Convergence Results for the Gaussian Mixture Implementation of the Extended-Target PHD Filter and Its Extended Kalman Filtering Approximation

The convergence of the Gaussian mixture extended-target probability hypothesis density (GM-EPHD) filter and its extended Kalman (EK) filtering approximation in mildly nonlinear condition, namely, the EK-GM-EPHD filter, is studied here. This paper proves that both the GM-EPHD filter and the EK-GM-EPHD filter converge uniformly to the true EPHD filter. The significance of this paper is in theory to present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which the two filters satisfy uniform convergence.

[1]  Ronald P. S. Mahler,et al.  PHD filters for nonstandard targets, I: Extended targets , 2009, 2009 12th International Conference on Information Fusion.

[2]  D. Clark,et al.  Group Target Tracking with the Gaussian Mixture Probability Hypothesis Density Filter , 2007, 2007 3rd International Conference on Intelligent Sensors, Sensor Networks and Information.

[3]  Vittorio Colao.  On the Convergence of Iterative Processes for Generalized Strongly Asymptotically ϕ-Pseudocontractive Mappings in Banach Spaces , 2012, J. Appl. Math..

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

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

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

[7]  Christian Lundquist,et al.  A Gaussian mixture PHD filter for extended target tracking , 2010, 2010 13th International Conference on Information Fusion.

[8]  Dietrich Fränken,et al.  Tracking of Extended Objects and Group Targets Using Random Matrices , 2008, IEEE Transactions on Signal Processing.

[9]  Oliver E. Drummond,et al.  A bibliography of cluster (group) tracking , 2004, SPIE Defense + Commercial Sensing.

[10]  Ba-Ngu Vo,et al.  A Consistent Metric for Performance Evaluation of Multi-Object Filters , 2008, IEEE Transactions on Signal Processing.

[11]  Ba-Ngu Vo,et al.  Convergence Analysis of the Gaussian Mixture PHD Filter , 2007, IEEE Transactions on Signal Processing.

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

[13]  J.W. Koch,et al.  Bayesian approach to extended object and cluster tracking using random matrices , 2008, IEEE Transactions on Aerospace and Electronic Systems.

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

[15]  Yeol Je Cho,et al.  Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications , 2012, J. Appl. Math..

[16]  Neil J. Gordon,et al.  Group and extended object tracking , 1999, Optics & Photonics.

[17]  Christian Lundquist,et al.  Tracking rectangular and elliptical extended targets using laser measurements , 2011, 14th International Conference on Information Fusion.

[18]  Chongzhao Han,et al.  Sequential Monte Carlo implementation and state extraction of the group probability hypothesis density filter for partly unresolvable group targets-tracking problem , 2010 .

[19]  I. R. Goodman,et al.  Mathematics of Data Fusion , 1997 .

[20]  Simon J. Godsill,et al.  Poisson models for extended target and group tracking , 2005, SPIE Optics + Photonics.

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

[22]  Christian Lundquist,et al.  Extended target tracking with a cardinalized probability hypothesis density filter , 2011, 14th International Conference on Information Fusion.

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

[24]  Fred Daum,et al.  Importance of resolution in multiple-target tracking , 1994, Defense, Security, and Sensing.

[25]  Gendai Gu,et al.  Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities , 2011, J. Appl. Math..

[26]  X. Rong Li,et al.  Survey of maneuvering target tracking: dynamic models , 2000, SPIE Defense + Commercial Sensing.