Robust estimation of structured covariance matrix for heavy-tailed distributions

Ying Sun, Prabhu Babu, Daniel P. Palomar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

In this paper, we consider the robust covariance estimation problem in the non-Gaussian set-up. In particular, Tyler's M-estimator is adopted for samples drawn from a heavy-tailed elliptical distribution. For some applications, the covariance matrix naturally possesses certain structure. Therefore, incorporating the prior structure information in the estimation procedure is beneficial to improving estimation accuracy. The problem is formulated as a constrained minimization of the Tyler's cost function, where the structure is characterized by the constraint set. A numerical algorithm based on majorization-minimization is derived for general structures that can be characterized as a convex set, where a sequence of convex programming is solved. For the set of matrices that can be decomposed as the sum of rank one positive semidefinite matrices, which has a wide range of applications, the algorithm is modified with much lower complexity. Simulation results demonstrate that the proposed structure-constrained Tyler's estimator achieves smaller estimation error than the unconstrained case.

Original languageEnglish (US)
Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5693-5697
Number of pages5
ISBN (Electronic)9781467369978
DOIs
StatePublished - Aug 4 2015
Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
Duration: Apr 19 2014Apr 24 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2015-August
ISSN (Print)1520-6149

Other

Other40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Country/TerritoryAustralia
CityBrisbane
Period4/19/144/24/14

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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