A comparison of "clutter-agnostic" PHD filters

Abstract

This paper describes a general approach for deriving PHD/CPHD filters that must estimate the background clutter process, rather than being provided with it a priori. I first derive general time- and measurementupdate equations for clutter-agnostic PHD filters. I then consider two different Markov motion models. For the Uncoupled Motion (UM) model, targets can transition only to targets, and clutter generators can transition only to clutter generators. For the Coupled Motion (CM) model, targets can transition to clutter generators and vice-versa. I demonstrate that R. Streit's "multitarget intensity filter" (MIF) is actually a PHD filter with a CM model. Streit has made the following claims for the MIF: it subsumes the conventional PHD filter as a special case, and can estimate both the clutter rate ? k+1 and the target-birth rate B k+1|k . I exhibit counterexamples to these claims. Because of the CM model, the MIF (1) does not subsume the conventional PHD filter as a special case; (2) cannot estimate B k+1|k when there are no clutter generators; and (3) cannot estimate ? k+1 when the target birth-rate and target death-rate are "conjugate." By way of contrast, PHD filters with UM models do include the PHD filter as a special case, and can estimate the clutter intensity function ? k+1 (z). I also show that the MIF is essentially identical to the UM-model PHD filter when the target birth-rate and death-rate are both small. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).