A Dynamics-Informed Non-Causal Deep Learning Framework for High-Precision SOP Positioning Using Low-Quality Data

Low Earth Orbit (LEO) satellite signals of opportunity (SOP) provide a viable positioning alternative in GNSS (Global Navigation Satellite System)-denied environments, yet their accuracy is fundamentally constrained by the low-quality orbital data typically available, such as SGP4 (Simplified General Perturbations model 4) predictions derived from Two-Line Elements (TLEs). To address this limitation, this paper proposes a dynamics-informed non-causal deep learning framework that enhances low-quality orbital data into high-fidelity trajectories for accurate SOP positioning. The proposed Non-Causal Dynamics-Informed Representation Temporal Convolutional Network (Non-Causal DIR-TCN) integrates phase space reconstruction and a Temporal Convolutional Network to explicitly model the chaotic dynamics inherent in LEO orbits, while relaxing the causality constraints of standard temporal convolutions to utilize both past and future context from the available SGP4 stream. Experimental results demonstrate that the framework significantly reduces orbit estimation errors and accelerates model convergence. When applied to LEO-SOP positioning, it achieves approximately 20% improvement in 2D positioning accuracy compared to conventional SGP4-based methods. This work effectively bridges the gap between accessible low-precision orbital data and high-accuracy state estimation, advancing the practical deployment of opportunistic signals for resilient positioning in challenging environments.