Deep learning for GNSS zenith tropospheric delay forecasting based on the informer model using 11-year ERA5 reanalysis data

Zenith Tropospheric Delay (ZTD) is one of the main atmospheric errors in the Global Navigation Satellite System (GNSS). In this study, we propose a novel ZTD forecasting model based on the deep-learning method named Informer-based ZTD (IBZTD) forecasting model using the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth generation reanalysis data (ERA5) from 2011 to 2021. With 72-hour historical GNSS-derived ZTDs as prior information, the subsequent 24-hour ZTDs can be forecasted. The IBZTD forecasting model achieves the best regression fit with post GNSS-derived ZTDs compared with GPT3 (Global Pressure and Temperature 3) and HGPT2 (Hourly Global Pressure and Temperature 2) models, especially in winter with a Root Mean Square Error (RMSE) of 1.51 cm and a Mean Absolute Error (MAE) of 1.15 cm. With the post GNSS-derived ZTDs as reference, in terms of the overall 24-hour forecasting accuracy for 9 GNSS stations in 2022, IBZTD forecasting model achieves a MAE of 1.66 cm and a RMSE of 2.21 cm, significantly outperforming the GPT3 model (MAE: 2.60 cm, RMSE: 3.37 cm), HGPT2 model (MAE: 3.23 cm, RMSE: 4.03 cm) and Long Short-Term Memory (LSTM) model (MAE: 2.65 cm, RMSE: 3.65 cm). An average time improvement of 17.8% and comparable forecasting precisions are achieved in the IBZTD forecasting model compared with the Transformer-based ZTD (TBZTD) forecasting model. Using predicted ZTD as prior constraints in Precise Point Positioning (PPP), the vertical convergence speed exhibits a significant improvement of 14.20%, 20.24%, 18.48%, and 19.39% in four seasons.