A t-Distribution-Based Particle Filter for Target Tracking
LI Shao-jun1, WANG Hong1,2, CHAI Tian-you3
1. Institute of Automation, Chinese Academy of Sciences, Beijing100080, China; 2. Control Systems Centre, University of Manchester, Manchester M60 1QD, UK; 3. Research Center of Automation, Northeastern University, Shenyang 110004, China
Abstract：For the predictive distribution and posterior distribution problem of target states in Bayesian tracking,a new particle filter,called the Student-t distribution Particle Filter(SPF),is developed based on multivariate student-t distributions by using sequential Monte Carlo methodology.To estimate probability density function(PDF) of the target state based on samples,a new Expectation Conditional Maximization Either(ECME) algorithm is introduced and embedded in the SPF.Under the student-t distribution assumption,it is shown theoretically that the SPF is asymptotically optimal in terms of the number of particles.In the tracking of maneuvering target,the performances of SPF,unscented Kalman filter(UKF) and the bootstrap particle filter(SIR) are compared in terms of accuracy.
[1] Anderson B D O,Moore J B.Optimal Filtering[M]. Englewood Ciffs,NJ:Prentice-Hall,1979. [2] Jazwinski A H.Stochastic Processes and Filtering Theory[M]. New York,USA:Academic Press,1970. [3] Chui C K,Chen G.Kalman Filtering with Real-Time Applications(Third Edition)[M]. Berlin,Germany:Springer-Verlag,1999. [4] Julier S J,Uhlmann J K.Unscented filtering and nonlinear estimation[J]. Proceedings of the IEEE,2004,92(3):401-422. [5] Gordon N J,Salmond D J,Smith A F M.Novel approach to nonlinear/non-Gaussian Bayesian state estimation[J]. IEE Proceedings-F,1993,140(2):107-113. [6] Maskell S,Gordon N.A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking[J]. IEEE Transactions on Signal Processing,2002,50(2):174-188. [7] Fearnhea P.Sequential Monte Carlo Methods in Filter Theory[D]. UK:University of Oxford,1998. [8] Doucet A,Godsill S,Andrieu C.Onsequential Monte Carlo sampiing methods for Bayesian filtering[J]. Statistical Computing,2000,10(3):197-208. [9] Liu J S,Chen R.Sequential Monte Carlo methods for dynamic systems[J]. Journal of the American Statistical Association,1998,93(443):1032-1044. [10] Pitt M,Shephard N.Filtering via simulation:auxiliary particle filters[J]. Journal of the American Statistical Association,1999,94(446):590-599. [11] AzimiSadjadi B,Krishnaprasad P S.Approximate nonlinear filtering and its application in navigation[J]. Automatica,2005,41(6):945-956. [12] Doucet A,Freitas N D,Gordon N.Sequential MonteCarlo Methods in Practice[M]. New York:Springer-Verlag,2001. [13] Crisan D,Doucet A.A survey of convergence results on particle filtering methods for practitioners[J]. IEEE Transactions on Signal Processing,2002,50(3):736-746. [14] Liu C H,Rubin D B.ML estimation of the t distribution using EM and its extensions,ECM and ECME[J]. Statistica Sinica,1995,5(1):19-39. [15] Li X R,Jilkov V P.Survey of maneuvering target tracking Part Ⅰ:dynamic models[J]. IEEE Transactions on Aerospace and Electronic Systems,2003,39(4):1333-1364.
