Estimation of the position and time of emission of a source

O. V. Chernoyarov, S. Dachian (), C. Farinetto and Yu. A. Kutoyants
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O. V. Chernoyarov: National Research University “MPEI”
S. Dachian: University of Lille
C. Farinetto: Le Mans University
Yu. A. Kutoyants: National Research University “MPEI”

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 1, No 5, 82 pages

Abstract: Abstract We consider the problem of the estimation of the position on the plane and of the moment of beginning of emission of a source by observations from K detectors on the plane. We propose the conditions of regularity and identifiability, which allow us to use two general theorems by Ibragimov and Khasminskii and to describe the asymptotic behavior of the maximum likelihood and Bayes estimators. Then we propose the construction of a linear estimator of unknown parameters and study its properties in slightly more general situation. Special attention is payed to condition of identifiability.

Keywords: Parameter estimation; Signal in white Gaussian noise; Inhomogeneous Poisson processes; Localization of a source; Asymptotic properties; 62M02; 62G10; 62G20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11203-021-09260-6

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