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Dynamic programming-based range-depth estimation of sperm whale echolocation clicks using a two-element array
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DOI：10.1016/j.apor.2026.105075.png)
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Abstract
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Sperm whales (Physeter macrocephalus) produce powerful broadband echolocation clicks for navigation and foraging, which are detectable over several kilometers in the ocean. Accurate range and depth localization of the whale source using these clicks is important for behavioral studies, to determine population size, and explore effects of, e.g., anthropogenic activities. As a practical, easy to deploy setup, we consider for localization a two hydrophone array vertically deployed from, e.g., a small vessel or buoy. Unlike existing approaches that perform localization per click, our solution exploits the sequential structure of sperm-whale echolocation clicks to formalize the localization solution as a hidden Markov model (HMM) whose states encode the whale’s range and depth. Emission probabilities are derived by the similarity between the expected and measured time-difference-of-arrival between the direct and first reflection paths, while considering uncertainties such as the hydrophones’ depth and the sound speed profile. The HMM is solved using dynamic programming for a batch localization solution. Region-of-interest (ROI) gating reduces the computational complexity towards real-time operation. Performance evaluation by emulations and a controlled sea experiment show that the proposed framework outperforms three reference methods in terms of localization accuracy, robustness to environmental uncertainty and computational efficiency. The implementation code is publicly available.
Keywords:
Passive acoustics
Sperm whale
Localization
Hidden Markov model
Time-difference of arrival
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ShareSaveTrack of a sperm whale from delays between direct and surface-reflected clicks.png)
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