Abstract
An implementable approximation of the infinite-dimensional discrete-time Kalman filter is derived for linear systems corrupted by white noise and evolving on Hilbert spaces. The proposed method works by projecting the actual solution of the filtering problem on suitable finite-dimensional subspaces of the original Hilbert space.The finite dimensional algorithm so obtained produces a sequence of approximate solutions converging towards the exact one when the dimension of the approximation increases. Both the finite and the infinite time horizon problems are considered.
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© 1993 Springer Science+Business Media New York
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Jetto, L. (1993). A Numerical Method for Computing the Approximate Solution of the Infinite-Dimensional Discrete-Time Optimal Linear Filtering Problem. In: Kárný, M., Warwick, K. (eds) Mutual Impact of Computing Power and Control Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2968-2_10
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DOI: https://doi.org/10.1007/978-1-4615-2968-2_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6291-3
Online ISBN: 978-1-4615-2968-2
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