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Detection of Spatially Correlated Gaussian Time Series

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Executive Summary

This paper addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. For Wide Sense Stationary (WSS) Gaussian processes, this is a problem of deciding between two different power spectral density matrices, one of them diagonal. Specifically, the authors show that for arbitrary Gaussian processes (not necessarily WSS) the Generalized Likelihood Ratio Test (GLRT) is given by the quotient between the determinant of the sample space-time covariance matrix and the determinant of its block-diagonal version.

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