Asymptotic statistics for location estimates of acoustic signals

Abstract

The passive sonar problem is to estimate the location (bearing, range, depth, etc.) of an acoustic source with data from an array of sensors. The purpose of this paper is to give the asymptotic distribution of location estimates of the true source location under weak assumptions on the signal-processing method and the environmental noise in which the signal is embedded. The estimates of location are taken to be the peaks of the estimated array power output (e.g., the ‘‘ambiguity surface’’), as usual, and the crucial assumption in the analysis is that the signal plus noise forms a strictly stationary stochastic process. The estimates are shown to be consistent, asymptotically normal, and the asymptotic covariance is given. The asymptotic standard deviation is found to be proportional to the inverse of the curvature of the array power output surface at the true source location and invariant under monotonic transformations of the array power. The use of these statistics is illustrated by the construction of an approximate confidence region for a true source location.