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Filtering of Large Signal Sets: An Almost Blind Case

Authors:
Anatholi Torokhti
Phil Howlett
Hamid Laga

Keywords: large signal sets; filtering; least squares linear estimator

Abstract:
We propose a new technique which allows to estimate any random signal from a large set of noisy observed data on the basis of information on only a few reference signals. The conceptual device behind the proposed estimator is a linear interpolation of an optimal incremental estimation applied to random signal pairs interpreted an extension of the Least Squares Linear (LSL) estimator. We consider the case of observations corrupted by an arbitrary noise (not by an additive noise only) and design the estimator in terms of the Moore-Penrose pseudoinverse matrix. Therefore, it is always well defined. The proposed estimator is justified by establishing an upper bound for the associated error and by showing that this upper bound is directly related to the expected error for an incremental application of the optimal LSL estimator. It is shown that such an estimator is possible under quite unrestrictive assumptions.

Pages: 101 to 105

Copyright: Copyright (c) IARIA, 2013

Publication date: July 21, 2013

Published in: conference

ISSN: 2308-4529

ISBN: 978-1-61208-283-7

Location: Nice, France

Dates: from July 21, 2013 to July 26, 2013