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DOI : 10.1002/acs.1272

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International Journal of Adaptive Control and Signal Processing 26 (2011) 30-53

Nonlinear system modeling and identification using Volterra-PARAFAC models

Gérard Favier 1, Alain Y. Kibangou 2, 3, Thomas Bouilloc 1

(2011)

Discrete-time Volterra models are widely used in various application areas. Their usefulness is mainly because of their ability to approximate to an arbitrary precision any fading memory nonlinear system and to their property of linearity with respect to parameters, the kernels coefficients. The main drawback of these models is their parametric complexity implying the need to estimate a huge number of parameters. Considering Volterra kernels of order higher than two as symmetric tensors, we use a parallel factor (PARAFAC) decomposition of the kernels to derive Volterra-PARAFAC models that induce a substantial parametric complexity reduction. We show that these models are equivalent to a set of Wiener models in parallel. We also show that Volterra kernel expansions onto orthonormal basis functions (OBF) can be viewed as Tucker models that we shall call Volterra-OBF-Tucker models. Finally, we propose three adaptive algorithms for identifying Volterra-PARAFAC models when input-output signals are complex-valued: the extended complex Kalman filter, the complex least mean square (CLMS) algorithm and the normalized CLMS algorithm. Some simulation results illustrate the effectiveness of the proposed identification methods.

1 :	Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
	Université Nice Sophia Antipolis [UNS] – CNRS : UMR7271
2 :	NeCS (INRIA Grenoble Rhône-Alpes / Gipsa-lab)
	CNRS : UMR5216 – INRIA – Gipsa-lab – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
3 :	Grenoble Images Parole Signal Automatique (GIPSA-lab)
	CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology

Équipe de recherche : NECS

Domaine

:

Informatique/Traitement du signal et de l'image Sciences de l'ingénieur/Traitement du signal et de l'image

Mots Clés : CLMS algorithm – extended KAlman filter – nonlinear system identification – nonlinear system modeling – PARAFAC – tensor decompositions – Volterra kernels – Volterra models – Wiener models

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Contributeur : Alain Kibangou <>

Soumis le : Lundi 16 Juillet 2012, 16:00:08

Dernière modification le : Lundi 16 Juillet 2012, 16:57:15