PHD filters of higher order in target number

TLDR

The multitarget recursive Bayes nonlinear filter is theoretically optimal but only tractable for a few targets, and prior work derived closed‑form PHD approximations while recent studies have called for a PHD filter that is higher‑order in target number. This paper shows that a higher‑order PHD filter in target number is indeed achievable. The authors derive a closed‑form cardinalized PHD (CPHD) filter that propagates both the PHD and the full probability distribution over target number.

Abstract

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.