Stochastic models and methods for multi-object tracking

The problem of multiple-object tracking consists in the recursive estimation of the state of several targets by using the information coming from an observation process. The objective of this thesis is to study the spatial branching processes and the measure-valued systems arising in multi-object tracking. We focus on a class of filters called Probability Hypothesis Density (PHD) filters by first analyzing their performance on simulated scenarii and then by studying their properties of stability and convergence. The thesis is organized in two parts: the first part overviews the techniques proposed in the literature and introduces the Probability Hypothesis Density filter as a tractable approximation to the full multi-target Bayes filter based on the Random Finite Sets formulation. A series of contributions concerning the numerical implementation of PHD filters are proposed as well as the analysis of their performance on realistic scenarios. The second part focuses on the theoretical aspects of the PHD recursion in the context of spatial branching processes. We establish the expression of the conditional distribution of a latent Poisson point process given an observation process and propose an alternative derivation of the PHD filter based on this result. Stability properties, long time behavior as well as the uniform convergence of a general class of stochastic filtering algorithms are discussed. Schemes to approximate the measurevalued equations arising in nonlinear multi-target filtering are proposed and studied.