On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Statistical Multisource-Multitarget Information Fusion
Statistical Multisource-Multitarget Information Fusion
The Gaussian Mixture Probability Hypothesis Density Filter
IEEE Transactions on Signal Processing
Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter
IEEE Transactions on Signal Processing - Part II
High-speed Sigma-gating SMC-PHD filter
Signal Processing
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An algorithm that is capable not only of tracking multiple targets but also of "track management"--meaning that it does not need to know the number of targets as a user input--is of considerable interest. In this paperwedevise a recursivetrack-managed filter via a quantized state-space ("bin") model. In the limit, as the discretization implied by the bins becomes as refined as possible (infinitesimal bins) we find that the filter equations are identical to Mahler's probability hypothesis density (PHD) filter, a novel track-managed filtering scheme that is attracting increasing attention. Thus, one contribution of this paper is an interpretation of, if not the PHD itself, at least what the PHD is doing. This does offer some intuitive appeal, but has some practical use as well: with this model it is possible to identify the PHD's "target-death" problem, and also the statistical inference structures of the PHD filters. To obviate the target death problem, PHD originator Mahler developed a new "cardinalized" version of PHD (CPHD). The second contribution of this paper is to extend the "bin-occupancy" model such that the resulting recursive filter is identical to the cardinalized PHD filter.