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<p>The non-stationarity of ionospheric total electron content (TEC) is a significant factor influencing the accuracy of ionospheric forecasting systems. Regarding TEC’s non-stationarity, this study proposes a non-stationary inverted transformer (NS-iTransformer) fusion model. The model decomposes TEC features into trend, seasonal, and residual components using seasonal and trend decomposition using loess (STL), applying a de-stationary attention mechanism to the non-stationary components and a multi-head attention mechanism to the stationary ones. TEC data from the Center for Orbit Determination in Europe (CODE), solar and geomagnetic data from NASA are used for experiment. Data from June 1, 1998 to December 31, 2020 are divided into training (June 1, 1998–May 31, 2017), validation (June 1, 2017–December 31, 2017), and test (January 1, 2018–December 31, 2020) sets. This study first conducts a test with optimal feature vectors derived from different solar and geomagnetic activity data, indicating that the AE index negatively impacts TEC prediction. It then empirically tests the respective performance of the IRI-2020, COPG-1 Day, Transformer, non-stationary transformer (NS-Transformer), inverted transformer (iTransformer) and the proposed NS-iTransformer model. Against the test set, our proposed model outperforms the other three models by 34.54–76.05%. All six models obtained predictions are substituted into three stations (URUM, WUH2 and HKSL) for single point positioning (SPP) correction experiments using the optimal dataset. The proposed prediction model has a better positioning improvement performance over other models, with its correction performance being closest to the posterior TEC truth correction results. This study significantly informs future ionospheric modeling, forecasting, and space weather applications.</p>

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Ionospheric TEC prediction using the non-stationary inverted transformer fusion model and its performance in Chinese region

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Ang Li,
  • Xuefen Zhu,
  • Mengying Lin,
  • Gangyi Tu,
  • Zhe Yan

摘要

The non-stationarity of ionospheric total electron content (TEC) is a significant factor influencing the accuracy of ionospheric forecasting systems. Regarding TEC’s non-stationarity, this study proposes a non-stationary inverted transformer (NS-iTransformer) fusion model. The model decomposes TEC features into trend, seasonal, and residual components using seasonal and trend decomposition using loess (STL), applying a de-stationary attention mechanism to the non-stationary components and a multi-head attention mechanism to the stationary ones. TEC data from the Center for Orbit Determination in Europe (CODE), solar and geomagnetic data from NASA are used for experiment. Data from June 1, 1998 to December 31, 2020 are divided into training (June 1, 1998–May 31, 2017), validation (June 1, 2017–December 31, 2017), and test (January 1, 2018–December 31, 2020) sets. This study first conducts a test with optimal feature vectors derived from different solar and geomagnetic activity data, indicating that the AE index negatively impacts TEC prediction. It then empirically tests the respective performance of the IRI-2020, COPG-1 Day, Transformer, non-stationary transformer (NS-Transformer), inverted transformer (iTransformer) and the proposed NS-iTransformer model. Against the test set, our proposed model outperforms the other three models by 34.54–76.05%. All six models obtained predictions are substituted into three stations (URUM, WUH2 and HKSL) for single point positioning (SPP) correction experiments using the optimal dataset. The proposed prediction model has a better positioning improvement performance over other models, with its correction performance being closest to the posterior TEC truth correction results. This study significantly informs future ionospheric modeling, forecasting, and space weather applications.