ON COMPUTING THE CRAMER-RAO BOUND AND COVARIANCE MATRICES FOR PEM ESTIMATES IN LINEAR STATE SPACE MODELS

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.