14th IFAC Symposium on System Identification, SYSID 2006

SYSID-2006 Paper Abstract


Paper ThA2.3

Söderström, Torsten (Uppsala Univ.)

On Computing the Cramer-Rao Bound and Covariance Matrices for PEM Estimates in Linear State Space Models

Scheduled for presentation during the Regular Session "Identification of Linear Systems II" (ThA2), Thursday, March 30, 2006, 11:10−11:30, Banquet Room

14th IFAC Symposium on System Identification, March 29 - 31, 2006, Newcastle, Australia

This information is tentative and subject to change. Compiled on July 22, 2018

Keywords Maximum Likelihood Methods, Grey Box Modelling, Multivariable System Identification


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 Cramer-Rao bound and the covariance matrix for maximum likelihood estimates are obtained.