Poisson Source Localization on the Plane. Cusp Case

Abstract

This work is devoted to the problem of estimation of the localization of Poisson source. The observations are inhomogeneous Poisson processes registered by the k ≥ 3 detectors on the plane. We study the asymptotic properties of the Bayes estimators in the asymptotic of large intensities. It is supposed that the intensity functions of the signals arriving in the detectors have cusp-type singularity. We show the consistency, limit distributions and the convergence of moments of these estimators.