Tracking targets with pairwise-Markov dynamics

Single- and multi-target tracking are both typically based on the hidden Markov chain (HMC) model. That is, the target process is a Markov chain, observed by an independent observation process. Since HMC independence assumptions are invalid in many practical applications, the pairwise Markov chain (PMC) model has been proposed as an approach for weakening them. Petetin and Desbouvries subsequently proposed a PMC generalization of the probability hypothesis density (PHD) filter, but their derivation was somewhat heuristic. The first major purpose of this paper is to construct a solid theoretical foundation for the Petetin-Desbouvries filter which turns out to be a multitarget HMC model rather than a true multitarget PMC model The second major purpose is to use this foundation to devise PMC versions of any random finite set (RFS) filter, thus allowing tracking of targets with non-HMC dynamics.