Optimal PHD filter for single-target detection and tracking
Ronald Maher · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
The PHD filter has attracted much international interest since its introduction in 2000. It is based on two approximations. First, it is a first-order approximation of the multitarget Bayes filter. Second, to achieve closed-form formulas for the Bayes data-update step, the predicted multitarget probability distribution must be assumed Poisson. In this paper we show how to derive an optimal PHD (OPHD) filter, given that target number does not exceed one. (That is, we restrict ourselves to the single-target detection and tracking problem.) We further show that, assuming no more than a single target, the following are identical: (1) the multitarget Bayes filter; (2) the OPHD filter; (3) the CPHD filter; and (4) the multi-hypothesis correlation (MHC) filter. We also note that all of these are generalizations of the probabilistic data association (IPDA) filter of Musicki, Evans, and Stankovic.