Filters for Spatial Point Processes
Artikel i vetenskaplig tidskrift, 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.

target tracking



PHD filter


hidden point process inference

Poisson point process prior

Gauss-Poisson point process


S. S. Singh

University of Cambridge

B. N. Vo

University of Melbourne

A. Baddeley

University of Western Australia

Sergey Zuev

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

SIAM Journal on Control and Optimization

0363-0129 (ISSN) 1095-7138 (eISSN)

Vol. 48 2275-2295