This article is part of the series Emerging Machine Learning Techniques in Signal Processing.

Open Access Research Article

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

Steven Van Vaerenbergh*, Javier Vía and Ignacio Santamaría

Author Affiliations

Department of Communications Engineering, University of Cantabria, 39005 Santander, Cantabria, Spain

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EURASIP Journal on Advances in Signal Processing 2008, 2008:875351  doi:10.1155/2008/875351


The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2008/1/875351


Received: 1 October 2007
Revisions received: 4 January 2008
Accepted: 12 February 2008
Published: 24 February 2008

© 2008 The Author(s).

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.

Abstract

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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