><div class="t m0 x12 hd y44 ff1 fs8 fc0 sc0 ls25 ws1">kk<span class="_ _8"></span>k<span class="_ _9"> </span>k<span class="_ _a"></span>k</div><div class="c x13 y45 w3 he"><div class="t m0 x0 hf y46 ff1 fs7 fc0 sc0 ls1 ws1">x</div></div><div class="t m0 x14 hf y43 ff1 fs7 fc0 sc0 ls1 ws1">l<span class="_ _b"> </span>fd<span class="_ _c"> </span>fda<span class="_ _5"> </span>A</div><div class="c x15 y47 w4 h10"><div class="t m0 x0 h11 y48 ff7 fs7 fc0 sc0 ls1 ws1">&#61501;</div></div><div class="t m0 x16 h5 y49 ff2 fs2 fc0 sc0 ls26 ws38"> <span class="_ _1"></span> <span class="_ _1"></span> (1) </div><div class="t m0 xa h5 y4a ff2 fs2 fc0 sc0 ls27 ws1">where</div><div class="t m0 x17 h12 y4b ff1 fs9 fc0 sc0 ls1 ws1">k</div><div class="t m0 x18 h13 y4c ff1 fsa fc0 sc0 ls1 ws1">l</div><div class="t m0 x19 h5 y4d ff2 fs2 fc0 sc0 ls28 ws1">, </div><div class="t m0 x1a h14 y4e ff1 fsb fc0 sc0 ls1 ws1">k</div><div class="c x1b y4f w5 h15"><div class="t m0 x1c h16 y50 ff1 fsc fc0 sc0 ls1 ws1">f</div></div><div class="t m0 x1d h16 y51 ff1 fsc fc0 sc0 ls1 ws1">d</div><div class="t m0 x1e h5 y4d ff2 fs2 fc0 sc0 ls1 ws1">,</div><div class="t m0 x1f h14 y4e ff1 fsb fc0 sc0 ls1 ws1">k</div><div class="c x20 y4f w6 h15"><div class="t m0 x1c h16 y50 ff1 fsc fc0 sc0 ls1 ws1">f</div></div><div class="t m0 x21 h16 y51 ff1 fsc fc0 sc0 ls29 ws1">da</div><div class="t m0 x22 h5 y4d ff2 fs2 fc0 sc0 ls2a ws39"> and </div><div class="t m0 x23 h14 y4b ff1 fsb fc0 sc0 ls1 ws1">k</div><div class="t m0 x24 h13 y4c ff1 fsa fc0 sc0 ls1 ws1">A</div><div class="t m0 x25 h5 y4d ff2 fs2 fc0 sc0 ls2b ws3a"> <span class="_ _d"></span>denotes the range, v<span class="_ _1"></span>elocity </div><div class="t m0 xa h5 y52 ff2 fs2 fc0 sc0 ls13 ws3b">(Doppler frequency), m<span class="_ _1"></span>aneuvering acceleration, an<span class="_ _1"></span>d the </div><div class="t m0 xa h5 y53 ff2 fs2 fc0 sc0 ls4 ws3c">intensity of a target at f<span class="_ _1"></span>rame </div><div class="t m0 x25 h17 y54 ff1 fsd fc0 sc0 ls1 ws1">k<span class="_ _e"> </span><span class="ff2 fs2 ls2b ws3d">, respectively. The system </span></div><div class="t m0 xa h5 y55 ff2 fs2 fc0 sc0 ls2c ws3e">dynamic model is defined as </div><div class="t m0 x26 h18 y56 ff2 fse fc0 sc0 ls1 ws1">3</div><div class="t m0 x25 h18 y57 ff2 fse fc0 sc0 ls1 ws1">1</div><div class="t m0 x27 h18 y58 ff2 fse fc0 sc0 ls1 ws1">2</div><div class="t m0 xe h18 y59 ff2 fse fc0 sc0 ls1 ws1">1</div><div class="t m0 x28 h18 y5a ff2 fse fc0 sc0 ls2d ws1">11</div><div class="t m0 x29 h18 y5b ff2 fse fc0 sc0 ls1 ws1">1</div><div class="t m0 x2a h18 y5c ff2 fse fc0 sc0 ls1 ws1">2</div><div class="t m0 x17 h19 y5d ff2 fsf fc0 sc0 ls2e ws1">12<span class="_ _f"></span>0<span class="_ _10"></span>0</div><div class="t m0 x2b h19 y5e ff2 fsf fc0 sc0 ls2f ws1">00<span class="_ _11"></span>0</div><div class="t m0 x17 h19 y5f ff2 fsf fc0 sc0 ls30 ws1">0120</div><div class="t m0 x26 h19 y60 ff2 fsf fc0 sc0 ls31 ws1">02<span class="_ _12"> </span>0<span class="_ _13"></span>0</div><div class="t m0 x17 h19 y61 ff2 fsf fc0 sc0 ls32 ws1">00<span class="_ _14"> </span>1<span class="_ _13"></span>0</div><div class="t m0 x26 h19 y62 ff2 fsf fc0 sc0 ls33 ws1">00<span class="_ _15"> </span>0</div><div class="t m0 x17 h19 y63 ff2 fsf fc0 sc0 ls32 ws1">00<span class="_ _14"> </span>0<span class="_ _13"></span>1</div><div class="t m0 x26 h19 y64 ff2 fsf fc0 sc0 ls33 ws1">00<span class="_ _16"></span>0</div><div class="t m0 x2c h1a y65 ff1 fse fc0 sc0 ls34 ws1">kk<span class="_ _17"> </span>k</div><div class="t m0 x2d h1b y5d ff1 fsf fc0 sc0 ls35 ws1">TL</div><div class="t m0 x2e h1b y5e ff1 fsf fc0 sc0 ls36 ws1">qT<span class="_ _18"> </span>L</div><div class="t m0 x2f h1b y5f ff1 fsf fc0 sc0 ls1 ws1">T</div><div class="t m0 x30 h1b y60 ff1 fsf fc0 sc0 ls37 ws1">qT</div><div class="c x31 y66 w7 h1c"><div class="t m0 x0 h1b y46 ff1 fsf fc0 sc0 ls1 ws1">x</div></div><div class="t m0 x32 h1b y67 ff1 fsf fc0 sc0 ls38 ws1">xv</div><div class="t m0 x33 h1b y68 ff1 fsf fc0 sc0 ls36 ws1">qT</div><div class="t m0 x34 h1b y69 ff1 fsf fc0 sc0 ls1 ws1">q</div><div class="t m1 x35 h1d y5d ff7 fs10 fc0 sc0 ls1 ws1">&#61548;</div><div class="t m1 x1f h1d y5f ff7 fs10 fc0 sc0 ls1 ws1">&#61548;</div><div class="t m1 x16 h1d y60 ff7 fs10 fc0 sc0 ls1 ws1">&#61548;</div><div class="c x36 y6a w8 h1e"><div class="t m0 x0 h1f y6b ff7 fse fc0 sc0 ls1 ws1">&#61485;</div></div><div class="t m0 x37 h1f y65 ff7 fse fc0 sc0 ls1 ws1">&#61485;</div><div class="t m0 x1b h20 y5d ff7 fsf fc0 sc0 ls39 ws1">&#61655;&#61508;</div><div class="t m0 x23 h20 y6c ff7 fsf fc0 sc0 ls3a ws1">&#61673;&#61689;</div><div class="t m0 x38 h20 y5e ff7 fsf fc0 sc0 ls1 ws1">&#61508;</div><div class="t m0 x18 h20 y6d ff7 fsf fc0 sc0 ls3b ws1">&#61673;&#61689;</div><div class="t m0 x23 h20 y6e ff7 fsf fc0 sc0 ls3a ws1">&#61674;&#61690;</div><div class="t m0 x18 h20 y6f ff7 fsf fc0 sc0 ls3b ws1">&#61674;&#61690;</div><div class="t m0 x23 h20 y70 ff7 fsf fc0 sc0 ls3a ws1">&#61674;&#61690;</div><div class="t m0 x18 h20 y71 ff7 fsf fc0 sc0 ls3b ws1">&#61674;&#61690;</div><div class="t m0 x39 h20 y72 ff7 fsf fc0 sc0 ls3c ws1">&#61501;&#61483;</div><div class="t m0 x23 h20 y73 ff7 fsf fc0 sc0 ls3a ws1">&#61674;&#61690;</div><div class="t m0 x18 h20 y74 ff7 fsf fc0 sc0 ls3b ws1">&#61674;&#61690;</div><div class="t m0 x23 h20 y75 ff7 fsf fc0 sc0 ls3a ws1">&#61674;&#61690;</div><div class="t m0 x18 h20 y76 ff7 fsf fc0 sc0 ls3b ws1">&#61674;&#61690;</div><div