PHD filters of second order in target number

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 an earlier paper at this conference we derived a closed-form cardinalized PHD CPHD), filter, which propagates not only the PHD but also the entire probability distribution on target number. Since the CPHD filter has computational complexity O(m3) in the number m of measurements, additional approximation is desirable. In this paper we discuss a second-order approximation called the "binomial filter."