Localization of two radioactive sources on the plane

• Published in: Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems Vol. 27; no. 1; pp. 1 - 23
• Main Authors: Chernoyarov, O. V., Dachian, S., Farinetto, C., Kutoyants, Yu. A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-04-2024; Springer Nature B.V; Springer Verlag
• Subjects: Localization; Mathematics; Mathematics and Statistics; Maximum likelihood estimators; Poisson density functions; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics; Statistics Theory; 62G20; Parameter estimation; 62G10; 62M02; Poisson process; Cusp-type singularity; parameter estimation; cusp-type singularity
• ISSN: 1387-0874; 1572-9311
• DOI: 10.1007/s11203-023-09297-9

The problem of localization on the plane of two radioactive sources by
K
detectors is considered. Each detector records a realization of an inhomogeneous Poisson process whose intensity function is the sum of signals arriving from the sources and of a constant Poisson noise of known intensity. The time of the beginning of emission of the sources is known, and the main problem is the estimation of the positions of the sources. The properties of the maximum likelihood and Bayesian 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.