Testing for Isotropy

Abstract

The presence of acoustic targets in the ocean produces an anisotropic field. Hence a hypothesis test for detection of these targets is formulated as H0 (isotropic noise field) versus H1 (anisotropic field). The outputs of N hydrophones are available. Two logical approaches become apparent, namely (1) to test the estimated element cross covariance matrix or equivalently the N×N cross-spectral matrices and (2)to test the power of the M beams formed from the N elements. The latter approach, although less direct, leads to an asymptotically uniformly most powerful invariant test providing that the beam powers are independent through design or suitable transformation. The test is to decide upon H0 if the spatial variance of the power does not exceed a threshold, and decide upon H1 if the variance does exceed that threshold. The test is written as where ∑ i=1M (Pi−P̄i)2≷H0H1 THRESHOLD, where P̄i= 1M ∑ i=1MPi, and Pi is the measured power (in decibels) in the ith beam. False alarm and miss probabilities are determined through the introduction of targets with various strengths into selected beams.