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

Abstract

In this article, 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.

20 pages, 3 figures, submitted to IEEE Transactions on Signal Processing

References in corpus (2)

• Regularized estimation of large covariance matrices
• Optimal rates of convergence for covariance matrix estimation

Cited by in corpus (5)

• Robust Kronecker Product PCA for Spatio-Temporal Covariance Estimation
• Robust Model Order Selection in Large Dimensional Elliptically Symmetric Noise
• Random Matrix Improved Covariance Estimation for a Large Class of Metrics
• Regularized Block Toeplitz Covariance Matrix Estimation via Kronecker Product Expansions
• Ratio-consistent estimation for long range dependent Toeplitz covariance with application to matrix data whitening