Abstract
Recently intense interest has been aroused in the system theory community concerning the connections between well-known problems in nonlinear estimation theory and the representation theory of Lie algebras. These connections are especially interesting in problems of estimating the state of a continuous time, finite state Markov chain observed in the presence of Gaussian white noise. In this paper we delineate characteristics of problems which admit low dimensional estimation algebras, and it is shown why these constitute a class of “easy” nonlinear filtering problems.
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References
Brockett, R. W. and J. M. C. Clark, “The Geometry of the Conditional Density Equations,” Proc. of the Oxford Conf. on Stochastic Systems, Oxford, England, 1978.
Humphreys, J. E., Introduction to Lie Algebras and Representation Theory, New York: Springer-Verlag GTM Series, 1972.
Van der Waerden, B. L., Einführung in die Algebraische Geometrie, Springer-Verlag, Grund. der Math. Wissenschaften 51, 1973.
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© 1981 D. Reidel Publishing Company
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Baillieul, J. (1981). Estimation Problems with Low Dimensional Filters. In: Hazewinkel, M., Willems, J.C. (eds) Stochastic Systems: The Mathematics of Filtering and Identification and Applications. NATO Advanced Study Institutes Series, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8546-9_27
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DOI: https://doi.org/10.1007/978-94-009-8546-9_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-8548-3
Online ISBN: 978-94-009-8546-9
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