Parameter Estimation in Nonlinear Systems with Auto and Crosscorrelated Noise

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 measurements corrupted by output additive auto and crosscorrelated noise. The efficiency of the obtained estimation scheme is illustrated via Monte-Carlo simulations. These simulations show that the proposed method improves significantly the statistical properties of the estimator and provides a more accurate confidence region around the estimated parameters, in comparison with classical methods. Furthermore, an appealing computational simplification is obtained due to the particular form taken by the Gohberg-Heinig formula.