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On a New Approach to the Solution of the Nonlinear Filtering Equation of Jump Processes

Published online by Cambridge University Press:  27 July 2009

Kaisheng Fan
Kaisheng Fan
Affiliation:
Department of Mathematics, The University of North Carolina at Charlotte, Charlotte, North Carolina 28223
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Abstract

An implementable on-line approach to solve the nonlinear filtering equation for a partially observed system in which both the state and observation processes are jump processes is presented. By making use of the special structure of jump processes, the new method allows us to obtain the solution of the resulting nonlinear filtering equation from solving a linear system of ordinary differential equations and a linear system of algebraic equations recursively and via a simple normalization procedure.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 1 , January 1996 , pp. 153 - 163
Copyright
Copyright © Cambridge University Press 1996

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References

1.Brémaud, P. (1981). Point process and queues: Martingale dynamics. Berlin: Springer-Verlag.CrossRefGoogle Scholar
2.Elliott, R.J. (1982). Stochastic calculus and applications. Berlin: Springer-Verlag.Google Scholar
3.Ethier, S.N. & Kurtz, T.G. (1986). Markov processes: Characterization and convergence. New York: Wiley.CrossRefGoogle Scholar
4.Gihman, I.I. & Skorohod, A.V. (1960). Stochastic differential equations. Berlin: Springer-Verlag.Google Scholar
5.Kliemann, W.H., Koch, G., & Marchetti, F. (1990). On the unnormalized solution of the filtering problem with counting process observations. IEEE Transactions on Information Theory 36: 1415–1425.CrossRefGoogle Scholar
6.Kurtz, T.G. & Ocone, O. (1988). Unique characterization of conditional distribution in nonlinear filtering. The Annals of Probability 16: 80–107.CrossRefGoogle Scholar
7.Yashin, A.I. (1970). Filtering of jump process. Automatikai Telemekhanika 5: 725–730.Google Scholar