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Analysis and Estimation of the States of Special Jump Markov Processes. II. Optimal Filtration in Wiener Noise

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Abstract

The second part was devoted to the rms-optimal filtration of the states of the Markov jump processes in continuous time which generalize the finite-state Markov processes. Equations for the conditional expectations and the probability density function were obtained. The Zakai equations for the corresponding unnormalized characteristics also were obtained. The proposed best nonlinear estimates were compared by way of a numerical example with the best linear estimates of the Kalman–Bucy filtration.

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REFERENCES

  1. Borisov, A.V., Analysis and Estimation of the States of Special Jump Markov Processes. I. Martingale Representation, Avtom. Telemekh., 2004, no. 1, pp. 50–65.

  2. Elliott, R.J., Aggoun, L., and Moore, J.B., Hidden Markov Models: Estimation and Control, Berlin: Springer-Verlag, 1995.

    Google Scholar 

  3. Loëve, M., Probability Theory, Princeton: Van Nostrand, 1963. Translated under the title Teoriya veroyatnostei, Moscow: Inostrannaya Literatura, 1962.

    Google Scholar 

  4. Elliott, R.J., Stochastic Calculus and Applications, New York: Springer, 1982. Translated under the title Stokhasticheskii analiz and ego prilozheniya, Moscow: Mir, 1986.

    Google Scholar 

  5. Liptser, R.Sh. and Shiryaev, A.N., Statistika sluchainykh protsessov (nelineinaya fil'tratsiya i smezhnye voprosy), Moscow: Nauka, 1974. Translated under the title Statistics of Random Processes, Berlin: Springer-Verlag, 1978.

    Google Scholar 

  6. Kloeden, P. and Platen, E., The Numerical Solution of Stochastic Differential Equations, Berlin: Springer-Verlag, 1992.

    Google Scholar 

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  1. Institute of Informatics Problems, Russian Academy of Sciences, Moscow Aviation Institute, Moscow, Russia

    A. V. Borisov

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  1. A. V. Borisov
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Borisov, A.V. Analysis and Estimation of the States of Special Jump Markov Processes. II. Optimal Filtration in Wiener Noise. Automation and Remote Control 65, 741–754 (2004). https://doi.org/10.1023/B:AURC.0000028322.97957.ca

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  • DOI: https://doi.org/10.1023/B:AURC.0000028322.97957.ca

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