Open Access

Adaptive Kernel Canonical Correlation Analysis Algorithms for Nonparametric Identification of Wiener and Hammerstein Systems

  • Steven Van Vaerenbergh1Email author,
  • Javier Vía1 and
  • Ignacio Santamaría1
EURASIP Journal on Advances in Signal Processing20082008:875351

Received: 1 October 2007

Accepted: 12 February 2008

Published: 24 February 2008


This paper treats the identification of nonlinear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, we follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, we show how kernel canonical correlation analysis (KCCA) emerges as the logical solution to this problem. We then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid overfitting problems, we discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm.

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Authors’ Affiliations

Department of Communications Engineering, University of Cantabria


© Steven Van Vaerenbergh et al. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.