点目标跟踪的非线性滤波算法研究
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摘要
目标跟踪技术已经在包括军事和民用的不同的领域中得到应用,它是当今国际上十分活跃的热门领域之一,而目标跟踪的核心为滤波算法。如何提出性能更好的非线性滤波算法,来对付实际系统的非线性、非高斯问题,并高效的应到到目标跟踪系统中,是本领域研究的热点和难点所在。
首先,在单目标跟踪系统,针对混合线性/非线性目标动态模型,提出一种新的混合滤波算法,算法采用Rao-Blackwellized思想,将线性状态与非线性状态进行分离,对非线性状态运用准高斯粒子滤波(quasi-Gaussian particle filtering,Q-GPF)算法进行估计,并将其后验分布近似为单个高斯分布,再利用非线性状态的估计值对线性状态进行卡尔曼滤波(Kalman filter,KF)估计。仿真结果表明新算法在精度不下降的前提下,计算复杂度大大下降。
其次,针对多目标跟踪应用,提出一种新的基于随机集的滤波算法,算法运用Rao-Blackwellized思想,通过挖掘分析“混合线性/非线性模型”的结构,采用序列蒙特卡洛(sequential Monte Carlo,SMC)方法预测与估计概率假设密度滤波器(probability hypothesis density filtering,PHD)迭代式中各个目标的非线性状态,并利用非线性状态粒子中包含的线性状态的信息,使用KF对线性状态进行预测与估计。以更好地估计PHD进而提高各目标状态估计精度。分析与仿真的结果表明,新算法在减少计算量的同时,提升了估计精度。
进一步,同样针对多目标跟踪提出一种新的概率假设密度滤波算法,算法在PHD滤波器迭代式计算之后,运用结合了mean-shift算法的核密度估计(kerneldensity estimation,KDE)理论进行PHD分布的二次估计、提取PHD峰值位置作为目标状态估计值。分析与仿真的结果表明新算法的估计精度有大幅的提高。
The target tracking technique has been applied in different kinds of martial and civil areas.It is one of the scientific topics which draw lots of research interests nowadays.The key of target tracking is filtering algorithm.It is a hotspot and nodus in target tracking technique research to propose more reliable non linear filtering algorithms to cope with the non linear and non Gaussian problem,and applied in practical tracking system efficiently.
Firstly,for single target tracking system,a novel mixed filtering algorithm is proposed for mixed linear/nonlinear state space models.The algorithm utilizes the idea of Rao-Blackwellized to separate the linear and nonlinear states.For the nonlinear states,the posterior distributions of the estimates,which are achieved by the quasi-Gaussian particle filter,are approximated as Gaussian distributions.Also,the linear states are estimated by the Kalman filter with the estimated nonlinear states. The simulation results show that the proposed method saves much computing time with no declined tracking accuracy performance.
Next,we proposed a novel random set based filtering algorithm for multi-target tracking(MTT) application.The algorithm,while utilizing the idea of Rao-Blackwell to enhance the estimating performance of the probability hypothesis density(PHD), adopts the sequential Monte Carlo(SMC) method to predict and estimate the nonlinear states of the multiple targets.In addition,the linear states are estimated by the Kalman filter(KF) with the information embedded in the estimated nonlinear states.Simulation results of the proposed method show that,in addition to reducing particle dimensions and computation complexity,the proposed method significantly enhances tracking accuracy
Moreover,another novel probability hypothesis density filtering algorithm is proposed for multi-target tracking applications.The algorithm utilizes the kernel density estimation theory and the mean-shift algorithm to further estimate the probability hypothesis density and then to extract target state estimates after the computation of the PHD recursive formula.The simulation results of the proposed method show that,the tracking accuracy of the proposed method is increased significantly.
