DeepION模型在太阳活跃期的SPP导航定位性能验证与研究

王梓童; 付海洋; 蒋卓君; 蔡迪嘉

doi:10.11999/JEIT250662

DeepION模型在太阳活跃期的SPP导航定位性能验证与研究

doi: 10.11999/JEIT250662 cstr: 32379.14.JEIT250662

复旦大学电磁波信息科学教育部重点实验室，上海市，200433

基金项目: 国家重点研发计划(2021YFA0717300)，国家自然科学基金(62231010), 上海科学技术委员会(23JC1400501)

详细信息

作者简介:
王梓童：男，学生，研究方向为[人工智能与电离层反演、卫星导航定位

付海洋：女，研究员、博导，研究方向为智能计算与人工智能、空间电离层波传播与成像、卫星导航高精度定位

蒋卓君：男，学生，研究方向为卫星导航定位、智能计算与人工智能

蔡迪嘉：女，学生，研究方向为人工智能与电离层反演

通讯作者:
付海洋　haiyang_fu@fudan.edu.cn

中图分类号: TN967.1
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出版历程
- 收稿日期: 2025-07-14
- 修回日期: 2026-05-12
- 录用日期: 2026-05-12
- 网络出版日期: 2026-06-01

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

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)

摘要

摘要: 精确的电离层建模对于空间天气监测和全球导航卫星系统(GNSS)定位至关重要，特别是在太阳活动导致地磁暴并引发电离层剧烈扰动的时段。本文提出了一种基于深度算子网络的电离层建模框架——DeepION模型，用于预测电离层关键参数，包括斜向总电子含量(STEC)、垂直总电子含量(VTEC)以及由STEC推导的总电子含量变化率指数(ROTI)。模型以卷积神经网络作为分支网络，从GNSS观测数据中提取射线特征，同时主干网络结合周期时间编码与时空坐标实现电离层参数的连续推理与预测。利用覆盖2024年5月一次典型地磁暴事件的连续28天全球GNSS数据集对模型进行训练与评估后，DeepION模型在STEC预报、高分辨率VTEC重构以及基于ROTI的电离层不规则扰动预测方面表现出了较强的鲁棒性。与传统的 CODE、NeQuick 和 Klobuchar 模型相比，DeepION 在电离层状态重构及 GNSS 单点定位(SPP)中均表现出更高的精度，并在扰动条件下显著降低了均方根误差(RMSE)，其中中纬度区域的定位误差较现有模型降低约 10%–50%。上述结果表明，所提出的 DeepION 模型在地磁暴扰动条件下能够有效提升电离层建模精度，并在单频 GNSS 定位改正中展现出良好的应用前景，为其在实际导航系统中的进一步应用奠定了基础。
- 全球导航卫星系统 /
- 电离层建模 /
- SPP单点定位 /
- 深度算子网络
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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图 1 DeepION模型架构

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图 2 2024年5月地磁暴期间关键空间天气参数与电离层变化

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图 3 273个全球GNSS站点分布图：红色方块为训练站，蓝色三角为验证站，绿色倒三角为测试站

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图 4 STEC预测结果(28天训练，3天预测)

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图 5 2024年5月13日NVSK站点的ROTI预测结果对比图。首行展示STEC观测值与预测值及其残差，中行为对应的ROT变化，下行为ROTI计算结果与预测误差。

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图 6 2024年5月13日00:00、12:00和23:00 UTC三个典型时刻下，不同电离层模型的VTEC对比，及12:00 UTC时刻在DeepION-VTEC上叠加了观测与预测的ROTI值。

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图 7 VTEC建模dSTEC评估

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图 8 VTEC建模SPP约束定位评估

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图 9 SPP约束定位误差统计

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表 1 SPP解算的处理策略

类型	项目	解算策略
基本信息	时间范围	2024年5月10日
	系统	仅使用GPS
	频率与伪距类型	L1 C/A码，对应RINEX格式中的C1C
	采样间隔	30秒
可建模误差	对流层	Saastamoinen模型
	电离层	Klobuchar模型、NeQuick模型、CODE-SH模型及DeepION模型
	随机与加权模型	高程角加权模型(伪距单位权中误差为0.3米)；15°以下加权降低
	地球自转	通过卫星位置进行修正，$ {\omega }_{e}=7.292115\times {10}^{-5}\; \text{rad/s} $
	相对论效应	通过卫星钟差进行修正
PNT参数	卫星位置与卫星钟差	使用IGS广播星历(BRDC)计算
PNT参数	接收机位置与接收机钟差	通过最小二乘平差估计

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表 2 2024年5月10日CUSV与NLIB站点的SPP定位精度统计结果(单位：米)

方向	CUSV站点				NLIB站点
方向	Klobuchar	Nequick	CODE-SH	DeepION	Klobuchar	Nequick	CODE-SH	DeepION
北向	2.3341	1.2796	0.9861	1.1673	3.2986	3.3627	2.0421	2.1161
东向	1.2759	1.0634	0.9313	0.8930	2.5064	2.5250	2.2240	2.2302
垂直向	6.0624	3.8052	3.9117	2.7500	7.0457	6.8331	5.8519	5.5182
水平	2.6590	1.6635	1.3564	1.4695	4.1439	4.2043	3.0208	3.0744
几何	6.6186	4.1522	4.1388	3.1180	8.1763	8.0231	6.5823	6.3167

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表 3 2024年5月11日CUSV与NLIB站点的SPP定位精度统计结果(单位：米)

方向	CUSV站点				NLIB站点
方向	Klobuchar	Nequick	CODE-SH	DeepION	Klobuchar	Nequick	CODE-SH	DeepION
北向	2.9536	4.9078	1.5190	1.6624	1.6813	1.5957	1.3462	1.1432
东向	1.2644	1.6091	1.3067	1.0583	0.8574	0.8211	0.7742	0.7820
垂直向	6.7673	9.1351	6.8998	6.7521	4.9630	2.8212	2.2047	2.0712
水平	3.2130	5.1646	2.0033	1.9709	1.8876	1.7945	1.5518	1.3853
几何	7.4919	10.4935	7.1849	7.0338	5.3096	3.3439	2.6961	2.4935

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