Graphical model approximations of random finite set filters

Abstract: Random finite sets (RFSs) has been a fruitful area of research in recent years, yielding new approximate filters such as the probability hypothesis density (PHD), cardinalised PHD (CPHD), and multiple target multi-Bernoulli (MeMBer). These new methods have largely been based on approximations that side-step the need for measurement-to-track association. Comparably, RFS methods that incorporate data association, such as Morelande and Challa's (M-C) method, have received little attention. This paper provides a RFS algorithm that incorporates data association similarly to the M-C method, but retains computational tractability via a recently developed approximation of marginal association weights. We describe an efficient method for resolving the track coalescence phenomenon which is problematic for joint probabilistic data association (JPDA) and related methods (including M-C). The method utilises a network flow optimisation, and thus is tractable for large numbers of targets. Finally, our derivation also shows that it is natural for the multi-target density to incorporate both a Poisson point process (PPP) component (representing targets that have never been detected) and a multi-Bernoulli component (representing targets under track). We describe a method of recycling, in which tracks with a low probability existence are transferred from the multi-Bernoulli component to the PPP component, effectively yielding a hybrid of M-C and PHD.