Improved linear least squares estimation using bounded data uncertainty

Handle URI:
http://hdl.handle.net/10754/582874
Title:
Improved linear least squares estimation using bounded data uncertainty
Authors:
Ballal, Tarig; Al-Naffouri, Tareq Y.
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.
KAUST Department:
Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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)
Issue Date:
Apr-2015
DOI:
10.1109/ICASSP.2015.7178607
Type:
Conference Paper
Additional Links:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178607
Appears in Collections:
Conference Papers; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBallal, Tarigen
dc.contributor.authorAl-Naffouri, Tareq Y.en
dc.date.accessioned2015-11-29T08:45:29Zen
dc.date.available2015-11-29T08:45:29Zen
dc.date.issued2015-04en
dc.identifier.doi10.1109/ICASSP.2015.7178607en
dc.identifier.urihttp://hdl.handle.net/10754/582874en
dc.description.abstractThis 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.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178607en
dc.titleImproved linear least squares estimation using bounded data uncertaintyen
dc.typeConference Paperen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)en
dc.conference.date19-24 April 2015en
dc.conference.nameIEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)en
dc.conference.locationSouth Brisbane, QLDen
dc.eprint.versionPost-printen
kaust.authorBallal, Tarigen
kaust.authorAl-Naffouri, Tareq Y.en
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