*3.5. Short-Term Stability of IFCB*

To investigate the short-term stability of IFCB, Figure 8 provides the average STD of IFCB with a one-day delay versus a two-day delay in 2022 for 65 to 71 days. From Figure 8, the average STD of the one-day-delayed and two-day-delayed IFCB was 0.6 and 0.7 cm, respectively. Essentially, the average STD of IFCB of a single satellite did not exceed 1 cm. The statistics for 7-day positioning of 21 stations were recorded using both one-day-delayed and two-day-delayed IFCB, as shown in Table 6. It can be seen that IFCB products with a one-day delay and a two-day delay could both obtain the same positioning performance as that of the same-day IFCB products to a certain extent, thereby validating the short-term stability of IFCB.

**Figure 8.** IFCB-STD statistics; blue is the STD of the difference between one-day delay and same day, and red is the STD of two-day delay and same day (DOY 65–71, 2022).

**Table 6.** Statistics of 7-day positioning accuracy and convergence time for 21 stations (RMS, unit: cm; convergence time, unit: min).


#### **4. Conclusions**

IFCB is crucial for high-precision triple-frequency PPP. In this paper, the time-varying characteristics of IFCB for the GPS, BDS-3, and Galileo were analyzed using 117 MGEX station observations, and it was found that the amplitude of GPS Block IIF satellites could reach 10–20 cm, the amplitude of Block III and BDS-3 satellites of the GPS was around 1–3 cm, and the amplitude of Galileo satellites was below 2 cm.

Then, the positioning performance of triple-frequency PPP before and after the IFCB correction was analyzed using the 7-day data from 21 MGEX stations. After the IFCB correction, the positioning performance of BDS-3 and Galileo systems changed negligibly, whereas for the GPS, the 3D positioning accuracies of triple-frequency PPP in static and kinematic modes were improved to 1.73 cm and 4.75 cm, respectively. Compared with the GPS triple-frequency PPP without any IFCB correction, the 3D accuracy post-IFCBcorrection improved by 27.39% and 17.34% (static mode and dynamic mode), and the convergence time improved by 10.55% and 15.22% (static mode and dynamic mode), respectively. In addition, the L5 phase post-check residuals of the GPS showed obvious systematic errors. However, the influence of bias could be eliminated by L5 after the IFCB correction. That is to say, the implementation of IFCB estimation can effectively solve the systematic bias problem arising from the multi-frequency positioning results, and realize the unification of traditional clock-difference products and multi-frequency precision positioning.

Since IFCB exhibits obvious periodic characteristics, the short-term stability of IFCB was also investigated in this paper, and the same positioning performance as that of the same day was obtained by using the IFCB products with a one-day delay and a twoday delay.

**Author Contributions:** Y.C., J.M. and S.G. conceived the idea and designed the experiments; Y.C., B.L. and Y.P. performed the experiments and analyzed the data; Y.C. wrote the main manuscript; J.M., S.G., L.Y. and H.L. reviewed the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Program of China (2021YFC3000504), the National Key Research and Development Program of China (2021YFB3900802), and the National Natural Science Foundation of China (41930535).

**Data Availability Statement:** The datasets analyzed in this study are managed by the IGS.

**Acknowledgments:** All authors gratefully acknowledge CODE and the IGS for providing the data, orbit, and clock products. The authors gratefully acknowledge the Chinese Academy of Surveying and Mapping, which provided the experimental environment.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

