An estimator of the inverse covariance matrix and its application to ML parameter estimation in dynamical systems

Abstract

An exact formula of the inverse covariance matrix of an autoregressive stochastic process is obtained using the Gohberg–Semencul explicit inverse of the Toeplitz matrix. This formula is used to build an estimator of the inverse covariance matrix of a stochastic process based on a single realization. In this paper, we show that this estimator can be conveniently applied to maximum likelihood parameter estimation in nonlinear dynamical system with correlated measurement noise. The efficiency of the estimation scheme is illustrated via Monte-Carlo simulations. It is shown that the statistical properties of the estimated parameters are largely improved using the proposed inverse covariance matrix estimator in comparison to the classical variance estimator.