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Filtering of large signal sets: An almost blind case

Torokhti, A., Howlett, P. and Laga, H.ORCID: 0000-0002-4758-7510 (2013) Filtering of large signal sets: An almost blind case. In: 8th International Multi-conference on Computing in the global Information Technology (ICCGI) 2013, 21 - 26 July 2013, Nice, France


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.

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