Robust mean-squared error estimation of multiple signals in linear systems affected by model and noise uncertainties

Amir Beck*, Aharon Ben-Tal, Yonina C. Eldar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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.

Original languageEnglish
Pages (from-to)155-187
Number of pages33
JournalMathematical Programming
Volume107
Issue number1-2
DOIs
StatePublished - 2006
Externally publishedYes

Keywords

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

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