Evaluation of DeepION model based on SPP Navigation Positioning During Active Solar Condition

WANG Zitong; FU Haiyang; JIANG Zhuojun; CAI Dijia

doi:10.11999/JEIT250662

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WANG Zitong, FU Haiyang, JIANG Zhuojun, CAI Dijia. Evaluation of DeepION model based on SPP Navigation Positioning During Active Solar Condition[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250662

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WANG Zitong, FU Haiyang, JIANG Zhuojun, CAI Dijia. Evaluation of DeepION model based on SPP Navigation Positioning During Active Solar Condition[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250662

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Evaluation of DeepION model based on SPP Navigation Positioning During Active Solar Condition

doi: 10.11999/JEIT250662 cstr: 32379.14.JEIT250662

Key Laboratory for Information Science of Electromagnetic Waves(MoE), Fudan University, Shanghai, Shanghai

Funds: The National Key Research and Development Program of China (2021YFA0717300), The National Science Foundation (62231010), Science and Technology Commission of Shanghai Municipality (23JC400501)

Received Date: 2025-07-14
Accepted Date: 2026-05-12
Rev Recd Date: 2026-05-12

Available Online: 2026-06-01

Abstract

Abstract

Objective Accurate characterization of ionospheric variability is a critical prerequisite for reliable Global Navigation Satellite System (GNSS) positioning, especially during geomagnetic storms when rapid and highly structured disturbances occur. Existing empirical and physics-based ionospheric models often struggle to represent storm-time ionospheric dynamics and small-scale irregularities in real time. This study aims to develop a unified data-driven ionospheric modeling framework that takes GNSS-derived Slant Total Electron Content (STEC) time series (estimated from GNSS observations) as input and learns the spatiotemporal mappings to key ionospheric parameters, including STEC, Vertical Total Electron Content (VTEC), and the Rate of TEC Index (ROTI). By leveraging deep operator learning, the proposed framework seeks to enhance short-term ionospheric modeling and forecasting capability under disturbed conditions and to provide more reliable ionospheric corrections for single-frequency GNSS positioning. Methods This study proposes a unified data-driven ionospheric modeling framework, named DeepION, based on the Deep Operator Network (DeepONet) architecture. The framework takes STEC time series as the primary input, and learns nonlinear spatiotemporal mappings to key ionospheric parameters. Specifically, DeepION enables modeling and prediction of STEC and VTEC, while ROTI is subsequently derived from the predicted STEC series. In the network design, a convolutional neural network (CNN) is employed as the branch network to extract spatiotemporal features from historical STEC time series. The trunk network consists of a multi-layer fully connected architecture with periodic time encoding, whose inputs include GNSS observation geometry and temporal information, enabling the model to capture the continuous temporal dynamics of ionospheric behavior. During data preprocessing, a VTEC-based modeling strategy is first applied to estimate and remove receiver Differential Code Biases (DCB), thereby obtaining high-quality STEC observations. The model is then trained and validated using the STEC observations during the May 2024 geomagnetic storm. The model outputs include ray-path STEC values, gridded VTEC fields, and derived ROTI time series. Furthermore, the proposed framework is evaluated by incorporating the model-derived VTEC corrections into GNSS Single Point Positioning (SPP) experiments. The modeled and observed ionospheric parameters are compared under both geomagnetically quiet and disturbed conditions to comprehensively assess the modeling accuracy and practical performance of DeepION. Results and Discussions The experimental results demonstrate that the proposed DeepION model can robustly characterize ionospheric spatiotemporal variability under different space weather conditions, capturing both large-scale structures and small-scale disturbances during geomagnetic storms. On STEC forecasting, the model achieves a Root Mean Square Error (RMSE) of 12.8 TECU over a 3-day prediction horizon, maintaining high consistency with observed GNSS measurements (Fig.4). Moreover, the model effectively predicts ionospheric irregularities, as shown by the close match between predicted and observed ROTI time series at mid-latitude stations NVSK (Fig.5). For VTEC modeling, DeepION-generated global VTEC maps accurately reproduce equatorial anomalies and storm-enhanced density regions, closely matching the CODE-SH benchmark while outperforming empirical models such as Klobuchar and NeQuick in both spatial resolution and structural fidelity (Fig.6). Further analysis of ray-path level performance shows that STEC derived from DeepION-based VTEC mapping yields the lowest residual errors at the mid-to-high latitude station NLIB, achieving an RMSE of 6.80 TECU, outperforming Klobuchar, NeQuick, and slightly improving upon CODE-SH (Fig. 7). In GNSS positioning applications, SPP results indicate that DeepION-derived ionospheric corrections consistently reduce positioning errors at both CUSV and NLIB stations, particularly in the vertical and geometric components during storm-time conditions, demonstrating enhanced robustness under intensified geomagnetic disturbances (Fig. 8, Fig. 9). Conclusions This study presents DeepION, a data-driven ionospheric modeling framework based on the Deep Operator Network architecture, which learns spatiotemporal relationships between GNSS-derived STEC observations and key ionospheric parameters. With a CNN-based branch network and a periodically encoded trunk network, DeepION models and predicts STEC and VTEC, and then derives ROTI from the predicted STEC series. Experiments using global GNSS data during the May 2024 geomagnetic storm show that DeepION can capture storm-time ionospheric variability and achieves stable performance in STEC forecasting and global VTEC reconstruction. Compared with conventional empirical and physics-based models, DeepION provides improved modeling accuracy and spatial representation. Furthermore, GNSS Single Point Positioning experiments indicate that ionospheric corrections derived from DeepION lead to reduced positioning errors at both mid- and high-latitude stations, particularly in the vertical and geometric components under disturbed geomagnetic conditions. These results highlight the practical value of DeepION for GNSS ionospheric correction during space weather events. Overall, DeepION offers a scalable framework for data-driven ionospheric modeling, and future work will extend it to multi-GNSS constellations, longer prediction lead time, and additional ionospheric observations.
- Global Navigation Satellite System,
- Ionospheric Modeling,
- Single Point Positioning,
- Deep Operator Network

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References(46)

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