Acoustic localization of resident killer whales for source-level estimation of echolocation clicks

To study the efficacy of resident killer whale echolocation clicks for foraging and other activities requires knowledge of the acoustic characteristics of their clicks, in particular, source levels. To compute apparent source level (ASL) from recordings of killer whales in the wild requires localization of the clicking animals, ideally including rigorous uncertainty estimates, to account for transmission losses from source to receiver. This paper considers acoustic localization of killer whales based on time-of-arrival-differences for clicks recorded at a 2 × 2 m2 array of 23 hydrophones. To quantify uncertainties, a Bayesian localization approach is formulated and two methods of solution are considered, one based on a linearized approximation and the other a nonlinear three-dimensional (3D) grid search. Simulations indicate significant linearization errors in 3D uncertainty (probability) distributions, confirming the superiority of the nonlinear localization. Results of this localization approach are used to calculate ASLs (with uncertainties) for echolocation clicks from Southern and Northern Resident killer whales determined to be directed approximately at the array (i.e., on-axis). Comparison of ASL values across varying ranges indicates a roughly logarithmic range dependence, consistent with whales adjusting their click levels based on distance to the target, approximately accounting for two-way spherical-spreading loss.