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Poisson source localization on the plane: change-point case

Author

Listed:
  • C. Farinetto

    (Le Mans University)

  • Yu. A. Kutoyants

    (Le Mans University
    Tomsk State University
    National Research University, “MPEI”)

  • A. Top

    (Le Mans University)

Abstract

We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single radioactive source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes. A method based on Bayesian change-point estimation is proposed to identify the location of the source’s coordinates. The asymptotic behavior of the Bayesian estimator is studied. In particular, the consistency and the asymptotic efficiency of the estimator are analyzed. The limit distribution and the convergence of the moments are also described. The similar statistical model could be used in GPS localization problems.

Suggested Citation

  • C. Farinetto & Yu. A. Kutoyants & A. Top, 2020. "Poisson source localization on the plane: change-point case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 675-698, June.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:3:d:10.1007_s10463-018-00704-0
    DOI: 10.1007/s10463-018-00704-0
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    References listed on IDEAS

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    1. S. Dachian, 2003. "Estimation of Cusp Location by Poisson Observations," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 1-14, January.
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    Cited by:

    1. Yury A. Kutoyants, 2021. "On localization of source by hidden Gaussian processes with small noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 671-702, August.

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