Technical Report 2005-019

Computing the Covariance Matrix for PEM Estimates and the Cramer-Rao Lower Bound for Linear State Space Models

Torsten Söderström

June 2005

The paper presents a complete and comprehensive algorithm for computing the asymptotic accuracy of estimated state space models. The parameterization is assumed to be give a uniquely identifiable system, but is otherwise general. It is assumed that the system matrices and the noise characteristics are smooth functions of the unknown parameters. Expressions for the asymptotic covariance matrix of the parameter estimates are derived for some variants of the prediction error method. As a special case for Gaussian distributed data, the Cramér-Rao bound and the covariance matrix for maximum likelihood estimates are obtained.

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