Markov chain Monte Carlo method for evaluating multi-frame data association hypotheses

This paper describes algorithms for probabilistically evaluating multi-frame data-association hypotheses formed in multiple-hypothesis, multiple-target tracking, using Markov chain Monte Carlo (MCMC) methods (also known as sequential Monte Carlo (SMC) methods). Each algorithm is designed to sequentially, randomly generate multi-frame data association hypotheses, and to converge to a stationary process with the a posteriori probabilities of the multi-frame hypotheses, as the stationary (target) probability distribution. The paper explores three sampling designs: the metropolis sampling, the metropolis sampling with Boltzman acceptance probability, and the metropolis-hasting sampling. Their performances are compared with each other and with the hypothesis evaluation obtained by a K-best hypothesis selection algorithm, using two simple examples.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  M.L. Miller,et al.  A comparison of two algorithms for determining ranked assignments with application to multitarget tracking and motion correspondence , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[3]  Samuel S. Blackman,et al.  Design and Analysis of Modern Tracking Systems , 1999 .

[4]  Chee Chong,et al.  Evaluation of a posteriori probabilities of multi-frame data association hypotheses , 2007, SPIE Optical Engineering + Applications.

[5]  Yakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking: Principles and Techniques , 1995 .

[6]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[7]  Chee-Yee Chong,et al.  Data association hypothesis evaluation for i.i.d. but non-Poisson multiple target tracking , 2004, SPIE Defense + Commercial Sensing.

[8]  Katta G. Murty,et al.  Letter to the Editor - An Algorithm for Ranking all the Assignments in Order of Increasing Cost , 1968, Oper. Res..

[9]  Ronald P. S. Mahler,et al.  Statistical Multisource-Multitarget Information Fusion , 2007 .

[10]  Aubrey B. Poore,et al.  Partial branch and bound algorithm for improved data association in multiframe processing , 1999, Defense, Security, and Sensing.

[11]  Ingemar J. Cox,et al.  On Finding Ranked Assignments With Application to Multi-Target Tracking and Motion Correspondence , 1995 .

[12]  Aubrey B. Poore,et al.  Multitarget tracking and multidimensional assignment problems , 1991, Defense, Security, and Sensing.

[13]  Songhwai Oh,et al.  Markov chain Monte Carlo data association for general multiple-target tracking problems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  C. Morefield.  Application of 0-1 integer programming to multitarget tracking problems , 1977 .

[15]  S. Mori,et al.  Tracking and classifying multiple targets without a priori identification , 1986 .

[16]  Stefano Coraluppi,et al.  All-Source Track and Identity Fusion , 2000 .

[17]  Chee-Yee Chong,et al.  Generalized Murty's algorithm with application to multiple hypothesis tracking , 2007, 2007 10th International Conference on Information Fusion.

[18]  Y. Bar-Shalom,et al.  m-best S-D assignment algorithm with application to multitarget tracking , 2001 .

[19]  Chee-Yee Chong,et al.  Evaluation of Data Association Hypotheses: Non-Poisson I.I.D. Cases , 2004 .

[20]  S.S. Blackman,et al.  Multiple hypothesis tracking for multiple target tracking , 2004, IEEE Aerospace and Electronic Systems Magazine.

[21]  Ronald P. S. Mahler,et al.  Unified sensor management using CPHD filters , 2007, 2007 10th International Conference on Information Fusion.

[22]  Donald Reid.  An algorithm for tracking multiple targets , 1978 .