Mathematics

On the identification of the source of emission on the plane

N. V. Arakelyan^a, Yu. A. Kutoyants<sup>b

a</sup> Université du Maine
^b Tomsk State University V.V.Kuibyshev

Abstract: We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by $K$ detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimates, we construct estimators of the position of source and the moment of the beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.

Keywords: Inhomogeneous Poisson process, parameter estimation,localization on the plane.

MSC: 62M02, 62G10 ,62G20

Received: 17.03.2019
Revised: 15.04.2019
Accepted: 25.04.2019

Language: English