Dr Sumeet Singh, Signal Processing Laboratory, Cambridge
Filters for spatial point processes

We consider the inference of a hidden spatial Point Process (PP) X on a CSMS (complete separable metric space) X, from a noisy observation y modeled as the realisation of another spatial PP Y on a CSMS Y. We consider a general model for the observed process Y which includes thinning and displacement and characterise the posterior distribution of X for a Poisson and Gauss-Poisson prior.  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 arget Tracking applications,  which is an important study area in Engineering. Accompanying numerical implementations based on Sequential Monte Carlo will be presented.