Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties |
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Authors: | Amir Beck Aharon Ben-Tal Yonina C Eldar |
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Institution: | (1) MINERVA Optimization Center, Department of Industrial Engineering, Technion–Israel Institute of Technology, Haifa, 32000, Israel;(2) Department of Electrical Engineering, Technion–Israel Institute of Technology, Haifa, 32000, Israel |
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Abstract: | 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.
The research was partially supported by BSF grant #2002038 |
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Keywords: | Minimax Mean-Squared Error Multiple Observations Robust Estimation Semidefinite Programming Block Circulant Matrices Discrete Fourier Transform |
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