# A Short-Term Forecasting Method of Inter-Frequency Clock Bias for GPS Block IIF Satellites
## 5 Conclusions  
Given that modernized GPS as well as the newly emerging navigation satellite systems provides triple-, quad-, and multi-frequency signals, but the IGS analysis centers traditionally use dual-frequency, such as GPS L1/L2, ionosphere-free combination model for precise satellite clock estimation, results in the obtained clock products containing time-varying parts of ionospheric-free combination uncalibrated phase delay of the satellites. Thus, the clock product cannot be directly applied to the third-frequency observation value (L5) for multi-frequency PPP. If the IFCB and receiver coordinates, tropospheric wet delay, ambiguity and other parameters are estimated together, it will increase the computational burden and lead to more time consumption, which is especially not conducive to real-time PPP and PPP network solutions.  
To resolve this problem, a month's observation data from 162 global uniformly distributed MGEX stations were selected to estimate the IFCB of nine GPS Block IIF satellites. Based on the analysis of the IFCB time-varying characteristics and the lag characteristics of the final ephemeris products, a modeling method of short-term IFCB prediction based on the epoch-by-epoch sliding Pearson autocorrelation function was proposed. The feasibility of the new method was verified by the Student's \(t\)-distribution, the comparison with the measured IFCB, posteriori residuals of the third-frequency carrier phase and the kinematic/static PPP solutions, respectively. A large number of experiments showed that the forecasted IFCB with a lag of 7 days had good consistency with the measured IFCB, which basically improved the positioning accuracy and convergence time of the three-frequency uncombined PPP with the same effect. Compared to no IFCB correction, the posterior residual at third frequency was significantly improved when the predicted IFCB correction was used, and the RMS value decreased by approximately 51.3%. The static and kinematic  
Figure 11: Kinematic PPP positioning errors for three different directions at HARB.  
solutions for triple-frequency uncombined PPP in 24 h can be improved by 33.2% and 17.2% and 50.2% and 39.7% in the horizontal and vertical directions, respectively, and the performance of convergence time also improved.  
All authors made significant contributions to this study. Conceptualization, C.Y. and Y.D.; methodology, S.X.; software, C.Y. and C.X.; validation, C.Y., H.W. and S.G.; formal analysis, C.Y.; resources, S.G.; writing--original draft preparation, C.Y.; writing--review and editing, C.X.; funding acquisition, C.Y. and Y.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Nature Science Foundation of China (grant number: 41974010) and the Beijing Key Laboratory of Urban Spatial Information Engineering (grant number: 20220120).  
The GPS precise ephemerides product provided by Wuhan University is available at [[ftp://igs.gnsswhu.cn](ftp://igs.gnsswhu.cn)]([ftp://igs.gnsswhu.cn](ftp://igs.gnsswhu.cn)). The MGEX observation for estimating the IFCB and evaluating the forecasting method is available at [[ftp://igs.ign.fr//pub/igs/data/](ftp://igs.ign.fr//pub/igs/data/)]([ftp://igs.ign.fr//pub/igs/data/](ftp://igs.ign.fr//pub/igs/data/)). The corrections of satellite and receiver PCO/PCV and the precise coordinates of the MGEX stations are available in file \"igs14.atx\" and \"igs20 Pwwwwd.snx\" released by IGS, respectively. All the data and products are publicly available through the respective organizations' website.  
The contribution of data from IGS is appreciated. We also would like to express our great appreciation to [PERSON] for kindly providing the IFCB software and related technical support.  
The authors declare no conflict of interest.