Reconstructing bird trajectories from pressure and wind data using a highly optimized hidden Markov model

Tracking technologies have widely expanded our understanding of bird migration routes, destinations and underlying strategies. However, determining the entire trajectory of small birds equipped with lightweight geolocators remains a challenge. We develop a highly optimized hidden Markov model (HMM) for reconstructing bird trajectories. The observation model is defined by pressure and, optionally, light measurements, while the movement model incorporates wind data to constrain consecutive positions based on realistic airspeeds. To reduce the computational costs associated with a large state space, we prune the HMM states and transitions based on flight and observation constraints to efficiently model the entire trajectory. The approach presented is based on a mathematically exact procedure and is fast to compute. We demonstrate how to compute (1) the most likely trajectory, (2) the marginal probability map of each stationary period, (3) simulated trajectories and (4) the wind conditions (wind support/drift) encountered by the bird during each migratory flight. We construct a version of an HMM optimized for reconstructing a bird's migration trajectory based on lightweight geolocator data. To render this approach easily accessible to researchers, we designed a dedicated R package GeoPressureR (https://raphaelnussbaumer.com/GeoPressureR/).