Physics-Guided Neural Network for Correcting Residual Ionospheric Error in GNSS Radio Occultation Bending Angle

Jihyeok Park, Jaehee Chang, Jiyun Lee

Peer Reviewed

Abstract:	Global Navigation Satellite System (GNSS) radio occultation (RO) achieves high accuracy retrievals in the upper troposphere and low stratosphere. However, residual ionospheric errors (RIE), which are remaining errors after the standard ionospheric correction of dual-frequency bending angles, emerge as systematic biases limiting retrieval accuracy toward higher altitudes (above ~35 km). The ray path separation of dual-frequency signals is the main contributor to RIE. Kappa correction, theoretically derived under the assumption of spherical symmetry to correct for such effects, exhibits reduced performance in mitigating RIEs in the presence of ionospheric horizontal gradients. To address this limitation, we propose a physics-guided deep learning framework named PhyGTRF (Physics-Guided Transformer) that refines RIE corrections by integrating the physics baseline (kappa correction) with an altitudinal sequence learning approach using a Transformer-based residual architecture. By treating each occultation event as a vertical sequence, PhyG-TRF captures both altitudinal dependencies and global environmental context—such as solar zenith angle and geomagnetic latitude—through a Multi-Head Self-Attention (MHSA) mechanism. A case-level adaptive weighting scheme based on the empirical CDF of the positive gradient ratio further enforces robustness in ionospheric asymmetry cases. Additionally, a Vector Adaptive Residual Layer (VARL) combines the physics baseline and the learned residual via a learned scaling gate, thereby capturing the complex asymmetry of the ionosphere. Utilizing simulated datasets generated via ray-tracing on a 3D ionospheric model, our framework demonstrates improved performance over the physics baseline and other machine learning models (XGBoost, Bi-GRU). Statistical analysis confirms that PhyG-TRF achieves a 52.1% reduction in RMSE over the physics baseline on the full test set (coefficient of determination (??^2) improving from 0.254 to 0.828). For the positive-trending RIE subset, RMSE is reduced by 70.0% and R² improves from ?2.52 to 0.684. The altitudinal sequence learning strategy further provides superior structural smoothness over point-wise models, as demonstrated by jitter analysis. These results highlight the model’s robust capability to resolve RIE, even in asymmetric ionospheric environments.
Published in:	Proceedings of the ION 2026 Pacific PNT Meeting April 13 - 16, 2026 Hilton Waikiki Beach Honolulu, Hawaii
Pages:	83 - 98
Cite this article:	Park, Jihyeok, Chang, Jaehee, Lee, Jiyun, "Physics-Guided Neural Network for Correcting Residual Ionospheric Error in GNSS Radio Occultation Bending Angle," Proceedings of the ION 2026 Pacific PNT Meeting, Honolulu, Hawaii, April 2026, pp. 83-98. https://doi.org/10.33012/2026.20597
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