Unreported large errors from two PAMGuard three-dimensional localizers of whale calls

Abstract

Confidence intervals of location (CIL) of calling marine mammals, derived from time-differences-of-arrival (TDOA) between receivers, depend on errors of TDOAs, receiver location, clocks, sound speeds, and location method. When these errors are minuscule, simulations yield small errors of PAMGuard's 3D simplex localizer when click sounds of beaked and sperm whales originate in a 1000 x 1000 x 1000 $\mbox{m}^3$ region using five receivers having horizontal and vertical separations of 1000 m and 150 m respectively. Realistic uncertainties of sound speed up to $\pm 10$ m/s lead to errors up to $10^{14}$ m. With clocks maintained by atomic standards and common practice of correcting TDOA from synchronization measurements at the start and end of an experiment, errors of location are up to $10^{4}$ m. Errors up to $10^2$ and $10^3$ m are found when the receiver's locations are uncertain within 10 and 40 m respectively. Errors of PAMGuard's 3D hyperbolic localizer are almost independent of the above uncertainties, yielding errors of location up to about $10^4$ m even when simulated errors are minuscule. Causes of PAMGuard's 3D location errors are unknown. These algorithms are briefly compared to another method designed to yield a reliable CIL.