Identification of Parametric (NARMAX) Models from Estimated Volterra Kernels

  • Xiao Zhao
  • Vasilis Z. Marmarelis

Abstract

A method for Nonlinear Auto-Regressive Moving-Average with exogenous input (NARMAX) model identification is proposed that is based on Volterra kernel estimates obtained from input-output data. The method relies on the fundamental relations between Volterra kernels and the parameters of NARMAX models, which are derived using “generalized harmonic balance”. The method identifies different order terms of the NARMAX model separately (up to 3rd-order), allowing easier determination of the structure of the NARMAX model and yielding better parameter estimates. Simulation results are compared with the prediction-error stepwise-regression estimation algorithm introduced by Billings and Voon (1986) and show that the proposed method yields more accurate parameter estimates in the presence of noise.

Keywords

Volterra Model eXogenous Input Volterra Kernel Accurate Parameter Estimate Good Parameter Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Billings, S. A., and Voon, W.S.F. (1986) A prediction-emor and stepwise-regression estimation algorithm for non-linear systems. Int. J. Control, 44:803–822.MATHCrossRefGoogle Scholar
  2. 2.
    Korenberg, M.J. (1987) Functional expansions, parallel cascades and nonlinear difference equations. In: Advanced Methods of Physiological System Modeling, Volume I, V.Z. Marmarelis (ed.), Biomedical Simulations Resource, University of Southern California, Los Angeles, California, pp. 221–240.Google Scholar
  3. 3.
    Leontaritis, I. J. and Billings, S. A. (1985) Input-output parametric models for non-linear systems. Part I: Deterministic non-linear systems. Int. J. Control, 41:303–328; Part II: Stochastic non-linear systems. Int. J. Control, 41:329–344.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Marmarelis, V.Z. (1989) Identification and modeling of a class of nonlinear systems. Math. Comp. Mod., 12:991–995.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Marmarelis, V. Z. (1993) Identification of nonlinear biological systems using Laguerre expansions of kernels. Ann. Biomed. Eng., 21:573–589.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Xiao Zhao
    • 1
  • Vasilis Z. Marmarelis
    • 1
  1. 1.Departments of Biomedical and Electrical EngineeringUniversity of Southern CaliforniaUSA

Personalised recommendations