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

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Abstract

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 ℒ 2. 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. copyright by EURASIP.

Original languageEnglish
JournalEuropean Signal Processing Conference
StatePublished - 1 Dec 2008
Event16th European Signal Processing Conference, EUSIPCO 2008 - Lausanne, Switzerland
Duration: 25 Aug 200829 Aug 2008

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