The author describes and evaluates a Bayesian method to reconstruct three-dimensional toothed whale trajectories from a series of echolocation signals. Localization by using passive acoustic data (time of arrival of source signals at receptors) is assisted by using visual data (coordinates of the whale when diving and resurfacing) and tag information (movement statistics). The efficiency of the Bayesian method is compared to the standard minimum mean squared error statistical approach by comparing the reconstruction results of 48 simulated sperm whale (Physeter macrocephalus) trajectories. The use of the advanced Bayesian method reduces bias (standard deviation) with respect to the standard method up to a factor of 8.9 (13.6). The author provides open-source software which is functional with acoustic data which would be collected in the field from any three-dimensional receptor array design. This approach renews passive acoustics as a valuable tool to study the underwater behavior of toothed whales.
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