Marginalized PHD Filters for multi-target filtering

Multi-target filtering aims at tracking an unknown number of targets from a set of observations. The Probability Hypothesis Density (PHD) Filter is a promising solution but cannot be implemented exactly. Suboptimal implementation techniques include Gaussian Mixture (GM) solutions, which hold only in linear and Gaussian models, and Sequential Monte Carlo (SMC) algorithms, which estimate the number of targets and their state parameters for a more general class of models. In this paper, we address the case of Gaussian models where the state can be decomposed into a linear component and a non-linear one, and we show that the use of SMC methods in such models can indeed be reduced. Our technique not only improves the estimate of the number of targets but also that of their state. We finally adapt the technique to linear and Gaussian jump Markov state space systems (JMSS) in order to reduce the intractability of existing solutions, and to JMSS with partially linear and partially non-linear state vector.