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Galerkin approximation for optimal linear filtering of infinite- dimensional linar systems. (English) Zbl 0662.93073

An explicitly computable, finite-dimensional approximation to the infinite-dimensional Kalman filter is studied. The approximation consists in the replacement of the original infinite-dimensional system by a finite dimensional one whose state approximates the projection of the true state on a given finite-dimensional space and in the use of a suitable finite-rank transformation of the original output. The approximate solution is shown to converge to the optimal solution for each sample path of the observation process.
Reviewer: G.DiMasi

MSC:

93E11 Filtering in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
93C25 Control/observation systems in abstract spaces
93C05 Linear systems in control theory
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