# A Short-Term Forecasting Method of Inter-Frequency Clock Bias for GPS Block IIF Satellites
## 4 Discussion  
In order to compare the positioning impact of the actual measurement of IFCB, forecasted IFCB and no IFCB correction on three-frequency uncombined PPP, datasets from 38 globally distributed MGEX stations were used to implement the post-processing multi-frequency PPP performance evaluation. Because the DOY 119 was the first day that could be used for verifying the prediction performance after a lag of 7 days, GPS observations on this day were used for triple-frequency PPP performance evaluation. Figure 8 shows the distribution of these test stations. All these stations could receive GPS three-frequency data, and the sampling interval of the observed data was 30 s. The precision orbital and clock were provided by the final products released by Wuhan University ([[ftp://igs.gsnswhu.cn](ftp://igs.gsnswhu.cn)]([ftp://igs.gsnswhu.cn](ftp://igs.gsnswhu.cn)), Wuhan, China, 18 April 2020). The precise coordinates of the stations are available in the file \"igs20 Pwwwwwd.snx\" released by IGS. During data processing, three strategies were used to implement the three-frequency uncombined kinematic PPP and static PPP models: (1) without IFCB correction (without IFCB); (2) the predicted IFCB with a time lag of 7 days (with pred-IFCB); (3) the actual measurement of the IFCB (with real-IFCB). Figure 7: Prediction residual of the IFCB for GPS Block IIF satellites. The blue and red lines indicate unconsidered periodic variation and considered periodic variation, respectively. The DJIG and YEL2 stations were taken as examples to show the uncombined PPP posterior residual at the third frequency as shown in Figure 9. Different colors represent different satellites. If the functional model was accurately established and the various modeling errors were precisely corrected, the posterior residuals of the three-frequency PPP should conform to the traditional stochastic noise distribution [32]. Figure 9 shows that in addition to the observed noise, the unmodeled systematic bias caused by IFCB was fused to the posterior residuals. When the IFCB correction was applied to three-frequency PPP, the posterior residuals improved significantly, and the average RMS of all Block IIF satellites for all stations was reduced from 0.43 to 0.21 cm, approximately 53.8%, which indicates that the systematic bias caused by IFCB was greatly diminished. In the same way, when the predicted IFCB with the time lag of 7 days was applied to the three-frequency PPP solution, the posterior residual was also significantly improved, and the percentage decrease was approximately 51.3%. The RMS statics show that the forecasted IFCB was basically the same as the actual measurement of the IFCB, and it could also meet the high-precision three-frequency uncombined PPP requirements. Based on above three schemes, triple-frequency uncombined static PPP and kinematic PPP post-processing were performed. Table 3 and Figure 10 show the mean coordinate errors and convergence time series of the GPS static PPP model, respectively, where the mean coordinate errors were obtained by averaging the coordinate errors time series of the last two hours of all stations in the 24 h solution, while the convergence time series were obtained by calculating the quadratic mean epoch by epoch. The analysis shows that the  
Figure 8: Distribution of the test stations. Figure 9: Phase observation residuals for triple-frequency uncombined PPP at the DJIG (left panel) and YEL2 (right panel) stations. positioning accuracy of 24 h PPP solutions under the three schemes was better than 2 cm in the horizontal direction and better than 3 cm in the vertical direction. Compared with no IFCB correction, PPP solutions using forecasted IFCB and measured IFCB increased by 33.2%, 14.3% and 17.2% and 35.1%, 14.9% and 18.7% in the east, north and vertical directions, respectively. In Table 3, although the positioning accuracy improved at the millimeter to centimeter scale, it is of great significance to the crustal movement monitoring required by high-precision positioning [33; 34; 35].