An optimal linear filter for estimation of random functions in Hilbert space
Date
2020
Authors
Howlett, P.
Torokhti, A.
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Journal article
Citation
ANZIAM Journal, 2020; 62(3):274-301
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Abstract
Let be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space H, and let be an associated square-integrable, zero-mean, random vector with realizations which are not observable in a Hilbert space K. We seek an optimal filter in the form of a closed linear operator X acting on the observable realizations of a proximate vector that provides the best estimate of the vector. We assume the required covariance operators are known. The results are illustrated with a typical example.
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Link to a related website: https://arxiv.org/pdf/2008.12485, Open Access via Unpaywall