Regional Tropospheric Delay Prediction Model Based on LSTM-Enhanced Encoder Network

Precise modeling of zenith tropospheric delay (ZTD) is essential for real-time high-precision positioning in global navigation satellite systems. Due to the stochastic variability of atmospheric water vapor across different regions, tropospheric delay exhibits strong regional characteristics. Empirical tropospheric delay models built on the reanalysis of meteorological data often show significant accuracy discrepancies across regions, failing to meet the needs for precise regional ZTD forecasting. Deep learning methods excel in learning complex patterns and dependencies from time-series data. Our study utilized ZTD data from 178 Nevada Geodetic Laboratory stations in Australia during 2023 as ground truth values and modeled them using a long short-term memory (LSTM)-enhanced encoder network. This model incorporated both spatial and temporal information as well as correlations with GPT3 ZTD. Predictions were compared with those from GPT3 ZTD, ERA5 ZTD, artificial neural network (ANN) ZTD, general regression neural network (GRNN) ZTD, and LSTM ZTD. The results showed that the LSTM-enhanced encoder ZTD achieved a root-mean-square error (RMSE) of 14.43 mm and a mean bias close to zero, with mean absolute error and mean correlation coefficient of 12.42 mm and 0.95, respectively. The proposed model outperforms the GPT3, ERA5, ANN, GRNN, and LSTM models, with respective RMSE improvements of approximately 62.3%, 12.3%, 61%, 59.9%, and 60% . In addition, we compared the spatial and temporal properties of the proposed model with those of the GPT3 and ERA5 models. The discussion section further analyzed the prediction performance of different neural network approaches under different prediction periods.