Source Separation of Sperm Whales' Echolocation Clicks

Echolocation clicks, which are used for both localization and locomotion, are often emitted by sperm whales (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Physeter macrocephalus</i>). The separation between the sources of overlapping echolocation clicks is a useful tool for biodiversity and behavioral analysis. The problem is challenging due to the similarities between these vocalizations. Current approaches for separating the sources of echolocation clicks are based on short-term signal features, but neglect similarities in the channel impulse response and between sequences of clicks. As a result, they cannot distinguish between sources over long periods of time and thus neglect the temporal relationships of echolocation clicks arranged as click sequences or trains. In this paper, we present a novel three-stage source separation algorithm that utilizes both temporal and spectral click attributes as well as spatial information derived from the arrival time delays between direct and reflected click paths. The algorithm separates clicks by first identifying click sequences in short time windows using MAP (Maximum a Posteriori) estimates, i.e. determining the most probable sequences from a series of measured clicks. These sequences are then grouped into click trains using a flow network model, which are defined as sets of consecutive clicks from a single whale with inter-click intervals (ICI) between 0.4 and 3 seconds. Finally, the resulting click trains are assigned to individual whales using a linear assignment approach. Our method also mitigate errors in the process of click identification. The algorithm is of low complexity and can be processed in real time. Performance evaluation using real measurements of sperm whale vocalizations, emulation of recorded data and noise, and a controlled sea experiment in which recorded echolocation clicks were played back shows better source separation performance compared to benchmarks. High accuracy in click verification and source attribution is demonstrated for different numbers of whales, even under challenging conditions such as overlapping clicks and low signal-to-noise ratio with multiple noise transients.