A maximum likelihood parameter estimation method for nonlinear dynamical systems

Abstract

Presents an original method for maximum likelihood parameter estimation in nonlinear dynamical systems with highly correlated residuals. The method relies on an autoregressive representation of the residuals to build an estimate of the inverse of its covariance matrix. Theoretical concepts are developed and we provide a successful application of the method on a two-parameters estimation problem with data collected on a real plant. This experimental study shows that the statistical properties of the estimated parameters are significantly improved with our method in comparison to classical estimation techniques that usually rely on an uncorrelated representation of the residuals. In addition, a far better estimation of the confidence region around the parameter vector is obtained.