An optimal linear filter for random signals with realisations in a separable Hilbert space

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dc.contributor.authorHowlett, P.
dc.contributor.authorPearce, C.
dc.contributor.authorTorokhti, A.
dc.date.issued2003
dc.description© Australian Mathematical Society 2003
dc.description.abstractLet u be a random signal with realisations in an infinitedimensional vector space X and v an associated observable random signal with realisations in a finitedimensional subspace Y X. We seek a pointwisebest estimate of u using a bounded linear filter on the observed data vector v. When x is a finitedimensional Euclidean space and the covariance matrix for v is nonsingular, it is known that the best estimate Ou of u is given by a standard matrix expression prescribing a linear meansquare filter. For the infinitedimensional Hilbert space problem we show that the matrix expression must be replaced by an analogous but more general expression using bounded linear operators. The extension procedure depends directly on the theory of the Bochner integral and on the construction of appropriate Hilbert Schmidt operators. An extended example is given.
dc.description.statementofresponsibilityP. G. Howlett, C. E. M. Pearce and A. P. Torokhti
dc.identifier.citationAustralia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2003; 44:485-500
dc.identifier.issn1446-1811
dc.identifier.urihttp://hdl.handle.net/2440/308
dc.language.isoen
dc.publisherAustralian Mathematical Society
dc.source.urihttp://www.austms.org.au/Publ/ANZIAM/V44P4/1707.html
dc.titleAn optimal linear filter for random signals with realisations in a separable Hilbert space
dc.typeJournal article
pubs.publication-statusPublished

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