首先,在单目标跟踪系统,针对混合线性/非线性目标动态模型,提出一种新的混合滤波算法,算法采用Rao-Blackwellized思想,将线性状态与非线性状态进行分离,对非线性状态运用准高斯粒子滤波(quasi-Gaussian particle filtering,Q-GPF)算法进行估计,并将其后验分布近似为单个高斯分布,再利用非线性状态的估计值对线性状态进行卡尔曼滤波(Kalman filter,KF)估计。仿真结果表明新算法在精度不下降的前提下,计算复杂度大大下降。
其次,针对多目标跟踪应用,提出一种新的基于随机集的滤波算法,算法运用Rao-Blackwellized思想,通过挖掘分析“混合线性/非线性模型”的结构,采用序列蒙特卡洛(sequential Monte Carlo,SMC)方法预测与估计概率假设密度滤波器(probability hypothesis density filtering,PHD)迭代式中各个目标的非线性状态,并利用非线性状态粒子中包含的线性状态的信息,使用KF对线性状态进行预测与估计。以更好地估计PHD进而提高各目标状态估计精度。分析与仿真的结果表明,新算法在减少计算量的同时,提升了估计精度。
进一步,同样针对多目标跟踪提出一种新的概率假设密度滤波算法,算法在PHD滤波器迭代式计算之后,运用结合了mean-shift算法的核密度估计(kerneldensity estimation,KDE)理论进行PHD分布的二次估计、提取PHD峰值位置作为目标状态估计值。分析与仿真的结果表明新算法的估计精度有大幅的提高。
The target tracking technique has been applied in different kinds of martial and civil areas.It is one of the scientific topics which draw lots of research interests nowadays.The key of target tracking is filtering algorithm.It is a hotspot and nodus in target tracking technique research to propose more reliable non linear filtering algorithms to cope with the non linear and non Gaussian problem,and applied in practical tracking system efficiently.
Firstly,for single target tracking system,a novel mixed filtering algorithm is proposed for mixed linear/nonlinear state space models.The algorithm utilizes the idea of Rao-Blackwellized to separate the linear and nonlinear states.For the nonlinear states,the posterior distributions of the estimates,which are achieved by the quasi-Gaussian particle filter,are approximated as Gaussian distributions.Also,the linear states are estimated by the Kalman filter with the estimated nonlinear states. The simulation results show that the proposed method saves much computing time with no declined tracking accuracy performance.
Next,we proposed a novel random set based filtering algorithm for multi-target tracking(MTT) application.The algorithm,while utilizing the idea of Rao-Blackwell to enhance the estimating performance of the probability hypothesis density(PHD), adopts the sequential Monte Carlo(SMC) method to predict and estimate the nonlinear states of the multiple targets.In addition,the linear states are estimated by the Kalman filter(KF) with the information embedded in the estimated nonlinear states.Simulation results of the proposed method show that,in addition to reducing particle dimensions and computation complexity,the proposed method significantly enhances tracking accuracy
Moreover,another novel probability hypothesis density filtering algorithm is proposed for multi-target tracking applications.The algorithm utilizes the kernel density estimation theory and the mean-shift algorithm to further estimate the probability hypothesis density and then to extract target state estimates after the computation of the PHD recursive formula.The simulation results of the proposed method show that,the tracking accuracy of the proposed method is increased significantly.
引文
[1].Y.Bar-Shalom and T.E.Fortmann.Tracking and Data Association[M].Diego,CA:Academic,1988
[2].凯S.M.统计信号处理基础:估计与检测理论[M].电子工业出版社,2003.
[3].B.D.O.ANDERSON,J.B.MOORE.Optimal filtering[M].Englewood Ciffs NJ:Prentice-Hall,1979.
[4].陈根社,文传源.航天器相对运动估计的一种并行推广卡尔曼滤波方法[J].航空学报,1996,17(1):43-51.
[5].S.J.JULIER,J.K.UHLMANN,H.F.DURRANT WHYTE.A new approach for filtering nonlinear systems[C]//Proceedings of the American Control Conference.Seattle,WA:IEEE,1995:1628-1632.
[6].N.J.GORDON,D.J.SALMOOD,A.F.M.SMITH.Novel approach to nonlinear/non-Gaussian Bayesian state estimation[J],IEE PROCEEDINGS-F,1993,140(2):107-113.
[7].M.SANJEEV ARULAMPALAM,SIMON MASKELLI,NEIL GORDON,et al.A tutorial on particle filters for online nonlinear non-Gaussian Bayesian tracking[J].IEEE Transactions on Signal Processing,2002,50(2):174-188.
