DeepION Model Evaluation for SPP Navigation Performance During Solar-active Periods

WANG Zitong; FU Haiyang; JIANG Zhuojun; CAI Dijia

doi:10.11999/JEIT250662

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WANG Zitong, FU Haiyang, JIANG Zhuojun, CAI Dijia. DeepION Model Evaluation for SPP Navigation Performance During Solar-active Periods[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250662

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WANG Zitong, FU Haiyang, JIANG Zhuojun, CAI Dijia. DeepION Model Evaluation for SPP Navigation Performance During Solar-active Periods[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250662

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DeepION Model Evaluation for SPP Navigation Performance During Solar-active Periods

doi: 10.11999/JEIT250662 cstr: 32379.14.JEIT250662

Key Laboratory for Information Science of Electromagnetic Waves(MoE), Fudan University, Shanghai 200433, China

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

Received Date: 2025-07-14
Accepted Date: 2026-05-12
Rev Recd Date: 2026-04-24

Available Online: 2026-06-01

Abstract

Abstract

Objective Accurate characterization of ionospheric variability is essential 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 have limited ability to represent storm-time ionospheric dynamics and small-scale irregularities in real time. This study develops a unified data-driven ionospheric modeling framework that uses GNSS-derived Slant Total Electron Content (STEC) time series as input and learns spatiotemporal mappings to key ionospheric parameters, including Vertical Total Electron Content (VTEC) and the Rate Of TEC Index (ROTI). By using deep operator learning, the proposed framework improves short-term ionospheric modeling and forecasting under disturbed conditions and provides more reliable ionospheric corrections for single-frequency positioning. Methods A unified data-driven ionospheric modeling framework, named DeepION, is proposed based on the Deep Operator Network (DeepONet) architecture. The framework uses STEC time series as the primary input and learns nonlinear spatiotemporal mappings to key ionospheric parameters. DeepION models and predicts STEC and VTEC, whereas ROTI is derived from the predicted STEC series. In the network design, a Convolutional Neural Network (CNN) is used as the branch network to extract spatiotemporal features from historical STEC time series. The trunk network uses a multilayer fully connected structure with periodic time encoding. Its inputs include GNSS observation geometry and temporal information, which allows the model to capture the continuous temporal dynamics of ionospheric behavior. During data preprocessing, a VTEC-based modeling strategy is first used to estimate and remove receiver Differential Code Bias (DCB), thereby providing high-quality STEC observations. The model is then trained and validated using GNSS observations collected during the May 2024 geomagnetic storm. Its outputs include ray-path STEC values, gridded VTEC fields, and derived ROTI time series. The proposed framework is further evaluated by incorporating model-derived VTEC corrections into Single Point Positioning (SPP) experiments. Modeled and observed ionospheric parameters are compared under both geomagnetically quiet and disturbed conditions to assess the modeling accuracy and practical performance of DeepION. Results and Discussions The experimental results show that DeepION robustly characterizes ionospheric spatiotemporal variability under different space weather conditions. It captures both large-scale structures and small-scale disturbances during geomagnetic storms. For STEC forecasting, the model achieves a Root Mean Square Error (RMSE) of 12.82 TECU over a 3-day prediction horizon and maintains high consistency with GNSS observations (Fig. 4). The model also predicts ionospheric irregularities accurately, as indicated by the close agreement between predicted and observed ROTI time series at the mid-latitude NVSK station (Fig. 5). For VTEC modeling, DeepION-generated global VTEC maps reproduce equatorial anomalies and storm-enhanced density regions. These maps closely match the Center for Orbit Determination in Europe Spherical Harmonic (CODE-SH) model and outperform the Klobuchar and NeQuick empirical models in spatial resolution and structural fidelity (Fig. 6). Further ray-path-level analysis shows that STEC derived from DeepION-based VTEC mapping yields the lowest residual error at the mid-to-high-latitude NLIB station. It achieves an RMSE of 6.80 TECU, outperforming Klobuchar and NeQuick and slightly improving on CODE-SH (Fig. 7). In GNSS positioning applications, the SPP results show that DeepION-derived ionospheric corrections consistently reduce positioning errors at both the CUSV and NLIB stations. The improvement is especially clear in the vertical and geometric components during storm-time conditions, indicating stronger robustness under intensified geomagnetic disturbances (Fig. 8, Fig. 9). Conclusions This study presents DeepION, a data-driven ionospheric modeling framework based on the DeepONet architecture. The framework 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 captures storm-time ionospheric variability and achieves stable performance in STEC forecasting and global VTEC reconstruction. Compared with conventional empirical and physics-based models, DeepION improves modeling accuracy and spatial representation. SPP experiments further show that ionospheric corrections derived from DeepION reduce positioning errors at both mid- and high-latitude stations, especially in the vertical and geometric components under disturbed geomagnetic conditions. These results indicate the practical value of DeepION for GNSS ionospheric correction during space weather events. Overall, DeepION provides a scalable framework for data-driven ionospheric modeling. Future work will extend it to multi-GNSS constellations, longer prediction lead times, and additional ionospheric observations.
- Global Navigation Satellite System(GNSS),
- Ionospheric modeling,
- Single Point Positioning(SPP),
- Deep Operator Network(DeepONet)

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References(46)

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