Geometric methods for structured covariance estimation

Lipeng Ning, Xianhua Jiang, Tryphon Georgiou

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

5 Scopus citations

Abstract

The problem considered in this paper is that of approximating a sample covariance matrix by one with a Toeplitz structure. The importance stems from the apparent sensitivity of spectral analysis on the linear structure of covariance statistics in conjunction with the fact that estimation error destroys the Toepliz pattern. The approximation is based on appropriate distance measures. To this end, we overview some of the common metrics and divergence measures which have been used for this purpose as well as introduce certain alternatives. In particular, the metric induced by Monge-Kantorovich transportation of the respective probability measures leads to an efficient linear matrix inequality (LMI) formulation of the approximation problem and relates to approximation in the Hellinger metric. We compare these with the maximum likelihood and the Burg method on a representative case study from the literature.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
Pages1877-1882
Number of pages6
StatePublished - Nov 26 2012
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2012 American Control Conference, ACC 2012
CountryCanada
CityMontreal, QC
Period6/27/126/29/12

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