Bowhead whale localization using time-difference-of-arrival data from asynchronous recorders

Abstract

This paper estimates bowhead whale locations and uncertainties using nonlinear Bayesian inversion of the time-difference-of-arrival (TDOA) of low-frequency whale calls recorded on onmi-directional asynchronous recorders in the shallow waters of the northeastern 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 clocks drifted out of synchronization. Hundreds of recorded whale calls are manually associated between recorders. The TDOA between hydrophone pairs are calculated from filtered waveform cross correlations and depend on the whale locations, hydrophone locations, relative recorder clock offsets, and effective waveguide sound speed. A nonlinear Bayesian inversion estimates all of these parameters and their uncertainties as well as data error statistics. The problem is highly nonlinear and a linearized inversion did not produce physically realistic results. Whale location uncertainties from nonlinear inversion can be low enough to allow accurate tracking of migrating whales that vocalize repeatedly over several minutes. Estimates of clock drift rates are obtained from inversions of TDOA data over two weeks and agree with corresponding estimates obtained from long-time averaged ambient noise cross correlations. The inversion is suitable for application to large data sets of manually or automatically detected whale calls.

Locating calling mammals with signal times amongst shadows and black holes in two-dimensional models

“…Signal times have been used for a century to locate signals on 2D surfaces even though objects are not usually on this surface. Their ubiquitous use up to the present suggests correctness of approach 1, 5,7,13,14,24,29 . The apparent discovery here of signal-speed singularities in 2D models suggests findings in thousands of papers could be re-evaluated.…”

“…Almost all previous 2D models set signal speed to a constant, independent of an object's location. In a small number of cases, 2D models constrain signal speeds to an interval of finitewidth 24,29 , and the reported interval does not ever appear to include zero. The surfaces utilized by 2D models must allow speed to vary with location to yield correct location.…”

“…Modeling locations in 2D is ubiquitous. Contemporary examples include locating calling mammals in the ocean 5,14,24,29 , sounds in a room via robots 6 , ships 26 , cell phones 13 , lightning 11 , wildlife radio transmitters 9 , aircraft radio emissions 10 , bistatic sonars 3 , and theoretical developments 7 . These models derive locations by translating TDOA or bistatic signal times to difference or sum of distance assuming signal speed is constant 3, [5][6][7][9][10][11]13,14,26 , the overwhelmingly-common case, or are constrained to a finite interval 24,29 , e.g.…”

Feasibility of a Passive Acoustic Monitoring (PAM) network for Harbour Porpoises on the Dutch Continental Shelf

“…Hydrophone arrays have been commonly used to locate and track different cetacean species over large distances (e.g. Watkins & Schevill, 1974;Freitag & Tyack, 1993;Thode, 2005;Tiemann et al, 2006;Warner et al, 2017). During foraging dives large toothed whales, such as sperm whales usually click in a 10 Hz-30 kHz frequency band (e.g.…”