Symbolic computation of fisher information matrices

The Fisher information matrix has several applications in linear systems theory. It appears in relation to the Cramer-Rao bound for unbiased estimators, methods for system identification, questions on identifiability and it defines the Fisher metric on manifolds of systems. In this paper state-space methods for the symbolic computation of explicit analytical expressions for the FIM are presented. These proceed by the solution of Lyapunov and Sylvester equations. To this end, methods based on Faddeev sequences are exploited.