Crosscumulants based approaches for the structure identification of Volterra models

In this paper, we address the problem of structure identification of Volterra models. It consists in estimating the model order and the memory length of each kernel. Two methods based on input-output crosscumulants are developed. The first one uses zero mean independent and identically distributed Gaussian input, and the second one concerns a symmetric input sequence. Simulations are performed on six models having different orders and kernel memory lengths to demonstrate the advantages of the proposed methods.

[1]  Nicholas Kalouptsidis,et al.  Third order Volterra system identification , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[2]  C. L. Nikias,et al.  Signal processing with higher-order spectra , 1993, IEEE Signal Processing Magazine.

[3]  O. Nelles.  Nonlinear System Identification , 2001 .

[4]  Nicholas Kalouptsidis,et al.  Blind identification of second order Hammerstein series , 2000, 2000 10th European Signal Processing Conference.

[5]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[6]  Nicholas Kalouptsidis,et al.  Blind identification of Volterra-Hammerstein systems , 2005, IEEE Transactions on Signal Processing.

[7]  V. J. Mathews,et al.  Polynomial Signal Processing , 2000 .

[8]  Tokunbo Ogunfunmi,et al.  Adaptive Nonlinear System Identification , 2007 .

[9]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[10]  Yun Li,et al.  High-order Volterra Model Predictive Control and its application to a nonlinear polymerisation process , 2005, Int. J. Autom. Comput..

[11]  Jean-Marc Le Caillec,et al.  Time series nonlinearity modeling: A Giannakis formula type approach , 2003, Signal Process..

[12]  Jerry M. Mendel,et al.  Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications , 1991, Proc. IEEE.

[13]  Nicholas Kalouptsidis,et al.  Second-order Volterra system identification , 2000, IEEE Trans. Signal Process..

[14]  Nicholas Kalouptsidis,et al.  Nonlinear system identification using Gaussian inputs , 1995, IEEE Trans. Signal Process..

[15]  Tokunbo Ogunfunmi,et al.  Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches , 2007 .

[16]  Gene H. Golub,et al.  Matrix computations , 1983 .

[17]  S. B. Kim,et al.  Applications Of Digital Polyspectral Analysis To Nonlinear Systems Modeling And Nonlinear Wave Phenomena , 1989, Workshop on Higher-Order Spectral Analysis.

[18]  Radhi M'hiri,et al.  An approach to polynomial NARX/NARMAX systems identification in a closed-loop with variable structure control , 2008, Int. J. Autom. Comput..

[19]  Nicholas Kalouptsidis,et al.  A cumulant based algorithm for the identification of input output quadratic systems , 2000, 2000 10th European Signal Processing Conference.

[20]  C. L. Nikias,et al.  Higher-order spectra analysis : a nonlinear signal processing framework , 1993 .

[21]  J. Lacoume,et al.  Statistiques d'ordre supérieur pour le traitement du signal , 1997 .