[8].Donald B.Reid.An Algorithm for Tracking Multiple Targets[J].IEEE transactions on AUTOMATIC CONTROL,1979,ac-24(6):843-854.
[9].Samuels.Blackman.Multiple Hypothesis Tracking For Multiple Target Tracking[J].IEEE A&E SYSTEMS MAGAZINE,2004,19(1):5-18.
[10].T.E.Fortmann,Y.Bar-Shalom,and M.Scheffe.Sonar tracking of multiple targets using joint probabilistic data association[J].IEEE Journal of OCEANIC ENGINEERING,1983,OE-8(3):173-184.
[11].R.L.Streit and T.E.Luginbuhl.Maximum likelihood method for probabilistic multi-hypothesis tracking[J].Proc.SPIE,1994,2235:5-7.
[12].C.Hue,J-P.Le Cadre,P.P Erez.Tracking Multiple Objects with Particle Filtering[J].IEEE transactions on AEROSPACE AND ELECTRONIC SYSTEMS.2002,38(3):791-812.
[13].C.Hue,J-P.Le Cadre,P.P Erez.Sequential Monte Carlo Methods for Multiple Target Tracking and Data Fusion[J].IEEE transactions on SIGNAL PROCESSING,2002,50(2):309-325.
[14].E.W.Karmen.Multiple target tracking based on symmetric measurement equations[J].IEEE transactions on AUTOMATIC CONTROL,1992,37(3):371-374.
[15].Ba-Ngu Vo,Sumeetpal Singh,Arnaud Doucet.Sequential Monte Carlo Methods for Multi-Target Filtering with Random Finite Sets[J].IEEE transactions on AEROSPACE AND ELECTRONIC SYSTEMS,2005,41(4):1224-1245.
[16].Ronald P.S.Mahler.Multitarget Bayes Filtering via First-Order Multitarget Moments[J].IEEE transactions on AEROSPACE AND ELECTRONIC SYSTEMS.2003,39(4):1152-1178.
[17].Wing-Kin Ma,Ba-Ngu Vo.Tracking an Unknown Time-Varying Number of Speakers Using TDOA Measurements:A Random Finite Set Approach[J].IEEE transactions on SIGNAL PROCESSING,2006,54(9):3291-3304.
[18].Ba-Ngu Vo and Wing-Kin Ma.The Gaussian Mixture Probability Hypothesis Density Filter[J].IEEE transactions on SIGNAL PROCESSING,2006,54(11):4091-4104.
[19].T.Zajic and R.Mahler.A particle-systems implementation of the PHD multi-target tracking filter[J].Proc.SPIE Signal Process.Sensor Fusion Target Recognit.XII,2003,5096:291-299.
[20].M.Tobias,A.D.Lanterman.Probability hypothesis density-based multitarget tracking with bistatic range and Doppler observations[J].IEE Proc.-Radar Sonar Navig.,2005,152(3):195-205.
[21].0.Erdinc,P.Willett,Y.Bar-Shalom.Probability Hypothesis Density Filter for Multitarget Multisensor Tracking[C]//7th International Conference on Information Fusion(FUSION),2005:146-153.
[22]．庄泽森,张建秋,尹建君．多目标跟踪的核粒子概率假设密度滤波算法[J]．航空学报,2008,已录用．
[23].Mahler,R.Global integrated data fusion[C].In Proceedings of the 7th National Symposium on Sensor Fusion,vol.1(unclassified),Sandia National Laboratories,Albuquerque,NM,1994,187-199.
[24].Rudolph van der Merwe.Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models[D].PhD.Thesis.Oregon Health & Science University,2004.
[25].Daniel L.Alspach and Harold W.Sorenson,Nonlinear Bayesian Estimation Using Gaussian Sum Approximations,IEEE Transaction on Automatic control,1972;17(4):439-448.
[26].GAO Yu,ZHANG Jianqiu,HU Bo.A polynomial prediction filter method for estimating multisensor dynamically varying biases[J].Chinese Journal of Aeronautics,2007,20(3):240-246.
[27].JOHAN NORDLUND.Recursive state estimation of nonlinear systems with applications to integrated navigation[R].LiTH-ISY-R-2321,Linkoping:Linkoping Univ.,2000.
