Please use this identifier to cite or link to this item:
Type: Journal article
Title: An optimal linear filter for random signals with realisations in a separable Hilbert space
Author: Howlett, P.
Pearce, C.
Torokhti, A.
Citation: Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2003; 44:485-500
Publisher: Australian Mathematical Society
Issue Date: 2003
ISSN: 1446-1811
Statement of
P. G. Howlett, C. E. M. Pearce and A. P. Torokhti
Abstract: Let 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.
Description: © Australian Mathematical Society 2003
Published version:
Appears in Collections:Applied Mathematics publications
Aurora harvest 6

Files in This Item:
There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.