ORCID Profile
0000-0002-8337-4678
Current Organisation
University of South Australia
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Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 2022
Publisher: Cambridge University Press (CUP)
Date: 07-2020
DOI: 10.1017/S1446181120000188
Abstract: Let $\\boldsymbol{f}$ be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space H , and let $\\boldsymbol{g}$ 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 $\\boldsymbol{f}_{\\epsilon } \\approx \\boldsymbol{f}$ that provides the best estimate $\\widehat{\\boldsymbol{g}}_{\\epsilon} = X \\boldsymbol{f}_{\\epsilon}$ of the vector $\\boldsymbol{g}$ . We assume the required covariance operators are known. The results are illustrated with a typical ex le.
Publisher: Elsevier BV
Date: 06-2015
Publisher: Elsevier BV
Date: 11-2023
Publisher: Elsevier BV
Date: 2019
Publisher: Elsevier BV
Date: 2019
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 04-02-2021
DOI: 10.21914/ANZIAMJ.V62.15576
Abstract: Let \\(\\boldsymbol{f}\\) be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space \\(H\\), and let \\(\\boldsymbol{g}\\) 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 \\(\\boldsymbol{f}_{\\epsilon} \\approx \\boldsymbol{f}\\) that provides the best estimate \\(\\widehat{\\boldsymbol{g}}_{\\epsilon} = X\\! \\boldsymbol{f}_{\\epsilon}\\) of the vector \\(\\boldsymbol{g}\\). We assume the required covariance operators are known. The results are illustrated with a typical ex le. doi:10.1017/S1446181120000188
No related grants have been discovered for Anatoli Torokhti.