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

✍ Scribed by B. David; G. Bastin

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 202 KB
• Volume: 37
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/s0005-1098(00)00127-8

✦ Synopsis

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 e$ciency 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.