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

Renaux, Alexandre; Najjar-Atallah, L.; Forster, Philippe; Larzabal, Pascal

doi:10.1109/tsp.2006.890928

Cited by 19 publications

(11 citation statements)

References 20 publications

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“…Fig . 1 superimposes the global MSE of the ML estimator evaluated over 1000 Monte Carlo trials, the BCRB, the BZB, the BAB (20), the WWB obtained by (19), and the WWB obtained by (21). The BAB is close to the BZB.…”

Section: Simulation Resultsmentioning

confidence: 90%

WeissWeinstein Bound for DataAided Carrier Estimation

Trees¹,

Bell²

2009

Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking

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Abstract-This letter investigates Bayesian bounds on the mean-square error (MSE) applied to a data-aided carrier estimation problem. The presented bounds are derived from a covariance inequality principle: the so-called Weiss and Weinstein family. These bounds are of utmost interest to find the fundamental MSE limits of an estimator, even for critical scenarios (low signal-to-noise ratio and/or low number of observations). In a data-aided carrier estimation problem, a closed-form expression of the Weiss-Weinstein bound (WWB) that is known to be the tightest bound of the Weiss and Weinstein family is given. A comparison with the maximum likelihood estimator and the other bounds of the Weiss and Weinstein family is given. The WWB is shown to be an efficient tool to approximate this estimator's MSE and to predict the well-known threshold effect.Index Terms-Carrier frequency estimation, estimators performance, Weiss and Weinstein family bounds.

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Section: Simulation Resultsmentioning

confidence: 90%

WeissWeinstein Bound for DataAided Carrier Estimation

Trees¹,

Bell²

2009

Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking

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“…(44) and after an optimization over the test points. The optimization over the test points can be done over a search grid or by using the ambiguity diagram of the array in order to reduce significantly the computational cost (see [18], [27], [34], [45], [46]). …”

Section: ) Unconditional Observation Modelmentioning

confidence: 99%

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

Renaux

Boyer

et al. 2014

Signal Processing

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In this paper, the Weiss-Weinstein bound is analyzed in the context of sources localization with a planar array of sensors. Both conditional and unconditional source signal models are studied. First, some results are given in the multiple sources context without specifying the structure of the steering matrix and of the noise covariance matrix.Moreover, the case of an uniform or Gaussian prior are analyzed. Second, these results are applied to the particular case of a single source for two kinds of array geometries: a non-uniform linear array (elevation only) and an arbitrary planar (azimuth and elevation) array.

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“…This model is a particular case of the model (68), where (80) with (81) Let . The likelihood of the observation is given by (82) Note that, if is assumed to be deterministic and in a digital communications context, some closed-form expressions of deterministic bounds can be found in [56].…”

Section: B Spectral Analysis Problemmentioning

confidence: 99%

“…The Chapman-Robbins bound and the Barankin bound have already been successfully applied to several estimation problems [28], [31], [44]- [55]. The use of the Abel bound, which can also handle the threshold phenomena, is still marginal [56].…”

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

Cited by 19 publications

References 20 publications

WeissWeinstein Bound for DataAided Carrier Estimation

WeissWeinstein Bound for DataAided Carrier Estimation

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

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

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