class="t m0 x23 h20 y77 ff7 fsf fc0 sc0 ls3a ws1">&#61674;&#61690;</div><div class="t m0 x18 h20 y78 ff7 fsf fc0 sc0 ls3b ws1">&#61675;&#61691;</div><div class="t m0 x23 h20 y79 ff7 fsf fc0 sc0 ls3a ws1">&#61675;&#61691;</div><div class="t m0 x3a h5 y7a ff2 fs2 fc0 sc0 ls3d ws3f">, (2) </div><div class="t m0 xa h5 y7b ff2 fs2 fc0 sc0 ls27 ws1">where</div><div class="c x3b y7c w9 h21"><div class="t m2 x0 h22 y7d ff7 fs11 fc0 sc0 ls1 ws1">&#61548;</div></div><div class="t m3 x3c h5 y7e ff2 fs2 fc0 sc0 ls2b ws40"> <span class="_ _19"></span>is the wavelength of the carrier frequency, </div><div class="t m3 x37 h23 y7f ff1 fs12 fc0 sc0 ls1 ws1">T</div><div class="t m3 x3d h5 y7e ff2 fs2 fc0 sc0 ls3e ws41"> and </div><div class="t m3 x3e h24 y80 ff1 fs13 fc0 sc0 ls1 ws1">L</div><div class="c x3f y81 wa h25"><div class="t m3 x0 h26 y82 ff7 fs13 fc0 sc0 ls1 ws1">&#61508;</div></div><div class="t m3 x40 h5 y83 ff2 fs2 fc0 sc0 ls2b ws42"> <span class="_ _1a"></span>are the coherent period and th<span class="_ _1"></span>e range resolution, </div><div class="t m3 xa h5 y84 ff2 fs2 fc0 sc0 ls2b ws1">respectively. </div><div class="t m3 x41 h27 y85 ff2 fs14 fc0 sc0 ls1 ws1">1<span class="_ _1b"></span><span class="ff1">k</span></div><div class="t m3 x42 h28 y86 ff1 fs15 fc0 sc0 ls1 ws1">v</div><div class="c x1e y87 wb h29"><div class="t m3 x0 h2a y88 ff7 fs14 fc0 sc0 ls1 ws1">&#61485;</div></div><div class="t m3 x43 h5 y86 ff2 fs2 fc0 sc0 ls2b ws43"> <span class="_ _8"></span>is a zero mean Gaussian white noise with </div><div class="t m3 xa h5 y89 ff2 fs2 fc0 sc0 ls2b ws1">covariance </div><div class="t m3 x44 h2b y8a ff1 fs16 fc0 sc0 ls1 ws1">Q</div><div class="t m3 x45 h5 y8b ff2 fs2 fc0 sc0 ls2a ws39"> and </div><div class="t m3 x13 h2c y8c ff2 fs5 fc0 sc0 ls1 ws1">1</div><div class="t m3 x1f h28 y8d ff1 fs15 fc0 sc0 ls1 ws1">q</div><div class="t m3 x46 h5 y8b ff2 fs2 fc0 sc0 ls4 ws44"> <span class="_ _1c"></span>is a constant which d<span class="_ _1"></span>enotes the </div><div class="t m3 xa h5 y8e ff2 fs2 fc0 sc0 ls2b ws32">variance of process noise. In the system m<span class="_ _1"></span>odel described in (1) </div><div class="t m3 xa h5 y8f ff2 fs2 fc0 sc0 ls3f ws45">and (2), if </div><div class="t m3 x45 h2d y90 ff1 fs17 fc0 sc0 ls1 ws1">k</div><div class="c x47 y91 wc h2e"><div class="t m3 x1c h2f y92 ff1 fs18 fc0 sc0 ls1 ws1">f</div></div><div class="t m3 x48 h2f y93 ff1 fs18 fc0 sc0 ls40 ws1">da</div><div class="t m3 x41 h5 y94 ff2 fs2 fc0 sc0 ls2c ws46"> <span class="_ _19"></span>equals to 0, the target per<span class="_ _0"></span>forms a constant </div><div class="t m3 xa h5 y95 ff2 fs2 fc0 sc0 ls1a ws47">veloci<span class="_ _0"></span>ty mov<span class="_ _0"></span>ing.