Estimation of Toeplitz Covariance Matrices in Large Dimensional Regime With Application to Source Detection

In this paper, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The consistency is then extended to the case where the aggregated matr...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on signal processing Vol. 63; no. 18; pp. 4903 - 4913
Main Authors Vinogradova, Julia, Couillet, Romain, Hachem, Walid
Format Journal Article
LanguageEnglish
Published IEEE 15.09.2015
Institute of Electrical and Electronics Engineers
Subjects
Concentration inequalities
Context
correlated noise
Covariance matrices
covariance matrix
Engineering Sciences
Estimation
Linear matrix inequalities
Mathematics
Noise
source detection
Statistics
Symmetric matrices
Index Terms—Covariance matrix
concentration inequalities
source detection
correlated noise
Online AccessGet full text

Cover

More Information
Summary:In this paper, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The consistency is then extended to the case where the aggregated matrix of time samples is corrupted by a rank one (or more generally, low rank) matrix. As an application of the latter, the problem of source detection in the context of large dimensional sensor networks within a temporally correlated noise environment is studied. As opposed to standard procedures, this application is performed online, i.e., without the need to possess a learning set of pure noise samples.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2015.2447493