Modeling and prediction of GPS inter-frequency clock bias for triple-frequency real-time precise point positioning

Abstract Precise GPS orbit and clock products released by the International GNSS Service (IGS) are referenced to the L1/L2 ionosphere-free combination, whereas using L5 observations in triple-frequency precise point positioning (PPP) introduces inter-frequency clock bias (IFCB). In this study, GPS L5 phase-specific IFCB values are estimated using observations from 110 globally distributed IGS stations during DOY 001–067, 2023, and their temporal characteristics, predictability, and impact on real-time PPP (RT-PPP) are investigated. The results show that GPS Block IIF satellites exhibit stronger IFCB variations and more evident periodic components than Block III satellites, indicating a greater need for IFCB correction. Four models, namely the harmonic function (HF), random forest (RF), support vector machine (SVM), and long short-term memory (LSTM) models, are developed for IFCB modeling and prediction. The three machine learning models outperform the HF model, with the RF model achieving the best prediction performance, yielding test coefficient of determination ( R 2 ), root mean square error (RMSE), and mean absolute error (MAE) values of 0.817, 2.642 mm, and 2.113 mm, respectively. Furthermore, the RT-PPP experiments show that IFCB correction mainly benefits the convergence stage, while its effect on final positioning accuracy is relatively limited. Moreover, RT-PPP using RF-predicted IFCB products achieves positioning accuracy and convergence performance comparable to those obtained with estimated IFCB products, demonstrating the suitability of the predicted products as external corrections for triple-frequency RT-PPP.