Nonlinear system modeling and identification using Volterra-PARAFAC models

Gérard Favier 1 Alain Y. Kibangou 2 Thomas Bouilloc 1
1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
Laboratoire I3S - SIS - Signal, Images et Systèmes
2 NECS - Networked Controlled Systems
Inria Grenoble - Rhône-Alpes, GIPSA-DA - Département Automatique
Abstract : 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.
keyword : Volterra models tensor decompositions Volterra kernels CLMS algorithm extended KAlman filter nonlinear system identification nonlinear system modeling PARAFAC Wiener models
Type de document :
Article dans une revue
International Journal of Adaptive Control and Signal Processing, Wiley, 2012, 26 (1), pp.30-53. 〈10.1002/acs.1272〉
Liste complète des métadonnées

Littérature citée [61 références]  Voir  Masquer  Télécharger
https://hal.archives-ouvertes.fr/hal-00642363
Contributeur : Alain Kibangou <>
Soumis le : lundi 16 juillet 2012 - 16:00:08
Dernière modification le : mardi 6 novembre 2018 - 01:14:48
Document(s) archivé(s) le : mercredi 17 octobre 2012 - 02:20:15

Fichier

IJACSP_26_2012.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

Collections

INRIA | GIPSA-NECS | I3S | GIPSA-DA | GIPSA | UNICE | UGA | UGA-TEST-TER | UNIV-COTEDAZUR

Citation

Gérard Favier, Alain Y. Kibangou, Thomas Bouilloc. Nonlinear system modeling and identification using Volterra-PARAFAC models. International Journal of Adaptive Control and Signal Processing, Wiley, 2012, 26 (1), pp.30-53. 〈10.1002/acs.1272〉. 〈hal-00642363〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

944

Téléchargements de fichiers

1195

Contact

support.ccsd.cnrs.fr
hal.support@ccsd.cnrs.fr
Logo CCSD