TY - JOUR
T1 - General classes of performance lower bounds for parameter estimation - Part II
T2 - Bayesian bounds
AU - Todros, Koby
AU - Tabrikian, Joseph
N1 - Funding Information:
Manuscript received May 05, 2009; revised March 07, 2010. Date of current version September 15, 2010. This work was supported in part by the Israel Science Foundation under Grant 1311/08. The authors are with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel (e-mail: [email protected]; [email protected]). Communicated by M. Lops, Associate Editor for Detection and Estimation. Digital Object Identifier 10.1109/TIT.2010.2059890
PY - 2010/10/1
Y1 - 2010/10/1
N2 - 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 WeissWeinstein 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 WeissWeinstein 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.
AB - 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 WeissWeinstein 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 WeissWeinstein 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.
KW - Bayesian bounds
KW - WeissWeinstein class
KW - maximum a posteriori probability (MAP) estimator
KW - mean-square-error bounds
KW - minimum-mean-square-error (MMSE) estimator
KW - parameter estimation
KW - performance bounds
KW - threshold signal-to-noise ratio (SNR)
UR - http://www.scopus.com/inward/record.url?scp=77956698816&partnerID=8YFLogxK
U2 - 10.1109/TIT.2010.2059890
DO - 10.1109/TIT.2010.2059890
M3 - Article
AN - SCOPUS:77956698816
SN - 0018-9448
VL - 56
SP - 5064
EP - 5082
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 10
M1 - 5571907
ER -