Matrix analysis
Matrix computations (3rd ed.)
Explicit Ziv-Zakai lower bound for bearing estimation
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 05
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
IEEE Transactions on Information Theory
A Fresh Look at the Bayesian Bounds of the Weiss-Weinstein Family
IEEE Transactions on Signal Processing
Bayesian bounds for matched-field parameter estimation
IEEE Transactions on Signal Processing
Explicit Ziv-Zakai lower bound for bearing estimation
IEEE Transactions on Signal Processing
Extended Ziv-Zakai lower bound for vector parameter estimation
IEEE Transactions on Information Theory
A Barankin-type lower bound on the estimation error of a hybrid parameter vector
IEEE Transactions on Information Theory
A bound on mean-square estimation error with background parameter mismatch
IEEE Transactions on Information Theory
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In this paper, a new class of Bayesian lower bounds is proposed. Derivation of the proposed class is performed via projection of each entry of the vector-function to be estimated on a Hilbert subspace of L2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform, applied on functions used for computation of bounds in the Weiss-Weinstein class. The integral transform generalizes the traditional derivative and sampling operators, used for computation of existing performance lower bounds, such as the Bayesian Cramér-Rao, Bayesian Bhattacharyya, and Weiss-Weinstein bounds. It is shown that some well-known Bayesian lower bounds can be derived from the proposed class by specific choice of the integral transform kernel. A new lower bound is derived from the proposed class using the Fourier transform kernel. The proposed bound is compared with other existing bounds in terms of signal-to-noise ratio (SNR) threshold region prediction in the problem of frequency estimation. The bound is shown to be computationally manageable and provides better prediction of the SNR threshold region, exhibited by the maximum a posteriori probability (MAP) and minimum-mean-square-error (MMSE) estimators.