A fresh look at the Bayesian bounds of the Weiss-Weinstein family

Alexandre Renaux, Philippe Forster, Pascal Larzabal, Christ D. Richmond, Arye Nehorai

Research output: Contribution to journalArticle

43 Scopus citations

Abstract

Minimal bounds on the mean square error (MSE) are generally used in order to predict the best achievable performance of an estimator for a given observation model. In this paper, we are interested in the Bayesian bound of the Weiss-Weinstein family. Among this family, we have Bayesian Cramér-Rao bound, the Bobrovsky-MayerWolf-Zakaï bound, the Bayesian Bhattacharyya bound, the Bobrovsky-Zakaï bound, the Reuven-Messer bound, and the Weiss-Weinstein bound. We present a unification of all these minimal bounds based on a rewriting of the minimum mean square error estimator (MMSEE) and on a constrained optimization problem. With this approach, we obtain a useful theoretical framework to derive new Bayesian bounds. For that purpose, we propose two bounds. First, we propose a generalization of the Bayesian Bhattacharyya bound extending the works of Bobrovsky, Mayer-Wolf, and Zakaï. Second, we propose a bound based on the Bayesian Bhattacharyya bound and on the Reuven-Messer bound, representing a generalization of these bounds. The proposed bound is the Bayesian extension of the deterministic Abel bound and is found to be tighter than the Bayesian Bhattacharyya bound, the Reuven-Messer bound, the Bobrovsky-Zakaï bound, and the Bayesian Cramér-Rao bound. We propose some closed-form expressions of these bounds for a general Gaussian observation model with parameterized mean. In order to illustrate our results, we present simulation results in the context of a spectral analysis problem.

Original languageEnglish (US)
Pages (from-to)5334-5352
Number of pages19
JournalIEEE Transactions on Signal Processing
Volume56
Issue number11
DOIs
StatePublished - Nov 3 2008

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Keywords

  • Bayesian bounds on the MSE
  • Weiss-Weinstein family

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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