<span class="_ _0"></span> If </div><div class="t m3 x12 h2d y96 ff1 fs17 fc0 sc0 ls1 ws1">k</div><div class="c x49 y97 wd h2e"><div class="t m3 x1c h2f y92 ff1 fs18 fc0 sc0 ls1 ws1">f</div></div><div class="t m3 xc h2f y98 ff1 fs18 fc0 sc0 ls40 ws1">da</div><div class="t m3 x4a h5 y99 ff2 fs2 fc0 sc0 ls41 ws3"> not equals to 0 and varies with<span class="_ _1"></span> time, </div><div class="t m3 xa h5 y9a ff2 fs2 fc0 sc0 ls4 ws48">the target moves with a varying v<span class="_ _1"></span>elocity, which may cause </div><div class="t m3 xa h5 y9b ff2 fs2 fc0 sc0 ls3 ws49">Doppler spread along Doppler channels in the co<span class="_ _1"></span>herent </div><div class="t m3 xa h5 y9c ff2 fs2 fc0 sc0 ls41 ws1">integration. </div><div class="t m3 xd h5 y9d ff2 fs2 fc0 sc0 ls2b ws4a">Target existence variable </div><div class="t m3 x4b h30 y9e ff2 fs19 fc0 sc0 ls42 ws1">(0,1<span class="_ _1d"></span>)</div><div class="t m3 x25 h31 y9f ff1 fs1a fc0 sc0 ls1 ws1">k</div><div class="t m3 x4c h32 y9e ff1 fs19 fc0 sc0 ls1 ws1">E<span class="_ _1e"> </span><span class="ff7">&#61646;</span></div><div class="t m3 x4d h5 ya0 ff2 fs2 fc0 sc0 ls43 ws4b">, is introduced here </div><div class="t m3 xa h5 ya1 ff2 fs2 fc0 sc0 ls13 ws4c">to indicate whether a target is present or not. Stat<span class="_ _1"></span>e 0 </div><div class="t m3 xa h5 ya2 ff2 fs2 fc0 sc0 ls4 ws4d">represents the event t<span class="_ _1"></span>hat a target is n<span class="_ _1"></span>ot present and 1<span class="_ _1"></span> denotes </div><div class="t m3 xa h5 ya3 ff2 fs2 fc0 sc0 ls2c ws4e">the opposite[4]. </div><div class="t m3 x4e h33 ya4 ff1 fs1b fc0 sc0 ls1 ws1">k</div><div class="c x41 ya5 we h34"><div class="t m3 x0 h35 y50 ff1 fs1c fc0 sc0 ls1 ws1">E</div></div><div class="t m3 x4f h5 ya6 ff2 fs2 fc0 sc0 ls2b ws4f"> <span class="_ _f"></span>is <span class="_ _0"></span>modeled as a two-state Markov chain. </div><div class="t m3 xa h5 ya7 ff2 fs2 fc0 sc0 ls2c ws16">The transitional probabilities of a target starts and ceases to </div><div class="t m3 xa h5 ya8 ff2 fs2 fc0 sc0 ls4 ws50">exist are defined as </div><div class="t m3 x1f h36 ya9 ff1 fs1d fc0 sc0 ls1 ws1">b</div><div class="c x49 yaa wf h37"><div class="t m3 x0 h38 yab ff1 fs1e fc0 sc0 ls1 ws1">P</div></div><div class="t m3 x50 h5 yac ff2 fs2 fc0 sc0 ls44 ws51"> and </div><div class="t m3 x24 h36 ya9 ff1 fs1d fc0 sc0 ls1 ws1">d</div><div class="c x14 yaa w10 h37"><div class="t m3 x0 h38 yab ff1 fs1e fc0 sc0 ls1 ws1">P</div></div><div class="t m3 x4c h5 yac ff2 fs2 fc0 sc0 ls23 ws37">, respectively. </div><div class="t m3 x51 h39 yad ff2 fs1f fc0 sc0 ls1 ws1">1</div><div class="t m3 x22 h3a yae ff2 fs20 fc0 sc0 ls45 ws1">{1<span class="_ _b"> </span>0<span