Continuous-Time Physics-Informed Neural ODEs for Multi-Target Direction of Arrival Tracking

Abstract

Direction-of-arrival (DoA) estimation has benefited substantially from advances in deep learning architectures. Despite the success of deep learning in static DoA estimation, most existing approaches rely on discrete snapshot processing, which complicates multi-target tracking and limits robustness under irregular sampling and signal occlusion. Conventional approaches formulate tracking as a discrete sequence regression task, which can degrade performance during target crossovers and signal occlusions. Neural ordinary differential equations have demonstrated effectiveness in modeling continuous-time dynamics and handling irregularly sampled time series; however, their application to multi-target array processing remains limited. In this paper, we propose the Factorized Physics-Informed Neural ODE (Phy-NODE), an architecture that integrates efficient static deep learning estimators with continuous-time dynamical modeling. The proposed framework factorizes the latent representation into independent state vectors, each governed by a learned differential equation. Training is performed using a tripleloss objective that combines sequence-level permutation-invariant training, motion smoothness regularization, and Bartlett beam-forming power maximization, drawing inspiration from physics-informed learning principles. The proposed method is evaluated on multi-target DoA tracking scenarios, with particular emphasis on robustness under signal occlusion conditions.