A general class of lower bounds in parameter estimation

Weinstein, E.; Weiss, A.J.

doi:10.1109/18.2647

Cited by 189 publications

(139 citation statements)

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“…(10), it is clear that the knowledge of η (α, β, u, v) for a particular problem leads to the Weiss-Weinstein bound (without the maximization procedure over the test-points and over the parameters s i ). Surprisingly, this simple expression is given in [40] only for s i = 1 2 , ∀i and not for the general case. Let us now detail this function η (α, β, u, v).…”

Section: B a General Results On The Weiss-weinstein Bound And Its Appmentioning

confidence: 99%

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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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Section: B a General Results On The Weiss-weinstein Bound And Its Appmentioning

confidence: 99%

“…The Weiss-Weinstein bound for a q × 1 real parameter vector θ is a q × q matrix denoted WWB and is given as follows [40] …”

Section: A Backgroundmentioning

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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“…On the estimation side, we submit evidence that the minimum mean square error (MMSE) estimator of this problem (the well-known conditional mean estimator) tightly achieves the Bayesian CR lower bound. This is a remarkable result, demonstrating that all the performance gains presented in the theoretical analysis part of our paper can indeed be achieved with the MMSE estimator, which in principle has a practical implementation (Weinstein & Weiss 1988). We end our paper with a simple example of what could be achieved using the Bayesian approach in terms of the astrometric precision when new observations of varying quality are used and we incorporate as prior information data from the USNO-B all-sky catalog.…”

Section: Introductionmentioning

confidence: 94%

“…Returning to our problem, the Bayes rule is the wellknown posterior mean of X c given a realization of the observations. More formally, for all i n ∈ N n the MMSE estimator is (Weinstein & Weiss 1988) …”

Section: Comparing the Bcr Lower Bound With The Performance Of The Opmentioning

confidence: 99%

Analysis of the Bayesian Cramér-Rao lower bound in astrometry

Echeverria

Silva

Mendez

et al. 2016

A&A

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Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims. We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (i.e., the position is a random variable) from observations that are statistically dependent on the position. Methods. We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background.Results. We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions. The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

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“…An important but much less explored alternative is to use the other Bayesian bounds in the literature, namely, Weiss-Weinstein, Bhattacharyya, and Bobrovsky-Zakai lower bounds [9]. All of the lower bounds mentioned above belong to a larger family of Bayesian bounds that is known today as the Weiss-Weinstein family of Bayesian bounds [10]. In the nonlinear filtering context, the recursive formulation of BCRB presented by Tichavský et al was long considered as the state-of-the art [11], even though a couple of tighter alternatives exist [12].…”

Section: Introductionmentioning

confidence: 99%