Parameter estimation in nonlinear systems with auto and crosscorrelated noise

  • Authors:

  • B. David;G. Bastin

  • Affiliations:

  • Center for Systems Engineering and Applied Mechanics, CESAME, Université catholique de Louvain, Batiment Euler, 4-6, Avenue Georges Lemaitre, B1348 Louvain-La-Neuve, Belgium;Center for Systems Engineering and Applied Mechanics, CESAME, Université catholique de Louvain, Batiment Euler, 4-6, Avenue Georges Lemaitre, B1348 Louvain-La-Neuve, Belgium

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2002

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Abstract

The Gohberg-Heinig explicit formula for the inversion of a block-Toeplitz matrix is used to build an estimator of the inverse of the covariance matrix of a multivariable autoregressive process. This estimator is then conveniently applied to maximum likelihood parameter estimation in nonlinear dynamical systems with output measurements corrupted by additive auto and crosscorrelated noise. An appealing computational simplification is obtained due to the particular form taken by the Gohberg-Heinig formula. The efficiency of the obtained estimation scheme is illustrated via Monte-Carlo simulations and compared with an alternative that is obtained by extending a classical technique of linear system identification to the framework of this paper. These simulations show that the proposed method improves significantly the statistical properties of the estimator in comparison with classical methods. Finally, the ability of the method to provide, in a straightforward way, an accurate confidence region around the estimated parameters is also illustrated.