Joint Covariance Estimation With Mutual Linear Structure

Ilya Soloveychik, Ami Wiesel

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them. Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation. Our technique is based on the application of principal component analysis in the matrix space. We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramér-Rao lower bound. Numerical simulations are presented to illustrate the performance benefits of the proposed method.

Original languageAmerican English
Article number7332953
Pages (from-to)1550-1561
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume64
Issue number6
DOIs
StatePublished - 15 Mar 2016

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

  • Joint covariance estimation
  • principal component analysis
  • structured covariance estimation
  • truncated SVD

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