Ionospheric TEC forecasting based on Transformer-LSTM ensemble algorithm

The global navigation satellite science (GNSS) total electron content (TEC) is a key parameter for characterizing the electron density distribution in the ionosphere. The temporal and spatial variations of TEC introduce propagation delays in satellite signals, leading to deviations in the measurement of signal propagation time by navigation systems, thus affecting positioning accuracy. Therefore, accurately predicting TEC is crucial for correcting satellite signal propagation delays and improving the positioning accuracy of satellite navigation systems. Addressing the issues of low temporal and spatial resolution and forecasting accuracy in existing TEC prediction models, this study uses TEC data with a 1-hour spatial resolution released by the European Positioning Center, covering global regions. The study constructs a forecasting model that combines Transformer and LSTM, processing TEC data from 2019 to 2023. The temporal variation and spatial distribution of TEC were analyzed, and a Transformer-LSTM prediction model was built and evaluated for its accuracy and applicability in different environments. The final results indicate that the standalone LSTM model shows higher prediction accuracy in high-latitude regions, but the accuracy significantly decreases in low-latitude regions. For five selected coordinate points, the RMSE values for the Transformer-LSTM model were 0.9436, 0.7384, 0.5548, 0.7693, and 0.688, representing improvements of 58.26%, 66.86%, 55.00%, 46.20%, and 58.07%, respectively, compared to the standalone LSTM model. These results effectively enhance the accuracy of TEC prediction. This study aims to improve the TEC forecasting model, enhancing prediction duration, spatial coverage, and accuracy, while reducing the impact of ionospheric delays on navigation positioning.