Simultaneous localization of multiple vocalizing humpback whale calls in an ocean waveguide with a single horizontal array using the array invariant

Abstract

The array invariant method, previously derived for instantaneous range and bearing estimation of a broadband impulsive source in a horizontally stratified ocean waveguide [Lee and Makris, J. Acoust. Soc. Am. 119, 336–351 (2006)], is generalized to instantaneously and simultaneously localize multiple uncorrelated broadband noise sources that not necessarily impulsive in the time domain. In an ideal Pekeris waveguide, we theoretically show that source range and bearing can be instantaneously obtained from beam-time migration lines measured with a horizontal array through range and bearing dependent differences that arise between modal group speeds along the array. We also show that this theory is approximately valid in a horizontally stratified ocean waveguide. A transform, similar to the Radon transform, is employed to enable simultaneous localization of multiple uncorrelated broadband noise sources without ambiguity using the array invariant method. The method is now applied to humpback whale vocalization data from the Gulf of Maine 2006 Experiment for humpback whale ranges up to tens of kilometers, where it is shown that accurate bearing and range estimation of multiple vocalizing humpback whales can be simultaneously made with little computational effort.