Localization of two radioactive sources on the plane

TL;DR

This paper investigates the problem of localizing two radioactive sources on a plane using multiple detectors, analyzing the properties of estimators under different signal regularities in a Poisson process framework.

Contribution

It provides a detailed analysis of the maximum likelihood and Bayesian estimators for source localization under various regularity conditions of the signals.

Findings

MLE and Bayesian estimators are characterized asymptotically.

Different regularity conditions affect the estimators' properties.

The study enhances understanding of source localization in noisy Poisson processes.

Abstract

It is considered the problem of localization on the plane of two radioactive sources by K detectors. Each detector records a realization of inhomogeneous Poisson process and the intensity function of this process is a sum of a signal arriving from the sources and the constant Poisson noise of known intensity. The time of the beginning of emissions of two sources is known and the main problem is the estimation of the position of the sources. The properties of the MLE and Bayessian estimators are described in the asymptotics of large signals in three situations of different regularities of the fronts of the signals: smooth, cusp-type and change-point type.