Topic
Cramér–Rao bound
About: Cramér–Rao bound is a research topic. Over the lifetime, 2897 publications have been published within this topic receiving 58659 citations. The topic is also known as: Cramér-Rao lower bound & Cramér–Rao lower bound.
Papers published on a yearly basis
Papers
More filters
TL;DR: The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established.
Abstract: The performance of the MUSIC and ML methods is studied, and their statistical efficiency is analyzed. The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established. The relationship between the MUSIC and ML estimators is investigated as well. A numerical study is reported of the statistical efficiency of the MUSIC estimator for the problem of finding the directions of two plane waves using a uniform linear array. An exact description of the results is included. >
2,552 citations
TL;DR: An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed and is shown to attain the Cramer-Rao lower bound near the small error region.
Abstract: An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed. The approach is noniterative and gives an explicit solution. It is an approximate realization of the maximum-likelihood estimator and is shown to attain the Cramer-Rao lower bound near the small error region. Comparisons of performance with existing techniques of beamformer, spherical-interpolation, divide and conquer, and iterative Taylor-series methods are made. The proposed technique performs significantly better than spherical-interpolation, and has a higher noise threshold than divide and conquer before performance breaks away from the Cramer-Rao lower bound. It provides an explicit solution form that is not available in the beamforming and Taylor-series methods. Computational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method. >
2,202 citations
TL;DR: A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality and is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems.
Abstract: A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.
1,333 citations
11 Apr 1988
TL;DR: The authors derive the Cramer-Rao bound (CRB) for the estimation problems mentioned above, and establish some useful properties of the CRB covariance matrix.
Abstract: The authors consider methods for solving the problem of finding the directions of multiple plane waves with linear arrays of sensors and the related one of estimating the parameters of multiple superimposed exponential signals in noise. Specifically, the MUSIC and maximum-likelihood (ML) methods have been proposed for solving these problems. The authors study the performance of the MUSIC and ML methods, and analyze their statistical efficiency. They also derive the Cramer-Rao bound (CRB) for the estimation problems mentioned above, and establish some useful properties of the CRB covariance matrix. The relationship between the MUSIC and ML estimators is investigated as well. >
865 citations
TL;DR: The performances of several signal-to noise ratio (SNR) estimation techniques reported in the literature are compared to identify the "best" estimator and some known estimator structures are modified to perform better on the channel of interest.
Abstract: The performances of several signal-to noise ratio (SNR) estimation techniques reported in the literature are compared to identify the "best" estimator. The SNR estimators are investigated by the computer simulation of baseband binary phase-shift keying (PSK) signals in real additive white Gaussian noise (AWGN) and baseband 8-PSK signals in complex AWGN. The mean square error is used as a measure of performance. In addition to comparing the relative performances, the absolute levels of performance are also established; the simulated performances are compared to a published Cramer-Rao bound (CRB) for real AWGN and a CRB for complex AWGN that is derived here. Some known estimator structures are modified to perform better on the channel of interest. Estimator structures for both real and complex channels are examined.
848 citations