TY - JOUR
T1 - Robust mean-squared error estimation of multiple signals in linear systems affected by model and noise uncertainties
AU - Beck, Amir
AU - Ben-Tal, Aharon
AU - Eldar, Yonina C.
PY - 2006
Y1 - 2006
N2 - This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N.
AB - This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N.
KW - Block Circulant Matrices
KW - Discrete Fourier Transform
KW - Minimax Mean-Squared Error
KW - Multiple Observations
KW - Robust Estimation
KW - Semidefinite Programming
UR - http://www.scopus.com/inward/record.url?scp=33644665380&partnerID=8YFLogxK
U2 - 10.1007/s10107-005-0683-3
DO - 10.1007/s10107-005-0683-3
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AN - SCOPUS:33644665380
SN - 0025-5610
VL - 107
SP - 155
EP - 187
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1-2
ER -