Abstract
Using the methods of the theory of optimal nonlinear filtering, we develop an algorithm for obtaining optimal estimates of the sequence of hidden states of discrete-valued Markov processes with abruptly changing parameters at unknown time. Optimal estimates of the states of Markov processes and of the time of appearance of an abrupt change in parameters are obtained as a result of interpolation by processing the entire observation sequence. The results of simulation of the algorithm work are presented.
Similar content being viewed by others
REFERENCES
A. N. Shiryaev, Statistical Sequential Analysis [in Russian], Nauka, Moscow (1976).
Yu. G. Sosulin and M. M. Fishman, Izv. Akad. Nauk SSSR, Ser. Tekh. Kiber., No. 3, 149 (1977).
M. H. A. Davis, IEEE Trans. Automat. Control., 20, No.2, 257 (1993).
N. Kligene and L. Telksnis, Avtomat. Telemekh., No. 10, 5 (1983).
I. V. Nikiforov, Sequential Detection of Changes in the Properties of Random Processes [in Russian], Nauka, Moscow (1983).
M. Basseville and A. Benveniste, eds., Detection of Abrupt Changes in Signals and Dynamical Systems Springer-Verlag, Berlin (1985).
V. A. Bukhalev, Recognition, Estimation, and Control in Systems with a Random Abruptly Changing Structure [in Russian], Fizmatlit, Moscow (1996).
G. D. Forney, Jr., Proc. IEEE., 61, No.3, 268 (1973).
L. R. Rabiner, Proc. IEEE., 77, No.2, 257 (1989).
I. L. MacDonald and W. Zucchini, Hidden Markov and Other Models for Discrete-Valued Time Series, CRC Press (1997).
R. L. Stratonovich, Conditional Markov Processes and their Application to the Theory of Optimal Control [in Russian], Moscow State Univ. Press, Moscow (1966).
R. Sh. Liptser and A. N. Shiryaev, Statistics of Random Processes [in Russian], Nauka, Moscow (1974).
V. I. Tikhonov and N. K. Kul'man, Nonlinear Filtering and Quasi-Coherent Reception of Signals [in Russian], Sovetskoe Radio, Moscow (1975).
A. M. Silaev, Avtomat. Telemekh., No. 10, 58 (1997).
A. V. Vanzha, A. A. Mal'tsev, and A. M. Silaev, Radiophys.. Quantum Electron., 36, No.6, 317 (1993).
A. V. Korolev and A. M. Silaev, Radiophys. Quantum Electron., 45, No.3, 230 (2002).
Author information
Authors and Affiliations
Additional information
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 628–639, July 2005.
Rights and permissions
About this article
Cite this article
Korolev, A.V., Silaev, A.M. Estimation of Markov Sequences with Jump-Like Variation of Parameters by the Interpolation Method. Radiophys Quantum Electron 48, 558–568 (2005). https://doi.org/10.1007/s11141-005-0100-z
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11141-005-0100-z