  The aim of this paper is two-fold. First we analyze the sequence of intensity
measures of a spatial branching point process arising in a multiple target
tracking context. We study its stability properties, characterize its long time
behavior and provide a series of weak Lipschitz type functional contraction
inequalities. Second we design and analyze an original particle scheme to
approximate numerically these intensity measures. Under appropriate regularity
conditions, we obtain uniform and non asymptotic estimates and a functional
central limit theorem. To the best of our knowledge, these are the first sharp
theoretical results available for this class of spatial branching point
processes.
