Multi-object filtering for pairwise Markov chains

The Probability Hypothesis Density (PHD) Filter is a recent solution to the multi-target filtering problem which consists in estimating an unknown number of targets and their states. The PHD filter equations are derived under the assumption that the dynamics of the targets and associated observations follow a Hidden Markov Chain (HMC) model. HMC models have been recently extended to Pairwise Markov Chains (PMC) models. In this paper, we focus on multi-target filtering when targets and associated measurements follow a PMC model, and we extend the classical PHD filter to such models. We also propose a Gaussian Mixture (GM) implementation of our PMC PHD filter for linear and Gaussian PMC. Our approach enables to extend multi-object filtering to more general tracking scenarios, and also enables to deduce an estimate of the measurement associated to each target.