[28].JOHAN NORDLUND.Sequential Monte Carlo Filters and Integrated Navigation[D].Linkoping:Linkoping Univ.,2002.
[29].YIN Jianjun,ZHANG Jianqiu,MIKE KLAASB.The marginal Rao-Blackwellized particle filter for mixed linear/nonlinear state space models[J].Chinese Journal of Aeronautics,2007,accepted.
[30].THOMAS SCHON,FREDRIK GUSTAFSSON.Marginalized Particle Filters for Mixed Linear/Nonlinear State-space Models[J].IEEE Transactions on Signal Processing,2005,53(7):2279-2289.
[31].THOMAS SCHON,FREDRIK GUSTAFSSON.The Marginalized Particle Filter in Practice[R].LiTH-ISY-R-2715,Linkoping:Linkoping Univ.,2005.A.Goshtasby,Image registration by local approximation methods,Image Vision Comput.,vol.6,no.4,Nov.1988:225-261.
[32].Vihola M.Rao-Blackwellised Particle Filtering in Random Set Multitarget Tracking[J].IEEE Transactions on Aerospace & Electronic Systems,2007,43(2):689-705.
[33].Yin J J,Zhang J Q,Zhuang Z S.Gaussian-sum PHD filtering algorithms for nonlinear non-Gaussian models[J].Chinese Journal of Aeronautics,2008,21(4):341-351.
[34].KAZUFUMI ITO,KAIQI XIONG.Gaussian filters for nonlinear filtering problems[J].IEEE Transactions on Automatic Control,2000,45(5):910-927.
[35].JAYESH H.KOTECHA,PETAR M.DJURIC'.Gaussian particle filtering[J].IEEE Transactions on Signal Processing,2003,51(10):2592-2601.
[36].JAYESH H.KOTECHA,PETAR M.DIURIC'.Gaussian sum particle filtering[J].IEEE Transactions on Signal Processing,2003,51(10):2602-2612.
[37].YUANXIN WU,DEWEN HU,MEIPING WU,et al.Quasi-Gaussian particle filtering[C]//V.N.Alexandrov et al.LNCS,Berlin Heidelberg:Springer,2006:689-696.
[38].Karlsson R,Sch(o|¨)n T.Complexity analysis of the marginalized particle filter[R].LiTH-ISY-R-2611,Linkoping:Linkoping Univ.,2004.
[39].Arnaud Doucet,Neil J.Gordon,Vikram Krishnamurthy.Particle filters for state estimation of jump Markov linear systems[J].IEEE Transactions on Signal Processing,2001,49(3),613-624.
[40].Arnaud Doucet.On sequential simulation-based methods for Bayesian filtering[R].CUED/F-INFENG/TR.310(1998),University of Cambridge CB2 1PZ Cambridge,1998.
[41].Hoffman J R,Mahler R P S.Multitarget miss distance via optimal assignment[J].IEEE Transactions on Systems,Man,And Cybernetics-Part A:Systems And Humans,2004,34(3):327-336.
[42].庄泽森,张建秋,尹建君.混合线性/非线性模型的准高斯Rao-Blackwellized粒子滤波法[J].航空学报,2008,29(1):450-455.
[43].Panta K,Vo B,Singh S.Improved probability hypothesis density(PHD)filter for multitarget tmcking[C]//Intelligent Sensing and Information Processing,2005.ICISIP 2005.2005:213-218.
[44].Bohyung Han,Dorin Comaniciu et al.Sequential Kernel Density Approximation and Its Application to Real-Time Visual Tracking[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.accepted.
[45].Ahmed Elgammal,Ramani Duraiswami et al.Background and Foreground Modeling Using Nonparametric Kernel Density Estimation for Visual Surveillance[J].PROCEEDINGS OF THE IEEE,2002,90(7):1151-1163.
[46].Cheng Chang and Rashid Ansari.Kernel Particle Filter for Visual Tracking[J].IEEE SIGNAL PROCESSING LETTERS,2005,12,(3):242-245.
[47].Cheng Chang,Rashid Ansari,Ashfaq Khokhar.Efficient Tracking of Cyclic Human Motion by Component Motion[J].IEEE SIGNAL PROCESSING LETTERS,2004,11(12):941-944.
