Performance bounds on matched-field methods for source localization and estimation of ocean environmental parameters

Xu, Wen

doi:10.1575/1912/3477

Cited by 35 publications

(26 citation statements)

References 40 publications

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“…Let, [see (52)- (54) As for the Bobrovsky-Zakaï bound and the Reuven-Messer bound, since and are parameter vectors left to the user, the highest bound that can be obtained with (55) is given by (57) We recognize the Weiss-Weinstein bound [42].…”

Section: D) Bobrovsky-zakaï Boundmentioning

confidence: 99%

“…The reader is referred to Xu et al [57]- [59], where the MLE performances are analyzed in the context of an underwater acoustic problem by way of the Ziv-Zakaï and of the Weiss-Weinstein bounds. The Ziv-Zakaï family bounds have been applied in other signal processing areas: time-delay estimation [60]; direction-of-arrival estimation [38], [61], [62]; and digital communication [63].…”

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confidence: 99%

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A Fresh Look at the Bayesian Bounds of the Weiss-Weinstein Family

Renaux

Forster

Larzabal³

et al. 2008

IEEE Trans. Signal Process.

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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.Index Terms-Bayesian bounds on the MSE, Weiss-Weinstein family.

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Section: D) Bobrovsky-zakaï Boundmentioning

confidence: 99%

mentioning

confidence: 99%

A Fresh Look at the Bayesian Bounds of the Weiss-Weinstein Family

Renaux

Forster

Larzabal³

et al. 2008

IEEE Trans. Signal Process.

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“…For lower bounds obtained by an optimization over test points, as the Barankin bound or the Weiss-Weinstein bound, it is known that this behavior is related to the ambiguity function of the problem. Indeed, the value of the test points which maximizes the bound are those for which the ambiguity function takes local maxima [9], [18]- [21].…”

Section: B Bounds For the Frequency Estimation Problem 1) Crb And Chrbmentioning

confidence: 99%

“…ChRB(h; 0 ) = CRB( 0 ) lim h!0 9(h; 0) = CRB 01 (0): (21) By reporting (21) in (8) lim h!0 AB 1;1 (h; 0 ) = CRB( 0 ):…”

Section: B Bounds For the Frequency Estimation Problem 1) Crb And Chrbmentioning

confidence: 99%

A Useful Form of the Abel Bound and Its Application to Estimator Threshold Prediction

Renaux

Najjar-Atallah

Forster

et al. 2007

IEEE Trans. Signal Process.

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Abstract-This correspondence investigates the Abel bound in order to predict the estimators mean square error (mse) threshold effect. A tractable and computationally efficient form of this bound is derived. This form combines the Chapman-Robbins and the Cramér-Rao bounds. This bound is applied to a data-aided carrier frequency estimation problem for which a closed-form expression is provided. An indicator of the signal-to-noise ratio threshold is proposed. A comparison with recent results on the Barankin bound (Chapman-Robbins version) shows the superiority of the Abel-bound version to predict the mse threshold without increasing the computational complexity.Index Terms-Abel bound (AB), carrier synchronization, minimal bounds on mean square error (mse), performance analysis, threshold prediction.

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“…The a priori pdf of θ is Gaussian with zero mean and variance σ 2 θ . Figure 1 superimposes the Bayesian Maximum Likelihood Estimator (BMLE) MSE [15], the Maximum A Posteriori Estimator (MAPE) MSE, the Bayesian…”

Section: Simulation Resultsmentioning

confidence: 99%