Mathematical Programming

, Volume 107, Issue 1–2, pp 155–187

Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties

Article

DOI: 10.1007/s10107-005-0683-3

Cite this article as:
Beck, A., Ben-Tal, A. & Eldar, Y. Math. Program. (2006) 107: 155. doi:10.1007/s10107-005-0683-3

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.

Keywords

Minimax Mean-Squared Error Multiple Observations Robust Estimation Semidefinite Programming Block Circulant Matrices Discrete Fourier Transform 

Mathematics Subject Classification (2000)

90C22 90C25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.MINERVA Optimization Center, Department of Industrial EngineeringTechnion–Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of Electrical EngineeringTechnion–Israel Institute of TechnologyHaifaIsrael

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