Abstract
In this paper an implementable approximation of the infinite-dimensional Kalman filter is proposed for linear distributed systems corrupted by white noise. It relies on a Galerkin type treatment of both the Riccati and the filter equations, and it is shown to converge to the best linear estimate of the state for each sample path of the noise. A basic tool is the study of the Riccati equation on the Hilbert space of Hilbert-Schmidt operators on the state space. Numerical results are given for a case concerning delay-differential equation.
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© 1987 Springer-Verlag
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Germani, A., Jetto, L., Piccioni, M. (1987). Galerkin approximation for optimal linear filtering of infinite dimensional linear systems. In: Germani, A. (eds) Stochastic Modelling and Filtering. Lecture Notes in Control and Information Sciences, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009049
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DOI: https://doi.org/10.1007/BFb0009049
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