Matrix analysis
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Digital processing of random signals: theory and methods
Digital processing of random signals: theory and methods
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
Convex Optimization
Efficient computation of the Bayesian Cramer-Rao bound on estimating parameters of Markov models
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Maximum Likelihood Estimation of Compound-Gaussian Clutter and Target Parameters
IEEE Transactions on Signal Processing
The joint MAP-ML criterion and its relation to ML and to extended least-squares
IEEE Transactions on Signal Processing
Threshold region performance of maximum likelihood direction of arrival estimators
IEEE Transactions on Signal Processing
On the High-SNR Conditional Maximum-Likelihood Estimator Full Statistical Characterization
IEEE Transactions on Signal Processing
Further results on Crame´r-rao bounds for parameter estimation in long-code DS/CDMA systems
IEEE Transactions on Signal Processing
A radar application of a modified Cramer-Rao bound: parameterestimation in non-Gaussian clutter
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
A Barankin-type lower bound on the estimation error of a hybrid parameter vector
IEEE Transactions on Information Theory
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In this paper, we study the properties of the hybrid Cramér-Rao bound (HCRB). We first address the problem of estimating unknown deterministic parameters in the presence of nuisance random parameters. We specify a necessary and sufficient condition under which the HCRB of the nonrandom parameters is equal to the Cramér-Rao bound (CRB). In this case, the HCRB is asymptotically tight [in high signal-to-noise ratio (SNR) or in large sample scenarios], and, therefore, useful. This condition can be evaluated even when the CRB cannot be evaluated analytically. If this condition is not satisfied, we show that the HCRB on the nonrandom parameters is always looser than the CRB. We then address the problem in which the random parameters are not nuisance. In this case, both random and nonrandom parameters need to be estimated. We provide a necessary and sufficient condition for the HCRB to be tight. Furthermore, we show that if the HCRB is tight, it is obtained by the maximum likelihood/maximum a posteriori probability (ML/MAP) estimator, which is shown to be an unbiased estimator which estimates both random and nonrandom parameters simultaneously optimally (in the minimum mean-square-error sense).