Abstract
The detection problem for a group of moving targets is a generalization of the classical detection problem for a single still target. Synthesis methods for joint detection and phase coordinate measurement for objects in the group are being developed in the theory of random streams of events. In this work, we propose a Poisson approximation for a Bernoullian stream of signals generated by a group target and observed in noises for small signal/noise ratios. Using this approximation, we can significantly simplify optimal detection and parameter estimation for a group target which are hard to implement exactly. Developing suboptimal algorithms is an important problem for a number of technical applications, including, in particular, radioand hydrolocation.
Similar content being viewed by others
References
Kuznetsov, P.I. and Stratonovich, R.L., On the Mathematical Theory of Correlated Random Points, Izv. Akad. Nauk SSSR, Ser. Mat., 1956, vol. 20, no. 2, pp. 167–168.
Nilsson, N.J., On the Optimum Range Resolution of Radar Signals in Noise, IRE Trans. Inf. Theory, 1961, vol. IT-7, no. 4, pp. 245–253.
Bol’shakov, I.A., Statisticheskie problemy vydeleniya potoka signalov iz shuma (Statistical Problems of Signal Stream Denoising), Moscow: Sovetskoe Radio, 1969.
Bakut, P.A., Zhulina, Yu.V., and Ivanchuk, N.A., Obnaruzhenie dvizhushchikhsya ob”ektov (Detection of Moving Objects), Moscow: Sovetskoe Radio, 1969.
Shiryaev, A.N., Statisticheskii posledovatel’nyi analiz (Statistical Sequential Analysis), Moscow: Nauka, 1969.
Sysoev, L.P., The Detection Probability Criterion on a Trajectory in the Control Problem for an Object in a Conflicting Environment, Probl. Upravlen., 2010, no. 6, pp. 64–70.
Lehmann, E.L., Testing Statistical Hypotheses, New York: Wiley, 1959. Translated under the title Proverka statisticheskikh gipotez, Moscow: Nauka, 1964.
Ivankin, E.F., Informatsionnye sistemy s aposteriornoi obrabotkoi rezul’tatov nablyudenii (Information Systems with Posterior Processing of Observation Results), Moscow: Goryachaya Liniya-Telekom, 2008.
Radzievskii, V.G., Sirota, A.A., and Borisov, Yu.A., Estimating the Coordinates of Measurement Sources in Multipositional Radiotechnical Systems under a Mixed Input Stream of Signal and Noise, Radiotekh., 1996, no. 6, pp. 43–49.
Dudnik, P.I., Kondratenkov, G.S., et al., Aviatsionnye radiolokatsionnye kompleksy i sistemy (Aviation Radiolocation Complexes and Systems), Moscow: VVIA, 2006.
Hwang, H.-K. and Zacharovas, V., Uniform Asymptotics of Poisson Approximation to the Poisson-Binomial Distribution, Theor. Veroyat. Primenen., 2010, vol. 55, no. 2, pp. 305–334.
Feller, W., An Introduction to Probability Theory and Its Applications, New York: Wiley, 1957. Translated under the title Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Moscow: Mir, 1964.
Stanley, R.P., Enumerative Combinatorics, Monterey: Wadsworth & Brooks/Cole, 1986. Translation under the title Perechislitel’naya kombinatorika, Moscow: Mir, 1990.
Author information
Authors and Affiliations
Additional information
Original Russian Text © M.E. Shaikin, 2012, published in Avtomatika i Telemekhanika, 2012, No. 6, pp. 52–72.
Rights and permissions
About this article
Cite this article
Shaikin, M.E. Applying random stream theory to the group target detection problem. Autom Remote Control 73, 976–991 (2012). https://doi.org/10.1134/S0005117912060045
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117912060045