Convergence Analysis of the Gaussian Mixture PHD Filter

The Gaussian mixture probability hypothesis density (PHD) filter was proposed recently for jointly estimating the time-varying number of targets and their states from a sequence of sets of observations without the need for measurement-to-track data association. It was shown that, under linear-Gaussian assumptions, the posterior intensity at any point in time is a Gaussian mixture. This paper proves uniform convergence of the errors in the algorithm and provides error bounds for the pruning and merging stages. In addition, uniform convergence results for the extended Kalman PHD Filter are given, and the unscented Kalman PHD Filter implementation is discussed

[1]  N. Ikoma,et al.  Tracking of feature points in image sequence by SMC implementation of PHD filter , 2004, SICE 2004 Annual Conference.

[2]  Ba-Ngu Vo,et al.  The GM-PHD Filter Multiple Target Tracker , 2006, 2006 9th International Conference on Information Fusion.

[3]  Martin Alexander Youngson,et al.  Linear Functional Analysis , 2000 .

[4]  Ba-Ngu Vo,et al.  The Gaussian Mixture Probability Hypothesis Density Filter , 2006, IEEE Transactions on Signal Processing.

[5]  S. Julier,et al.  A General Method for Approximating Nonlinear Transformations of Probability Distributions , 1996 .

[6]  D. Salmond.  Tracking in Uncertain Environments , 1989 .

[7]  H. Sorenson,et al.  Recursive bayesian estimation using gaussian sums , 1971 .

[8]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  B. Vo,et al.  A closed-form solution for the probability hypothesis density filter , 2005, 2005 7th International Conference on Information Fusion.

[10]  Ba-Ngu Vo,et al.  GM-PHD filter multitarget tracking in sonar images , 2006, SPIE Defense + Commercial Sensing.

[11]  Daniel E. Clark,et al.  Convergence results for the particle PHD filter , 2006, IEEE Transactions on Signal Processing.

[12]  James Ting-Ho Lo,et al.  Finite-dimensional sensor orbits and optimal nonlinear filtering , 1972, IEEE Trans. Inf. Theory.

[13]  Daniel E. Clark,et al.  Bayesian multiple target tracking in forward scan sonar images using the PHD filter , 2005 .

[14]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[15]  Jason L. Williams.  Gaussian Mixture Reduction for Tracking Multiple Maneuvering Targets in Clutter , 2003 .

[16]  R. Mahler.  Multitarget Bayes filtering via first-order multitarget moments , 2003 .

[17]  Aaron D. Lanterman,et al.  Probability hypothesis density-based multitarget tracking with bistatic range and Doppler observations , 2005 .

[18]  Sumeetpal S. Singh,et al.  Convergence of the SMC Implementation of the PHD Filte , 2006 .

[19]  Sumeetpal S. Singh,et al.  Sequential monte carlo implementation of the phd filter for multi-target tracking , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[20]  A. Doucet,et al.  Sequential Monte Carlo methods for multitarget filtering with random finite sets , 2005, IEEE Transactions on Aerospace and Electronic Systems.