Estimation of Toeplitz covariance matrices in large dimensional regime with application to source detection large

Publication Type:

Journal Article

Source:

IEEE Transactions on Signal Processing, Volume 63, Number 18, p.4903-4913 (2015)

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 par- ticular 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.

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