Localization of Two Radioactive Sources on the Plane

O. Chernoyarov (1, 2) , S. Dachian (3) , C. Farinetto (4) , Yu. Kutoyants (4)

1 MPEI - Moscow Power Engineering Institute
2 Tomsk State University [Tomsk]
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 LMM - Laboratoire Manceau de Mathématiques

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.

Mots clés: Poisson process; parameter estimation; cusp-type singularity

Domaines: Théorie [stat.TH]

O. Chernoyarov, S. Dachian, C. Farinetto, Yu. Kutoyants. Localization of Two Radioactive Sources on the Plane. Statistical Inference for Stochastic Processes, 2024, 27 (1), pp.1-23. ⟨10.1007/s11203-023-09297-9⟩. ⟨hal-03687265v2⟩