Long-Term GNSS Satellite Clock Error Forecasting Using Inter-Satellite Comparison Data and RBF Neural Networks

Accurate long-term prediction of GNSS satellite clock errors is essential for autonomous navigation, real-time precise point positioning (PPP), and continuous positioning, navigation, and timing (PNT) services when real-time clock products are unavailable or delayed. However, conventional methods, such as quadratic polynomial fitting and Kalman filtering, have limited capability in modeling nonlinear and non-stationary clock behaviors over long prediction intervals, especially under abnormal onboard atomic clock conditions. To address this issue, an inter-satellite comparison data (ISCD)-based radial basis function neural network (RBFNN) model is proposed for long-term satellite clock error prediction. Through correlation analysis, reference satellite clocks closely related to the target satellite are selected, and both ISCD and satellite-ground comparison data are integrated to establish a nonlinear prediction model. Experiments using GPS and Galileo satellite clock datasets demonstrate that the proposed method significantly improves long-term prediction accuracy. For 180-day prediction, the proposed model reduces the RMSE by more than 60% for GPS satellites and approximately 99% for Galileo satellites with abnormal clock behavior compared with conventional methods. Rolling prediction experiments further verify the robustness and stability of the proposed model.