[48].Cheng Chang and Rashid Ansari.Kernel Particle Filter:Iterative Sampling for Efficient Visual Tracking[C]//Proceedings of 2003 International Conference on Image Processing.Barcelona,Spain:The Institute of Electrical and Electronics Engineers Signal Processing Society,2003:977-980.
[49].Y.Cheng,Mean shift,mode seeking,and clustering[J].IEEE Trans.Pattern Anal.Mach.Intell.,1995,17(8):790-799.
[50].Comaniciu,D.and P.Meer.Mean Shift analysis and application[C]//Proceedings of the seventh IEEE International Conference.Computer Vision.1999.
[51].Comaniciu,D.and P.Meer,Mean Shift:A Robust application toward feature space analysis[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002.24(5):603-619.
[52].Dorin Comaniciu.An Algorithm for Data-Driven Bandwidth Selection[J].IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,2003,25(2):281-288.
[53].A.Elgammal,R.Duraiswami,and L.S.Davis,Efficient Kernel Density Estimation Using the Fast Gauss Transform with Applications to Color Modeling and Tracking[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.2003.25(11):1499-1504.
[54].Yang C,Improved Fast Gauss Transform and Efficient Kernel Density Estimation[C]// Proceedings Ninth IEEE International Conference on Computer Vision.Nice,France:IEEE Computer Society Technical Committee on Pattern Analysis and Machine Intelligence,2003:664-671.
[2].凯S.M.统计信号处理基础:估计与检测理论[M].电子工业出版社,2003.
[3].B.D.O.ANDERSON,J.B.MOORE.Optimal filtering[M].Englewood Ciffs NJ:Prentice-Hall,1979.
[4].陈根社,文传源.航天器相对运动估计的一种并行推广卡尔曼滤波方法[J].航空学报,1996,17(1):43-51.
[5].S.J.JULIER,J.K.UHLMANN,H.F.DURRANT WHYTE.A new approach for filtering nonlinear systems[C]//Proceedings of the American Control Conference.Seattle,WA:IEEE,1995:1628-1632.
[6].N.J.GORDON,D.J.SALMOOD,A.F.M.SMITH.Novel approach to nonlinear/non-Gaussian Bayesian state estimation[J],IEE PROCEEDINGS-F,1993,140(2):107-113.
[7].M.SANJEEV ARULAMPALAM,SIMON MASKELLI,NEIL GORDON,et al.A tutorial on particle filters for online nonlinear non-Gaussian Bayesian tracking[J].IEEE Transactions on Signal Processing,2002,50(2):174-188.
[8].Donald B.Reid.An Algorithm for Tracking Multiple Targets[J].IEEE transactions on AUTOMATIC CONTROL,1979,ac-24(6):843-854.
[9].Samuels.Blackman.Multiple Hypothesis Tracking For Multiple Target Tracking[J].IEEE A&E SYSTEMS MAGAZINE,2004,19(1):5-18.
[10].T.E.Fortmann,Y.Bar-Shalom,and M.Scheffe.Sonar tracking of multiple targets using joint probabilistic data association[J].IEEE Journal of OCEANIC ENGINEERING,1983,OE-8(3):173-184.
[11].R.L.Streit and T.E.Luginbuhl.Maximum likelihood method for probabilistic multi-hypothesis tracking[J].Proc.SPIE,1994,2235:5-7.
[12].C.Hue,J-P.Le Cadre,P.P Erez.Tracking Multiple Objects with Particle Filtering[J].IEEE transactions on AEROSPACE AND ELECTRONIC SYSTEMS.2002,38(3):791-812.
[13].C.Hue,J-P.Le Cadre,P.P Erez.Sequential Monte Carlo Methods for Multiple Target Tracking and Data Fusion[J].IEEE transactions on SIGNAL PROCESSING,2002,50(2):309-325.
[14].E.W.Karmen.Multiple target tracking based on symmetric measurement equations[J].IEEE transactions on AUTOMATIC CONTROL,1992,37(3):371-374.
