  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.
