Performance of Bayesian parameter estimators for linear signal models

In this short paper the Bayesian estimation of parameters of discrete time, linear, finite-dimensional stochastic systems is discussed. Upper bounds for the estimator mean-square error are obtained under the assumption of a finite parameter set. Necessary and sufficient conditions are established for exponential convergence of the Bayesian estimate to the true parameter values in the mean-square error sense for systems with measurements which are stationary Gaussian random processes. The conditions for convergence are given in terms of a finite set of signal model Markov parameters. The performance results for parameter estimation are shown to yield bounds on the performance of the nonlinear state estimators for the class of signal models under discussion.