Determining the probability of correct resolution of the left–right ambiguity in towed array sonar

Abstract

When a towed sonar array is straight, it has the difficulty that it cannot distinguish a contact on the left from one at the same angle on the right. When the array isnotstraight and its shape known, we calculate the probability that the left–right ambiguity is resolved correctly, using the Neyman–Pearson hypothesis testing framework, assuming a delay-sum beamformer, a single-frequency contact, and Gaussian noise. We also initially consider the noise field to be uncorrelated and show that the evaluation of the probability of correct resolution reduces to evaluating a one-dimensional integral. We find, as expected, that the probability increases, as the signal-to-noise ratio and the lateral deviation of the array from straight increase. For demonstration purposes, we also evaluate the probability of correct resolution for two representative shapes the array might assume in practice. Finally, we consider a more realistic, correlated noise field and we show that the initial assumption of an uncorrelated noise field provides a good approximation when the lateral deviation of the array is sufficiently large.