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On localization of source by hidden Gaussian processes with small noise

Author

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  • Yury A. Kutoyants

    (Le Mans University
    Tomsk State University)

Abstract

We consider the problem of identification of the position of some source by observations of K detectors receiving signals from this source. The time of arriving of the signal to the k-th detector depends of the distance between this detector and the source. The signals are observed in the presence of small Gaussian noise. The properties of the MLE and Bayesian estimators are studied in the asymptotic of small noise.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:4:d:10.1007_s10463-020-00763-2
    DOI: 10.1007/s10463-020-00763-2
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    References listed on IDEAS

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    1. Pavel Chigansky, 2009. "Maximum likelihood estimator for hidden Markov models in continuous time," Statistical Inference for Stochastic Processes, Springer, vol. 12(2), pages 139-163, June.
    2. Kallianpur, G. & Selukar, R. S., 1991. "Parameter estimation in linear filtering," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 284-304, November.
    3. 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.
    4. O. V. Chernoyarov & S. Dachian & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: cusp case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1137-1157, October.
    5. O. V. Chernoyarov & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: the smooth case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 411-435, May.
    6. Kutoyants, Yury A., 2019. "On parameter estimation of the hidden Ornstein–Uhlenbeck process," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 248-263.
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