Detection of correlated time series in a network of sensor arrays

This paper considers the problem of testing for the independence among multiple random vectors with each random vector representing a time series captured at one sensor. Implementing the Generalized Likelihood Ratio Test involves testing the null hypothesis that the composite covariance matrix of the channels is block-diagonal through the use of a generalized Hadamard ratio. These results are then extended to the problem of detecting the presence of correlated time series when several observers each employ an array of sensors. Assuming wide-sense stationary processes in both time and space, results on large block-Toeplitz matrices suggest the use of a broadband integral of a frequency-wavenumber dependent Hadamard ratio as an alternative test statistic.