Poisson source localization on the plane: the smooth case

O. V. Chernoyarov and Yu. A. Kutoyants ()
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O. V. Chernoyarov: National Research University “MPEI”
Yu. A. Kutoyants: Le Mans University

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 4, No 1, 435 pages

Abstract: Abstract We consider the problem of localization of a Poisson source using observations of inhomogeneous Poisson processes. We assume that k detectors are distributed on the plane and each detector generates observations of the Poisson processes, whose intensity functions depend on the position of the source. We study asymptotic properties of the maximum likelihood and Bayesian estimators of the source position on the plane assuming that the amplitude of the intensity functions are large. We show that under regularity conditions these estimators are consistent, asymptotically normal and asymptotically efficient in the minimax mean-square sense. Then we propose some simple consistent estimators and these estimators are further used to construct asymptotically efficient One-step MLE-process.

Keywords: Inhomogeneous Poisson process; Source localization; GPS-localization; Sensors; Maximum likelihood estimator; Bayes estimators; One-step MLE (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00184-019-00738-1

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