class="_ _1f"></span>}</div><div class="t m3 x43 h3b yad ff1 fs1f fc0 sc0 ls46 ws1">bk<span class="_ _1c"></span>k</div><div class="t m3 x41 h3c yae ff1 fs20 fc0 sc0 ls47 ws1">PP<span class="_ _11"></span>E<span class="_ _5"> </span>E</div><div class="t m3 x52 h3d yad ff7 fs1f fc0 sc0 ls1 ws1">&#61485;</div><div class="c x2f yaf w11 h3e"><div class="t m3 x0 h3f yb0 ff7 fs20 fc0 sc0 ls1 ws1">&#61501;</div></div><div class="t m3 x36 h3f yae ff7 fs20 fc0 sc0 ls48 ws1">&#61501;&#61501;</div><div class="t m3 xe h5 yb1 ff2 fs2 fc0 sc0 ls49 ws52">, <span class="_ _0"></span> <span class="_ _0"></span> <span class="_ _0"></span>(3.1) </div><div class="t m3 x38 h40 yb2 ff2 fs21 fc0 sc0 ls1 ws1">1</div><div class="t m3 x22 h41 yb3 ff2 fs22 fc0 sc0 ls4a ws1">{0<span class="_ _5"> </span>1<span class="_ _20"></span>}</div><div class="t m3 x43 h42 yb2 ff1 fs21 fc0 sc0 ls4b ws1">dk<span class="_ _21"></span>k</div><div class="t m3 x41 h43 yb3 ff1 fs22 fc0 sc0 ls4c ws1">PP<span class="_ _10"></span>E<span class="_ _b"> </span>E</div><div class="t m3 x53 h44 yb2 ff7 fs21 fc0 sc0 ls1 ws1">&#61485;</div><div class="c x2f yb4 w12 h3e"><div class="t m3 x0 h45 yb0 ff7 fs22 fc0 sc0 ls1 ws1">&#61501;</div></div><div class="t m3 x36 h45 yb3 ff7 fs22 fc0 sc0 ls4d ws1">&#61501;&#61501;</div><div class="t m3 xe h5 yb5 ff2 fs2 fc0 sc0 ls4e ws53">. <span class="_ _1"></span> <span class="_ _1"></span> (3.2) </div><div class="t m3 xa h5 yb6 ff2 fs2 fc0 sc0 ls41 ws22">The transition matrix is gi<span class="_ _1"></span>ven by </div><div class="c x54 yb7 w13 h46"><div class="t m4 x0 h47 yb8 ff7 fs23 fc0 sc0 ls1 ws1">&#61531;</div></div><div class="c x55 yb7 w14 h46"><div class="t m4 x0 h47 yb8 ff7 fs23 fc0 sc0 ls1 ws1">&#61533;</div></div><div class="t m3 x1f h48 yb9 ff2 fs24 fc0 sc0 ls4f ws1">1,<span class="_ _22"></span>;<span class="_ _13"></span>,<span class="_ _23"></span>1</div><div class="t m3 x56 h49 yba ff1 fs25 fc0 sc0 ls50 ws1">bbd<span class="_ _6"> </span>d</div><div class="t m3 x57 h4a yb9 ff1 fs24 fc0 sc0 ls51 ws1">PPP<span class="_ _2"> </span>P<span class="_ _24"></span><span class="ff7 ls52">&#61653;&#61501;<span class="_"> </span>&#61485;<span class="_ _25"> </span>&#61485;</span></div><div class="t m3 x58 h5 ybb ff2 fs2 fc0 sc0 ls53 ws54">. <span class="_ _0"></span> <span class="_ _0"></span> <span class="_ _0"></span> (4) </div><div class="c x59 ybc w15 h4b"><div class="t m3 x0 h4c ybd ff8 fs26 fc0 sc0 ls1 ws1">978-1-4244-5812-7/10/$26.00 &#169;2010 IEEE<span class="fc1 sc0"> </span></div></div><div class="c x5a ybc w16 h4b"><div class="t m3 x0 h4c ybd ff8 fs26 fc0 sc0 ls1 ws1">955</div></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>
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