Convergence analysis of the alternating RELS algorithm for the identification of the reduced complexity Volterra model

In this paper, we provide a sufficient convergence condition of the alternating recursive extended least squares (RELS) algorithm proposed for the identification of the reduced complexity Volterra model describing stochastic nonlinear systems. The reduced Volterra model used is the third order PARAFC-Volterra model provided using the parallel factor (PARAFAC) tensor decomposition of the Volterra kernels of order higher than two of the classical Volterra model. The recursive stochastic algorithm alternating recursive extended least squares (ARELS) consists of the execution in an alternating way of the classical RELS algorithm developed to identify the linear stochastic input-output models. The ARELS convergence was proved using the ordinary differential equation (ODE) method. It is noted that the ARELS algorithm convergence cannot be ensured when the disturbance acting on the system to be identified has specific features. The ARELS algorithm is tested using Monte Carlo simulation under the determined suffi...

[1]  T. Lai,et al.  Extended least squares and their applications to adaptive control and prediction in linear systems , 1986 .

[2]  Rasmus Bro,et al.  MULTI-WAY ANALYSIS IN THE FOOD INDUSTRY Models, Algorithms & Applications , 1998 .

[3]  Masayoshi Tomizuka,et al.  A Convex Optimization Approach for Solving the Robust Strictly Positive Real (SPR) Problem , 2012 .

[4]  Thomas Bouilloc Applications de décompositions tensorielles à l'identification de modèles de Volterra et aux systèmes de communication MIMO-CDMA , 2011 .

[5]  José Ragot,et al.  Nonlinear system modeling based on bilinear Laguerre orthonormal bases. , 2013, ISA transactions.

[6]  Mark Beale,et al.  Neural Network Toolbox™ User's Guide , 2015 .

[7]  Stephen A. Billings,et al.  Identification of nonlinear systems with non-persistent excitation using an iterative forward orthogonal least squares regression algorithm , 2015, Int. J. Model. Identif. Control..

[8]  Walter A. Frank An efficient approximation to the quadratic Volterra filter and its application in real-time loudspeaker linearization , 1995, Signal Process..

[9]  Gianni Bianchini Synthesis of robust strictly positive real discrete-time systems with l/sub 2/ parametric perturbations , 2002 .

[10]  Stephen A. Billings,et al.  An iterative orthogonal forward regression algorithm , 2015, Int. J. Syst. Sci..

[11]  Kais Bouzrara,et al.  Non-linear predictive controller for uncertain process modelled by GOBF-Volterra models , 2013, Int. J. Model. Identif. Control..

[12]  David G. Messerschmitt,et al.  Nonlinear Echo Cancellation of Data Signals , 1982, IEEE Trans. Commun..

[13]  Gérard Favier,et al.  Blind equalization of nonlinear channels using a tensor decomposition with code/space/time diversities , 2009, Signal Process..

[14]  Gérard Favier,et al.  IDENTIFICATION OF SVD-PARAFAC BASED THIRD-ORDER VOLTERRA MODELS USING AN ARLS ALGORITHM , 2005 .

[15]  Francis J. Doyle,et al.  Identification and Control Using Volterra Models , 2001 .

[16]  Anis Khouaja Modélisation et identification de systèmes non-linéaires à l'aide de modèles de volterra à complexité réduite , 2005 .

[17]  Fabien Courreges,et al.  Enhanced Kalman gain in RLS algorithm for identification accuracy with low excitation and heavy noise , 2014, Int. J. Model. Identif. Control..

[18]  Yoshinobu Kajikawa Subband parallel cascade Volterra filter for linearization of loudspeaker systems , 2008, 2008 16th European Signal Processing Conference.

[19]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[20]  Nicholas Kalouptsidis,et al.  Input-output identification of nonlinear channels using PSK, QAM and OFDM inputs , 2009, Signal Process..

[21]  Lieven De Lathauwer,et al.  An enhanced line search scheme for complex-valued tensor decompositions. Application in DS-CDMA , 2008, Signal Process..

[22]  Junghsi Lee,et al.  A fast recursive least squares adaptive second order Volterra filter and its performance analysis , 1993, IEEE Trans. Signal Process..

[23]  Rasmus Bro,et al.  A comparison of algorithms for fitting the PARAFAC model , 2006, Comput. Stat. Data Anal..

[24]  Gérard Favier,et al.  Selection of generalized orthonormal bases for second-order Volterra filters , 2005, Signal Process..

[25]  Gérard Favier,et al.  Identification of PARAFAC-Volterra cubic models using an Alternating Recursive Least Squares algorithm , 2004, 2004 12th European Signal Processing Conference.

[26]  João Cesar M. Mota,et al.  Blind identification of multiuser nonlinear channels using tensor decomposition and precoding , 2009, Signal Process..

[27]  Walter Kellermann,et al.  Fast adaptation of frequency-domain volterra filters using inherent recursions of iterated coefficient updates , 2007, 2007 15th European Signal Processing Conference.

[28]  Pierre Comon,et al.  Enhanced Line Search: A Novel Method to Accelerate PARAFAC , 2008, SIAM J. Matrix Anal. Appl..

[29]  Lennart Ljung,et al.  On positive real transfer functions and the convergence of some recursive schemes , 1977 .