Estimation of the position and time of emission of a source

Chernoyarov, Oleg V.; Dachian, Sergueı̈; Farinetto, Christian; Kutoyants, Yury A.

doi:10.1007/s11203-021-09260-6

Cited by 2 publications

(4 citation statements)

References 9 publications

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“…Mathematical statements are less known. This work is a continuation of a study initiated in [9] and then developed in [1,[4][5][6]15], where it was always supposed that there is only one source on the plane. In the works [5,6,9] it was supposed that the moment of the beginning of the emission τ 0 is known and the unknown parameter was just the position of the source.…”

Section: Introductionmentioning

confidence: 85%

“…Of course, it will be interesting to see the conditions of identifiability in the situation where the beginning of the emissions of these sources are unknown and have to be estimated together with the positions. In the case of one source such problem was discussed in the work [4].…”

Section: Discussionmentioning

confidence: 99%

“…The function ψ(•) describes the fronts of the signals. As in our preceding works (see, e.g., [4]) we take…”

Section: Model Of Observationsmentioning

confidence: 99%

“…In the works [5,6,9] it was supposed that the moment of the beginning of the emission τ 0 is known and the unknown parameter was just the position of the source. The case where τ 0 is unknown too and we have to estimate both τ 0 and the position of the source was treated in [1,4]. In all these works the properties of the maximum likelihood estimator (MLE) and of the Bayesian estimators (BEs) of the position (or of τ 0 and of the position) where described.…”

Section: Introductionmentioning

confidence: 99%

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Localization of two radioactive sources on the plane

Chernoyarov,

Dachian,

Farinetto

et al. 2022

Preprint

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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.

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