TY - GEN

T1 - Improved linear least squares estimation using bounded data uncertainty

AU - Ballal, Tarig

AU - Al-Naffouri, Tareq Y.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/4

Y1 - 2015/4

N2 - This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.

AB - This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.

UR - http://hdl.handle.net/10754/582874

UR - http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178607

UR - http://www.scopus.com/inward/record.url?scp=84946055287&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2015.7178607

DO - 10.1109/ICASSP.2015.7178607

M3 - Conference contribution

SN - 9781467369978

SP - 3427

EP - 3431

BT - 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -