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

Publication ,  Journal Article
Renaux, A; Forster, P; Larzabal, P; Richmond, CD; Nehorai, A
Published in: IEEE Transactions on Signal Processing
November 3, 2008

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. © 2008 IEEE.

Duke Scholars

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

November 3, 2008

Volume

56

Issue

11

Start / End Page

5334 / 5352

Related Subject Headings

  • Networking & Telecommunications
 

Citation

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Renaux, A., Forster, P., Larzabal, P., Richmond, C. D., & Nehorai, A. (2008). A fresh look at the Bayesian bounds of the Weiss-Weinstein family. IEEE Transactions on Signal Processing, 56(11), 5334–5352. https://doi.org/10.1109/TSP.2008.927075
Renaux, A., P. Forster, P. Larzabal, C. D. Richmond, and A. Nehorai. “A fresh look at the Bayesian bounds of the Weiss-Weinstein family.” IEEE Transactions on Signal Processing 56, no. 11 (November 3, 2008): 5334–52. https://doi.org/10.1109/TSP.2008.927075.
Renaux A, Forster P, Larzabal P, Richmond CD, Nehorai A. A fresh look at the Bayesian bounds of the Weiss-Weinstein family. IEEE Transactions on Signal Processing. 2008 Nov 3;56(11):5334–52.
Renaux, A., et al. “A fresh look at the Bayesian bounds of the Weiss-Weinstein family.” IEEE Transactions on Signal Processing, vol. 56, no. 11, Nov. 2008, pp. 5334–52. Scopus, doi:10.1109/TSP.2008.927075.
Renaux A, Forster P, Larzabal P, Richmond CD, Nehorai A. A fresh look at the Bayesian bounds of the Weiss-Weinstein family. IEEE Transactions on Signal Processing. 2008 Nov 3;56(11):5334–5352.

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

November 3, 2008

Volume

56

Issue

11

Start / End Page

5334 / 5352

Related Subject Headings

  • Networking & Telecommunications