[15].Ba-Ngu Vo,Sumeetpal Singh,Arnaud Doucet.Sequential Monte Carlo Methods for Multi-Target Filtering with Random Finite Sets[J].IEEE transactions on AEROSPACE AND ELECTRONIC SYSTEMS,2005,41(4):1224-1245.
[16].Ronald P.S.Mahler.Multitarget Bayes Filtering via First-Order Multitarget Moments[J].IEEE transactions on AEROSPACE AND ELECTRONIC SYSTEMS.2003,39(4):1152-1178.
[17].Wing-Kin Ma,Ba-Ngu Vo.Tracking an Unknown Time-Varying Number of Speakers Using TDOA Measurements:A Random Finite Set Approach[J].IEEE transactions on SIGNAL PROCESSING,2006,54(9):3291-3304.
[18].Ba-Ngu Vo and Wing-Kin Ma.The Gaussian Mixture Probability Hypothesis Density Filter[J].IEEE transactions on SIGNAL PROCESSING,2006,54(11):4091-4104.
[19].T.Zajic and R.Mahler.A particle-systems implementation of the PHD multi-target tracking filter[J].Proc.SPIE Signal Process.Sensor Fusion Target Recognit.XII,2003,5096:291-299.
[20].M.Tobias,A.D.Lanterman.Probability hypothesis density-based multitarget tracking with bistatic range and Doppler observations[J].IEE Proc.-Radar Sonar Navig.,2005,152(3):195-205.
[21].0.Erdinc,P.Willett,Y.Bar-Shalom.Probability Hypothesis Density Filter for Multitarget Multisensor Tracking[C]//7th International Conference on Information Fusion(FUSION),2005:146-153.
[22]．庄泽森,张建秋,尹建君．多目标跟踪的核粒子概率假设密度滤波算法[J]．航空学报,2008,已录用．
[23].Mahler,R.Global integrated data fusion[C].In Proceedings of the 7th National Symposium on Sensor Fusion,vol.1(unclassified),Sandia National Laboratories,Albuquerque,NM,1994,187-199.
[24].Rudolph van der Merwe.Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models[D].PhD.Thesis.Oregon Health & Science University,2004.
[25].Daniel L.Alspach and Harold W.Sorenson,Nonlinear Bayesian Estimation Using Gaussian Sum Approximations,IEEE Transaction on Automatic control,1972;17(4):439-448.
[26].GAO Yu,ZHANG Jianqiu,HU Bo.A polynomial prediction filter method for estimating multisensor dynamically varying biases[J].Chinese Journal of Aeronautics,2007,20(3):240-246.
[27].JOHAN NORDLUND.Recursive state estimation of nonlinear systems with applications to integrated navigation[R].LiTH-ISY-R-2321,Linkoping:Linkoping Univ.,2000.
[28].JOHAN NORDLUND.Sequential Monte Carlo Filters and Integrated Navigation[D].Linkoping:Linkoping Univ.,2002.
[29].YIN Jianjun,ZHANG Jianqiu,MIKE KLAASB.The marginal Rao-Blackwellized particle filter for mixed linear/nonlinear state space models[J].Chinese Journal of Aeronautics,2007,accepted.
[30].THOMAS SCHON,FREDRIK GUSTAFSSON.Marginalized Particle Filters for Mixed Linear/Nonlinear State-space Models[J].IEEE Transactions on Signal Processing,2005,53(7):2279-2289.
[31].THOMAS SCHON,FREDRIK GUSTAFSSON.The Marginalized Particle Filter in Practice[R].LiTH-ISY-R-2715,Linkoping:Linkoping Univ.,2005.A.Goshtasby,Image registration by local approximation methods,Image Vision Comput.,vol.6,no.4,Nov.1988:225-261.
[32].Vihola M.Rao-Blackwellised Particle Filtering in Random Set Multitarget Tracking[J].IEEE Transactions on Aerospace & Electronic Systems,2007,43(2):689-705.
[33].Yin J J,Zhang J Q,Zhuang Z S.Gaussian-sum PHD filtering algorithms for nonlinear non-Gaussian models[J].Chinese Journal of Aeronautics,2008,21(4):341-351.
