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  • Research Article
  • Open Access

An Adaptive Nonlinear Filter for System Identification

EURASIP Journal on Advances in Signal Processing20092009:859698

  • Received: 12 March 2009
  • Accepted: 8 May 2009
  • Published:


The primary difficulty in the identification of Hammerstein nonlinear systems (a static memoryless nonlinear system in series with a dynamic linear system) is that the output of the nonlinear system (input to the linear system) is unknown. By employing the theory of affine projection, we propose a gradient-based adaptive Hammerstein algorithm with variable step-size which estimates the Hammerstein nonlinear system parameters. The adaptive Hammerstein nonlinear system parameter estimation algorithm proposed is accomplished without linearizing the systems nonlinearity. To reduce the effects of eigenvalue spread as a result of the Hammerstein system nonlinearity, a new criterion that provides a measure of how close the Hammerstein filter is to optimum performance was used to update the step-size. Experimental results are presented to validate our proposed variable step-size adaptive Hammerstein algorithm given a real life system and a hypothetical case.


  • Linear System
  • Nonlinear System
  • Estimation Algorithm
  • Full Article
  • Hypothetical Case

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Authors’ Affiliations

Department of Electrical Engineering, Santa Clara University, Santa Clara, CA 95053, USA


© I. J. Umoh and T. Ogunfunmi. 2009

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.