TY - GEN
T1 - Performance bounds for constrained parameter estimation
AU - Routtenberg, Tirza
AU - Tabrikian, Joseph
PY - 2012/10/12
Y1 - 2012/10/12
N2 - In this paper, we propose a new class of lower bounds on the mean-squared error (MSE) in non-Bayesian constrained parameter estimation. The new class includes lower bounds on the MSE of any constrained-unbiased estimator, where the constrained-unbiasedness is defined for the first time using the Lehmann-unbiasedness. The proposed class of constrained lower bounds is derived by employing Cauchy-Schwarz inequality and it can be used to derive various bounds for constrained parameter estimation. For example, it is demonstrated that the constrained Cramér-Rao bound (CCRB) is a special case of the proposed class. In addition, the new constrained Hammersley-Chapman-Robbins bound (CHCRB) is derived by using this class. Finally, the CCRB and CHCRB are exemplified in the estimation of the eigenvalues of a structured covariance matrix subject to signal subspace constraints. It is shown that the proposed CHCRB is tighter than the CCRB at any signal-to-noise ratio.
AB - In this paper, we propose a new class of lower bounds on the mean-squared error (MSE) in non-Bayesian constrained parameter estimation. The new class includes lower bounds on the MSE of any constrained-unbiased estimator, where the constrained-unbiasedness is defined for the first time using the Lehmann-unbiasedness. The proposed class of constrained lower bounds is derived by employing Cauchy-Schwarz inequality and it can be used to derive various bounds for constrained parameter estimation. For example, it is demonstrated that the constrained Cramér-Rao bound (CCRB) is a special case of the proposed class. In addition, the new constrained Hammersley-Chapman-Robbins bound (CHCRB) is derived by using this class. Finally, the CCRB and CHCRB are exemplified in the estimation of the eigenvalues of a structured covariance matrix subject to signal subspace constraints. It is shown that the proposed CHCRB is tighter than the CCRB at any signal-to-noise ratio.
KW - Cauchy-Schwarz inequality
KW - Cramér-Rao bound
KW - Lehmann-unbiased
KW - Non-Bayesian constrained estimation
KW - mean-square-error (MSE)
UR - http://www.scopus.com/inward/record.url?scp=84867224840&partnerID=8YFLogxK
U2 - 10.1109/SAM.2012.6250553
DO - 10.1109/SAM.2012.6250553
M3 - Conference contribution
SN - 9781467310710
T3 - Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
SP - 513
EP - 516
BT - 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012
T2 - 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012
Y2 - 17 June 2012 through 20 June 2012
ER -