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Generalized eigenvector algorithm for nonlinear system identification with non-white inputs

D T Westwick1, R E Kearney

  • 1Department of Biomedical Engineering, McGill University, Montréal, Québec, Canada.

Annals of Biomedical Engineering
|September 23, 1997
PubMed
Summary
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This study introduces a new method for nonlinear system identification using colored inputs, overcoming limitations of traditional techniques. The robust algorithm accurately corrects for input distortion, enabling analysis in physiological systems.

Area of Science:

  • Engineering
  • Systems Biology
  • Signal Processing

Background:

  • Traditional nonlinear system identification methods require specific white, Gaussian test inputs, limiting their application.
  • Identifying nonlinear dynamics with colored (non-white) inputs is crucial for physiological systems but poses significant challenges.

Purpose of the Study:

  • To develop an advanced method for nonlinear system identification applicable to highly colored input signals.
  • To extend the parallel cascade method to handle non-white inputs effectively and robustly.

Main Methods:

  • Developed an extension of the parallel cascade method optimized for constrained minimum mean squared error.
  • Implemented a deconvolution technique to correct for non-white input spectrum distortion.
  • Introduced a low-rank projection operation to stabilize the deconvolution process against ill-conditioning.

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Main Results:

  • The extended method precisely corrects for distortion introduced by non-white input spectra.
  • The low-rank projection effectively stabilizes the deconvolution, enhancing robustness.
  • The algorithm demonstrates practical applicability by identifying a known analog nonlinear system from experimental data.

Conclusions:

  • The developed method overcomes the limitations of traditional nonlinear system identification techniques.
  • This approach offers a robust and versatile tool for analyzing nonlinear systems with colored inputs, particularly in physiological studies.
  • The method requires minimal constraints on the nature of the test input signal.