Poisson Source Localization on the Plane. Cusp Case

TL;DR

This paper investigates the asymptotic properties of Bayes estimators for localizing a Poisson source with cusp-type signal singularities using multiple detectors on a plane.

Contribution

It provides a detailed analysis of the consistency, limit distributions, and moment convergence of Bayes estimators in a cusp case for Poisson source localization.

Findings

Bayes estimators are consistent in the cusp case.

Limit distributions of estimators are characterized.

Moment convergence of estimators is established.

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 $k\geq 3$ detectors on the plane. We study the behavior 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.