Technical communique: Initial estimates for the dynamics of a Hammerstein system

Authors:
J. Schoukens;W. D. Widanage;K. R. Godfrey;R. Pintelon
Affiliations:
Department ELEC, Vrije Universiteit Brussel, Pleinlaan 2, B1050 Brussels, Belgium;School of Engineering, University of Warwick, Coventry CV4 7AL, UK;School of Engineering, University of Warwick, Coventry CV4 7AL, UK;Department ELEC, Vrije Universiteit Brussel, Pleinlaan 2, B1050 Brussels, Belgium
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

This paper studies the generation of initial estimates for the dynamic part of a Hammerstein model. It will be shown that ARMAX or Box-Jenkins models result in better initial estimates than ARX or output-error (OE) models even in the absence of disturbing noise. This will be proven by noticing that a static nonlinear system can be replaced by a static gain plus a nonlinear noise source that acts in a completely similar way to disturbing noise for the study of the second-order properties of the estimators in the prediction error framework.