Test for spatial stationarity and applications

This paper presents a test which accepts or rejects, based on the data collected by an array of N sensors, the hypothesis that the sampled tempo-spatial field is spatially stationary. The proposed test is applicable to arrays in an arbitrary but known 3-dimensional geometry. It is based on the estimated second order spatial cumulant spectrum matrix, which is theoretically diagonal for a stationary spatial field. We show how the proposed test can be used for robust detection of a source in shallow water.