Bayesian Inversion of Time-difference-of-arrival Data to Localize Bowhead whales in the Chukchi Sea

This paper develops and illustrates a Bayesian inversion for bowhead whale localization and nonlinear uncertainty estimation using time-difference-of-arrivals (TDOA) of whale calls recorded on omni-directional asynchronous recorders in the Chukchi Sea, Alaska. A Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by 0.5–9.2 km, was deployed for several months over which time their internal clocks drifted out of synchronization. Hundreds of recorded whale calls are manually annotated and associated between recorders. The TDOA of whale calls recorded on independent hydrophone pairs are calculated from waveform cross-correlations. These TDOA data depend on the whale locations, hydrophone locations, relative recorder clock drifts, and an effective waveguide sound speed, all of which are considered unknown parameters (with varying levels of prior information) in the Bayesian inversion. In many cases localization uncertainties are sufficiently small to allow tracking whales that vocalize repeatedly over several minutes. Estimates of clock drift rates are obtained from inversions of TDOA data over several weeks. The inversion is computationally efficient and suitable for application to large datasets of manually- or automatically detected whale calls