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 language | English (US) |
|---|---|
| Pages (from-to) | 5334-5352 |
| Number of pages | 19 |
| Journal | IEEE Transactions on Signal Processing |
| Volume | 56 |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 3 2008 |
| Externally published | Yes |
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Keywords
- Bayesian bounds on the MSE
- Weiss-Weinstein family
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering
Cite this
A fresh look at the Bayesian bounds of the Weiss-Weinstein family. / Renaux, Alexandre; Forster, Philippe; Larzabal, Pascal; Richmond, Christ; Nehorai, Arye.
In: IEEE Transactions on Signal Processing, Vol. 56, No. 11, 03.11.2008, p. 5334-5352.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A fresh look at the Bayesian bounds of the Weiss-Weinstein family
AU - Renaux, Alexandre
AU - Forster, Philippe
AU - Larzabal, Pascal
AU - Richmond, Christ
AU - Nehorai, Arye
PY - 2008/11/3
Y1 - 2008/11/3
N2 - 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.
AB - 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.
KW - Bayesian bounds on the MSE
KW - Weiss-Weinstein family
UR - http://www.scopus.com/inward/record.url?scp=54949113694&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=54949113694&partnerID=8YFLogxK
U2 - 10.1109/TSP.2008.927075
DO - 10.1109/TSP.2008.927075
M3 - Article
AN - SCOPUS:54949113694
VL - 56
SP - 5334
EP - 5352
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 11
ER -