Parameter estimation in nonlinear systems with auto and crosscorrelated noise

The Gohberg-Heinig explicit formula for the inversion of a block-Toeplitz m atrix is used to build an estimator of the inverse of the covariance matrix of a multivariable autoregressive process. This estimator is then convenie ntly applied to maximum likelihood parameter estimation in nonlinear dynami cal systems with output measurements corrupted by additive auto and crossco rrelated noise. An appealing computational simplification is obtained due t o the particular form taken by the Gohberg-Heinig formula. The efficiency o f 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 method s. Finally, the ability of the method to provide, in a straightforward way, an accurate confidence region around the estimated parameters is also illu strated. (C) 2001 Elsevier Science Ltd. All rights reserved.