The forward-backward Probability Hypothesis Density smoother

A forward-backward Probability Hypothesis Density (PHD) smoother involving forward filtering followed by backward smoothing is derived. The forward filtering is performed by Mahler's PHD recursion. The PHD backward smoothing recursion is derived using Finite Set Statistics (FISST) and standard point process theory. Unlike the forward PHD recursion, the proposed backward PHD recursion is exact and does not require the previous iterate to be Poisson.

[1]  R. Mahler,et al.  PHD filters of higher order in target number , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[2]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[3]  Masahito Yamada,et al.  Structural Time Series Models and the Kalman Filter , 1989 .

[4]  Bing Chen,et al.  Multisensor tracking of a maneuvering target in clutter using IMMPDA fixed-lag smoothing , 2000, IEEE Trans. Aerosp. Electron. Syst..

[5]  Wolfgang Koch,et al.  Fixed-interval retrodiction approach to Bayesian IMM-MHT for maneuvering multiple targets , 2000, IEEE Trans. Aerosp. Electron. Syst..

[6]  Ba-Ngu Vo,et al.  A closed form solution to the Probability Hypothesis Density Smoother , 2010, 2010 13th International Conference on Information Fusion.

[7]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

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

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

[10]  A. K. Mahalanabis,et al.  Improved multi-target tracking in clutter by PDA smoothing , 1990 .

[11]  Ba-Ngu Vo,et al.  The Cardinality Balanced Multi-Target Multi-Bernoulli Filter and Its Implementations , 2009, IEEE Transactions on Signal Processing.

[12]  David Suter,et al.  Joint Detection and Estimation of Multiple Objects From Image Observations , 2010, IEEE Transactions on Signal Processing.

[13]  William Dale Blair,et al.  One-step fixed-lag smoothers for Markovian switching systems , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[14]  Kumaradevan Punithakumar,et al.  Improved multi-target tracking using probability hypothesis density smoothing , 2007, SPIE Optical Engineering + Applications.

[15]  G. Kitagawa.  Non-Gaussian State—Space Modeling of Nonstationary Time Series , 1987 .

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

[17]  Ba-Ngu Vo,et al.  Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter , 2007, IEEE Transactions on Signal Processing.

[18]  J. Meditch.  A survey of data smoothing for linear and nonlinear dynamic systems , 1973 .

[19]  Ba Tuong Vo,et al.  Random finite sets in Multi-object filtering , 2008 .

[20]  T. Mattfeldt.  Stochastic Geometry and Its Applications , 1996 .

[21]  Daniel E. Clark.  First-moment multi-object forward-backward smoothing , 2010, 2010 13th International Conference on Information Fusion.

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

[23]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .