Unreported large errors in a common method for sound source localization of marine mammals

Confidence intervals of location 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. Simulations demonstrate Ishmael, a TDOA locator based on uncorrected least squares minimization (ULSM), yields errors with mean, standard deviation, and maximum of 0.1, 0.2, and 0.9 km, respectively, due to sensitivity to inputs and numerical implementation when applied to scenarios with minuscule errors; e.g., five clock-synchronized receivers residing on the vertices of a square with one in its center. This sensitivity can mask other causes of location error due to small uncertainties in receiver location and sound speed. Realistic uncertainties of sound speed up to ±7.5 m/s lead to errors up to 4 km. With unsynchronized clocks and common practice of correcting TDOA from synchronization measurements at the start and end of an experiment, errors of location are 10 to 1000 km. These problems occur because ULSM was not designed to account for all errors. ULSM is also available in PAMGuard and other systems and is used to study behavior and abundance of calling marine mammals. ULSM is briefly compared to another method designed to account for errors.