A new Bayesian lower bound on the mean square error of estimators

In this paper, the Weiss-Weinstein family of Bayesian lower bounds on the mean-square-error of estimators is extended to an integral form. A new class of Bayesian lower bounds is derived from this integral form by approximating each entry of the vector of estimation error in a closed Hilbert subspace of L₂. This Hilbert subspace is spanned by a set of linear transformations of elements in the domain of an integral transform of a particular function, which is orthogonal to any function of the observations. It is shown that new Bayesian bounds can be derived from this class by selecting the particular function from a known set and modifying the kernel of the integral transform. A new computationally manageable lower bound is derived from the proposed class using the kernel of the Fourier transform. The bound is computationally manageable and provides better prediction of the signal-to-noise ratio threshold region, exhibited by the maximum a-posteriori probability estimator. The proposed bound is compared with other known bounds in terms of threshold SNR prediction in the problem of frequency estimation.