Improved linear least squares estimation using bounded data uncertainty

Abstract
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.

Citation
Ballal, T., & Al-Naffouri, T. Y. (2015). Improved linear least squares estimation using bounded data uncertainty. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). doi:10.1109/icassp.2015.7178607

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

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

Conference/Event Name
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

DOI
10.1109/ICASSP.2015.7178607

Additional Links
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178607

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