Estimating second-order Volterra system parameters from noisy measurements based on an LMS variant or an errors-in-variables method

Authors:
Zoé Sigrist;Eric Grivel;BenoíT Alcoverro
Affiliations:
Université Bordeaux 1, IPB, ENSEIRB-MATMECA, IMS, Département LAPS, UMR CNRS 5218, Bít A4, 351 cours de la Libération, 33405 Cedex, Talence, France and Commissariat í l'En ...;Université Bordeaux 1, IPB, ENSEIRB-MATMECA, IMS, Département LAPS, UMR CNRS 5218, Bít A4, 351 cours de la Libération, 33405 Cedex, Talence, France;Commissariat í l'Energie Atomique, CEA CESTA, BP 2, 33114 Le Barp, France
Venue:
Signal Processing
Year:
2012

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Abstract

This paper deals with the identification of a nonlinear SISO system modelled by a second-order Volterra series expansion when both the input and the output are disturbed by additive white Gaussian noises. Two methods are proposed. Firstly, we present an unbiased on-line approach based on the LMS. It includes a bias correction scheme which requires the variance of the input additive noise. Secondly, we suggest solving the identification problem as an errors-in-variables issue, by means of the so-called Frisch scheme. Although its computational cost is high, this approach has the advantage of estimating the Volterra kernels and the variances of both the additive noises and the input signal, even if the signal-to-noise ratios at the input and the output are low.