Graphical model approximations to the full Bayes random finite set filter
Dr J.L. Williams (Defence Science and Technology Organisation)
NICTA SML SEMINARDATE: 2011-04-07
TIME: 11:00:00 - 12:00:00
LOCATION: NICTA - 7 London Circuit
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ABSTRACT:
Abstract: Random finite sets (RFS) has been a fruitful area of research in recent years, yielding new approximate filters such as the probability hypothesis density (PHD), cardinalised PHD (CPHD), and multiple target multi-Bernoulli (MeMBer). Comparably, little work has been done in developing implementations of the full Bayes RFS filter. In this paper, we assume a structured form for the full multiple target RFS distribution, and show that this structure is maintained by the prediction and update operations. The form involves the union of a Poisson point process (PPP) and a structure similar to a MeMBer distribution, but with a particular form of coupling between the single target components; this suggests a new family of hybrid algorithms combining these components. Subsequently, we show that sum-product loopy belief propagation (LBP) can be used to perform inference on the distribution, approximating it by a MeMBer distribution, the components of which approximately incorporate the impact of data association. We also describe an efficient implementation of the related max-product LBP algorithm, which can be used to implement multiple dimensional assignment (MDA), yielding a closely related multiple hypothesis tracking (MHT) algorithm. Finally, we describe how this points to a hybrid algorithm that uses the MDA solution to fix coalescence, a major problem with the sum-product based filter.
