Reduced spatio-temporal complexity MMPP and image-based tracking filters for maneuvering targets

We present reduced-complexity nonlinear filtering algorithms for image-based tracking of maneuvering targets. In image-based target tracking, the mode of the target is observed as a Markov modulated Poisson process (MMPP) and the aim is to compute optimal estimates of the target's state. We present a reduced complexity algorithm in two steps. First, a gauge transformation is used to reexpress the filtering equations in a form that is computationally more efficient for time discretization than naive discretization of the filtering equations. Second, a spatial aggregation algorithm with guaranteed performance bounds is presented for the time-discretized filters. A numerical example illustrating the performance of the resulting reduced-complexity filtering algorithms for a switching turn-rate model is presented.

[1]  H. Khalil,et al.  Aggregation of the policy iteration method for nearly completely decomposable Markov chains , 1991 .

[2]  Subhrakanti Dey,et al.  Reduced-complexity filtering for partially observed nearly completely decomposable Markov chains , 2000, IEEE Trans. Signal Process..

[3]  Robin J. Evans,et al.  Image-enhanced multiple model tracking , 1999, Autom..

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

[5]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[6]  Wolfgang Fischer,et al.  The Markov-Modulated Poisson Process (MMPP) Cookbook , 1993, Perform. Evaluation.

[7]  Robert J. Elliott,et al.  Filters for estimating Markov modulated poisson processes and image-based tracking , 1997, Autom..

[8]  P. Brémaud Point Processes and Queues , 1981 .

[9]  Pierre Bertrand,et al.  Discrete-time estimation of a Markov chain with marked point process observations. Application to Markovian jump filtering , 2001, IEEE Trans. Autom. Control..

[10]  Robust continuous-time smoothers without two-sided stochastic integrals , 2002, IEEE Trans. Autom. Control..

[11]  Carl D. Meyer,et al.  Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems , 1989, SIAM Rev..

[12]  V. Krishnamurthy Adaptive estimation of hidden nearly completely decomposable Markov chains with applications in blind equalization , 1994 .

[13]  Pierre Bertrand,et al.  An image-based filter for discrete-time markovian jump linear systems , 1996, Autom..

[14]  J. M. Clark The Design of Robust Approximations to the Stochastic Differential Equations of Nonlinear Filtering , 1978 .

[15]  Vikram Krishnamurthy,et al.  Time discretization of continuous-time filters and smoothers for HMM parameter estimation , 1996, IEEE Trans. Inf. Theory.

[16]  Yaakov Bar-Shalom,et al.  Discrete-time point process filter for mode estimation , 1992 .

[17]  Iven M. Y. Mareels,et al.  Reduced-complexity estimation for large-scale hidden Markov models , 2003, IEEE Transactions on Signal Processing.

[18]  A. Bensoussan Stochastic Control of Partially Observable Systems , 1992 .

[19]  David D. Sworder,et al.  Image-enhanced tracking , 1989 .