Abstract
The problem considered is non-linear filtering of Gaussian observations of a Markov jump-diffusion with an embedded Markov chain, that is described by stochastic differential equations driven by Brownian motions and a random Poisson measure. The modelling potential of this class of Markov processes is illustrated by some simple realistic examples.
For the evolution of the conditional expectation of the Markov process decomposed representations are given. They are used as a basis to obtain approximate filtering algorithms that are free of decision making mechanisms. These algorithms are discussed for the examples given.
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References
Tugnait J.K., Detection and estimation for abruptly changing systems. Automatica, 18 (1982), 607–615.
Basseville M., Benveniste A., Design and comparative study of some sequential jump detection algorithms for digital signals. IEEE Transactions on ASSP, 31 (1983), 521–535.
Gihman I.I., Skohorod A.V., Stochastic differential equations, Springer-Verlag, Berling, 1972.
Davis M.H.A., The application of nonlinear filtering to fault detection in linear systems, IEEE Transactions on Automatic Control, 20 (1975), 257–259.
Kwakernaak H., Filtering for systems excited by Poisson white noise. Eds: A. Bensoussan, J.L. Lions, Control theory, numerical methods and computer systems; Springer Lecture Notes in Economics and Mathematical Systems, Vol. 107, Berlin, 1975, 468–492.
Au S.P., Haddad A.H., Suboptimal sequential estimation-detection scheme for Poisson driven linear systems. Information Sciences, 16 (1978), 95–113.
Loparo K.A., Roth Z., Suboptimal nonlinear filters for systems with random structure, IEEE Conf. on Decision and Control, 1981, 320–323.
Au S.P., Haddad A.H., Poor H.V., A state estimation algorithm for linear systems driven simultaneously by Wiener and Poisson processes, IEEE Trans. on Automatic Control, 27 (1982), 617–626.
Brockett R.W., Blankenship G.L., A representation theorm for linear differential equations with Markovian coefficients, Proc. 1977 Allerton Conf. on Circuits and Systems Theory, Urbana, Illinois, 671–679.
Liptser R.S., Shiryayev A.N., Statistics of random processes, Part I and II, Springer Verlag, 1977, 1978.
Marcus S.I., Modeling and analysis of stochastic differential equations driven by point processes, IEEE Transactions on Information Theory, 24 (1978), 164–172.
Snyder D.L., Random point processes, New York, Wiley, 1975.
Davis M.H.A., Pathwise nonlinear filtering, Eds: M. Hazewinkel, J.C. Willems, Stochastic systems: the mathematics of filtering and indentification and applications, Proc. of the NATO Advanced Study Institute, Les Arcs, 1980, D. Reidel, Dordrecht, 1981, 505–528.
Blom H.A.P., A sophisticated tracking algorithm for ATC surveillance radar data, Proceedings of the International Conference on Radar, Paris, may 1984, session B III.
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© 1984 Springer-Verlag
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Blom, H.A.P. (1984). Markov jump-diffusion models and decision-making-free filtering. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004981
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DOI: https://doi.org/10.1007/BFb0004981
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