Geodesic
On the identification of the source of emission on the plane
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 75-81.

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We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by $K$ detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimates, we construct estimators of the position of source and the moment of the beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.
Keywords: Inhomogeneous Poisson process, parameter estimation,localization on the plane. 
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N. V. Arakelyan; Yu. A. Kutoyants. On the identification of the source of emission on the plane. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 75-81. http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a0/

[1] H. E. Baidoo-Williams, R. Mudumbai, E. Bai, S. Dasgupta, “Some Theoretical Limits on Nuclear Source Localization and Tracking”, Proceedings of the Information Theory and Applications Workshop (ITA), 2015, 270–274

[2] G. F. Knoll, Radiation Detection and Measurement, 4th Edition, Wiley, N.Y., 2010

[3] X. Luo, GPS Stochastic Modelling, Springer, Heidelberg, 2013, 331 pp. | MR

[4] C. C. Pu, Development of a New Collaborative Ranging Algorithm for RSSI Indore Location Tracking in WSN, PhD Thesis, Dongseo University, South Korea, 2009

[5] O. V. Chernoyarov, Yu. A. Kutoyants, “Poisson Source Localization on the Plane: Smooth Case”, Metrika, 2019 (to appear); arXiv: 1806.06382v1 [math.ST]

[6] O. V. Chernoyarov, S. Dachian, Yu. A. Kutoyants, “Poisson Source Localization on the Plane: Cusp Case”, Annales of the Institute of Statistical Mathematics, 2019 (to appear); arXiv: 1806.06400v1 [math.ST]

[7] C. Farinetto, Yu. A. Kutoyants, A. Top, “Poisson Source Localization on the Plane: Change-Point Case”, Annales of the Institute of Statistical Mathematics, 2019 (to appear); arXiv: 1806.06381v1 [math.ST]

[8] Yu. A. Kutoyants, “Intensity Parameter Estimation of Intensity of an Inhomogeneous Poisson Process”, Problems of Control and Information Theory, 8:2 (1979), 137–149 (in Russian) | MR

[9] Yu. A. Kutoyants, Statistical inference for Spatial Poisson Processes, Springer, New York–Berlin, 1998 | MR

[10] S. Dachian, “Estimation of Cusp Location by Poisson Observations”, Statist. Inference Stoch. Processes, 6:1 (2003), 1–14 | DOI | Zbl

[11] S. Dachian, “Estimation of the Location of a 0-Type or $\infty$-Type Singularity by Poisson Observations”, A Journal of Theoretical and Applied Statistics, 45:5 (2011), 509—523 | MR