Bayesian Multi-Object Filtering for Pairwise Markov Chains

Random finite sets (RFS) are recent tools for addressing the multi-object filtering problem. The probability hypothesis density (PHD) Filter is an approximation of the multi-object Bayesian filter, which results from the RFS formulation of the problem and has been used in many applications. In the RFS framework, it is assumed that each target and associated observation follow a hidden Markov chain (HMC) model. HMCs conveniently describe some physical properties of practical interest for practitioners, but they also implicitly imply restrictive independence properties which, in practice, may not be satisfied by data. In this paper, we show that these structural limitations of HMC models can somehow be relaxed by embedding them into the more general class of pairwise Markov chain (PMC) models. We thus focus on the computation of the PHD filter in a PMC framework, and we propose a practical implementation of the PHD filter for a particular class of PMC models.