TY - GEN

T1 - MSE estimation of multichannel signals with model uncertainties

AU - Beck, Amir

AU - Eldar, Yonina C.

AU - Ben-Tal, Aharon

PY - 2005

Y1 - 2005

N2 - We consider the problem of multichannel estimation, in which we seek to estimate multiple input vectors that are observed through a set of linear transformations and corrupted by additive noise. The input vectors xk are known to satisfy a weighted norm constraint. We discuss both the case where the linear transformations are fixed (certain) and the case where they are only known to reside in some deterministic uncertainty set. We seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of the linear transformations and possible values of X k. We show that for an arbitrary choice of weighting matrix, the minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP). In the case in which the linear transformations are fixed and the norms are unweighed, the minimax MSE multichannel estimator has an explicit closed from solution. Finally, we demonstrate through examples, that the minimax MSE estimator can significantly increase the performance over conventional least-squares based methods.

AB - We consider the problem of multichannel estimation, in which we seek to estimate multiple input vectors that are observed through a set of linear transformations and corrupted by additive noise. The input vectors xk are known to satisfy a weighted norm constraint. We discuss both the case where the linear transformations are fixed (certain) and the case where they are only known to reside in some deterministic uncertainty set. We seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of the linear transformations and possible values of X k. We show that for an arbitrary choice of weighting matrix, the minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP). In the case in which the linear transformations are fixed and the norms are unweighed, the minimax MSE multichannel estimator has an explicit closed from solution. Finally, we demonstrate through examples, that the minimax MSE estimator can significantly increase the performance over conventional least-squares based methods.

UR - http://www.scopus.com/inward/record.url?scp=33646787862&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2005.1415942

DO - 10.1109/ICASSP.2005.1415942

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:33646787862

SN - 0780388747

SN - 9780780388741

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - IV49-IV52

BT - 2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05

Y2 - 18 March 2005 through 23 March 2005

ER -