New lower bounds to the variance of signal parameter estimators using Bayesian inference

The Cramer-Rao lower bound (CRLB) characterizes the variance of joint estimators, including the maximum likelihood (ML) estimator, but it is not tenable for Bayesian marginal estimation. The theory of the CRLB is extended, therefore, within the Bayesian framework, to yield lower bounds to Bayesian marginal estimator variance for the first time. The theory confers a formal procedure for reducing the parameterization of the CRLB. The current procedure for achieving this is to average the CRLB, but it is shown that the new marginal formalism yields greater lower bounds. The marginal bounds are derived for a general signal class, and evaluated for the marginal estimator of difference frequency between two closely spaced tones