Filters for Spatial Point Processes

Journal article, 2009

We study the general problem of estimating a "hidden" point process X, given the realization of an "observed" point process Y (possibly defined in different spaces) with known joint distribution. We characterize the posterior distribution of X under marginal Poisson and Gauss-Poisson priors and when the transformation from X to Y includes thinning, displacement, and augmentation with extra points. These results are then applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion. The dynamics of X considered are general enough for many target tracking applications.