[34].KAZUFUMI ITO,KAIQI XIONG.Gaussian filters for nonlinear filtering problems[J].IEEE Transactions on Automatic Control,2000,45(5):910-927.
[35].JAYESH H.KOTECHA,PETAR M.DJURIC'.Gaussian particle filtering[J].IEEE Transactions on Signal Processing,2003,51(10):2592-2601.
[36].JAYESH H.KOTECHA,PETAR M.DIURIC'.Gaussian sum particle filtering[J].IEEE Transactions on Signal Processing,2003,51(10):2602-2612.
[37].YUANXIN WU,DEWEN HU,MEIPING WU,et al.Quasi-Gaussian particle filtering[C]//V.N.Alexandrov et al.LNCS,Berlin Heidelberg:Springer,2006:689-696.
[38].Karlsson R,Sch(o|¨)n T.Complexity analysis of the marginalized particle filter[R].LiTH-ISY-R-2611,Linkoping:Linkoping Univ.,2004.
[39].Arnaud Doucet,Neil J.Gordon,Vikram Krishnamurthy.Particle filters for state estimation of jump Markov linear systems[J].IEEE Transactions on Signal Processing,2001,49(3),613-624.
[40].Arnaud Doucet.On sequential simulation-based methods for Bayesian filtering[R].CUED/F-INFENG/TR.310(1998),University of Cambridge CB2 1PZ Cambridge,1998.
[41].Hoffman J R,Mahler R P S.Multitarget miss distance via optimal assignment[J].IEEE Transactions on Systems,Man,And Cybernetics-Part A:Systems And Humans,2004,34(3):327-336.
[42].庄泽森,张建秋,尹建君.混合线性/非线性模型的准高斯Rao-Blackwellized粒子滤波法[J].航空学报,2008,29(1):450-455.
[43].Panta K,Vo B,Singh S.Improved probability hypothesis density(PHD)filter for multitarget tmcking[C]//Intelligent Sensing and Information Processing,2005.ICISIP 2005.2005:213-218.
[44].Bohyung Han,Dorin Comaniciu et al.Sequential Kernel Density Approximation and Its Application to Real-Time Visual Tracking[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.accepted.
[45].Ahmed Elgammal,Ramani Duraiswami et al.Background and Foreground Modeling Using Nonparametric Kernel Density Estimation for Visual Surveillance[J].PROCEEDINGS OF THE IEEE,2002,90(7):1151-1163.
[46].Cheng Chang and Rashid Ansari.Kernel Particle Filter for Visual Tracking[J].IEEE SIGNAL PROCESSING LETTERS,2005,12,(3):242-245.
[47].Cheng Chang,Rashid Ansari,Ashfaq Khokhar.Efficient Tracking of Cyclic Human Motion by Component Motion[J].IEEE SIGNAL PROCESSING LETTERS,2004,11(12):941-944.
[48].Cheng Chang and Rashid Ansari.Kernel Particle Filter:Iterative Sampling for Efficient Visual Tracking[C]//Proceedings of 2003 International Conference on Image Processing.Barcelona,Spain:The Institute of Electrical and Electronics Engineers Signal Processing Society,2003:977-980.
[49].Y.Cheng,Mean shift,mode seeking,and clustering[J].IEEE Trans.Pattern Anal.Mach.Intell.,1995,17(8):790-799.
[50].Comaniciu,D.and P.Meer.Mean Shift analysis and application[C]//Proceedings of the seventh IEEE International Conference.Computer Vision.1999.
[51].Comaniciu,D.and P.Meer,Mean Shift:A Robust application toward feature space analysis[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002.24(5):603-619.
[52].Dorin Comaniciu.An Algorithm for Data-Driven Bandwidth Selection[J].IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,2003,25(2):281-288.
[53].A.Elgammal,R.Duraiswami,and L.S.Davis,Efficient Kernel Density Estimation Using the Fast Gauss Transform with Applications to Color Modeling and Tracking[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.2003.25(11):1499-1504.
[54].Yang C,Improved Fast Gauss Transform and Efficient Kernel Density Estimation[C]// Proceedings Ninth IEEE International Conference on Computer Vision.Nice,France:IEEE Computer Society Technical Committee on Pattern Analysis and Machine Intelligence,2003:664-671.