Stochastic Systems Group  

A PhysicalSpace Approach for the Probability Hypothesis Density and Cardinalized PHD Filters
Peter Willett
University of Connecticut
The probability hypothesis density (PHD) filter, an automatically trackmanaged multitarget tracker, is attracting increasing but cautious attention. Its derivation is elegant and mathematical, and thus of course many engineers fear it; perhaps that is currently limiting the number of researchers working on the subject. In this paper, we explore a physicalspace approach  a bin model  which leads us to arrive the same filter equations as the PHD. Unlike the original derivation of the PHD filter, the concepts used are the familiar ones of conditional probability. The original PHD suffers from a "targetdeath" problem in which even a single missed detection can lead to the apparent disappearance of a target. To obviate this, PHD originator Mahler has recently developed a new "cardinalized" version of PHD (CPHD). We are able to extend our physicalspace derivation to the CPHD case as well. We stress that the original derivations are mathematically correct, and need no embellishment from us; our contribution here is to offer an alternative derivation, one that we find appealing.
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