Bayesian Sound Source Localisation of Aerial-Hawking Bats Using an Array of Synchronised Passive Acoustic Monitors

Monitoring animals from their vocalisations has proven indispensable for ecological research, with applications ranging from unbiased population estimation for biodiversity assessment to kinematic and acoustic quantification for research into evolutionary adaptation. Near-field sound source localisation techniques infer the location of vocalising animals by estimating the signal propagation delay across a spatially distributed array of passive acoustic monitors using either the times of arrival (ToA) or time differences of arrival (TDoA). As with all real-world measurements, ToA and TDoA estimates are subject to noise and uncertainty, particularly for ultrasonic sounds. With the development of low-cost synchronised passive acoustic monitors, many of the historical logistical barriers to deploying receiver arrays for sound source localisation have been ameliorated. Yet, the problems of uncertainty quantification, robustness, and open availability of analysis software remain core challenges to the greater adoption of sound source localisation in ecological research. In this paper, we address these existing limitations by considering a Bayesian approach to sound source localisation and trajectory estimation of the aerial-hawking common pipistrelle bat (Pipistrellus pipistrellus). We estimate the posterior distribution of ultrasonic echolocation call source locations via a general-purpose Markov chain Monte Carlo (MCMC) sampler, extending this model to infer continuous flight trajectories using a smooth Gaussian process prior. The resulting tool effectively captures measurement uncertainty, producing a principled probabilistic estimate of sound source localisation. We validate the model through simulation-based calibration checking and demonstrate the efficacy of this approach for field deployment using an array of five GPS-synchronised AudioMoth receivers to track free flying bats, achieving a median predicted precision of 25cm. Our approach has the potential to improve bat population estimates from passive acoustic data.