Detection of Spatially Correlated Time Series From a Network of Sensor Arrays

This paper addresses the problem of testing for the independence among multiple ( ≥ 2) random vectors. The generalized likelihood ratio test tests the null hypothesis that the composite covariance matrix of the channels is block-diagonal, using a generalized Hadamard ratio. Using the theory of Gram determinants, we show that this Hadamard ratio is stochastically equivalent to a product of scalars, which are independently drawn from a beta distribution under the null hypothesis. This result is then used to derive an asymptotic null distribution, which can be used to identify an appropriate threshold when the sample support is large. These results are then extended to the problem of detecting the presence of spatially correlated time series when each observer employs an array of sensors. Assuming wide-sense stationary processes in both time and space, the likelihood ratio is shown to involve a Hadamard ratio of an estimated cross-spectral matrix at every frequency/wavenumber pair. The proposed detector is compared to several alternative detectors, using simulated space-time fields.