A novel uncertainty-aware 3D tracking solver based on physics-informed neural networks

Accurate 3D fish localization supports understanding of movement, behavior, and habitat use. Traditional solvers such as Approximate Maximum Likelihood (AML) are vulnerable to multipath, time of arrival (TOA) measurement errors, and synchronization errors, while Yet Another Positioning Solver (YAPS) can degrade with sparse detections. We introduce a physics-informed neural network (PINN) solver that models trajectories as continuous, physics-constrained functions, minimizes the negative log-likelihood of TOA noise, and quantifies uncertainty via ensemble training. We validated the approach using synthetic experiments and field deployments in the Salish Sea and a dam tailrace. Under synthetic scenarios with abrupt turns, accelerations, and gaps, the solver achieved sub-meter root mean square (RMS) errors of 0.30–0.80 m and >83% efficiency. In the Salish Sea, RMS error was 1.17–2.24 m with 23–76% efficiency, reducing RMS by ~60% versus AML, and reducing RMS by >75% versus YAPS. In the tailrace, RMS error was 0.81–0.93 m with >92% efficiency, reducing RMS by ~35% versus AML and by >80% versus YAPS. The proposed PINN solver delivers accurate localization across challenging conditions, enabling fine-scale ecological monitoring.