Deep Neural Networks for GNSS Coordinate Time Series Modeling and Prediction

High-precision GNSS coordinate time series modeling and prediction provide a critical reference for applications such as crustal deformation, structural safety monitoring, and regional or global reference frame maintenance. A Deep neural network framework based on Transformer was applied to 22 GNSS stations, each with 1000 days, in which data is preprocessed using a synchronization sliding window. The overall fitting and prediction trends exhibit a high degree of consistency with the original time series. The average fitting RMSE and MAE are 3.40 mm and 2.64 mm, respectively, while the corresponding average prediction RMSE and MAE are 3.54 mm and 2.77 mm. In comparison to the LSTM model, the proposed method achieved a redu78ction in RMSE and MAE by 20.7% and 19.6%, respectively. Furthermore, when benchmarked against the traditional least squares approach, the improvements were even more pronounced, with RMSE and MAE decreasing by 35.7% and 37.8%, respectively. The approach demonstrates robustness and effectiveness under conditions of discontinuous data. Therefore, it could be used as a convenient alternative to predict GNSS coordinate time series and will be of wide practical value in the fields of reference frame maintenance and deformation early warning.