*3.1. Data Introduction and Processing Strategy*

To ensure the continuity of IFCB series and to avoid the influence of IFCB calculation occasionality, 117 globally distributed MGXE stations for 43–71 days in 2022 were selected for the IFCB estimation, whereas 21 stations for 65–71 days in 2022 were selected for the experimental validation, and the distribution of stations is shown in Figure 1. To analyze the impact of IFCB on the positioning accuracy, two schemes were selected to evaluate the positioning performance of PPP following the IFCB correction, where scheme-1 "PPP" represents triple-frequency PPP positioning without IFCB correction and scheme-2 "PPP + IFCB" represents triple-frequency PPP positioning with IFCB correction. Meanwhile, in order to analyze the short-term stability of IFCB, the PPP accuracy with IFCB correction was analyzed using one-day-delayed and two-day-delayed IFCB products, where the difference in the IFCB of adjacent days was analyzed. In such scenarios, "PPP + IFCB1" means IFCB was delayed by one day and "PPP + IFCB2" means IFCB was delayed by two days. For other data processing strategies, see Table 2. In this work, the PCO and PCV of the GPS Block IIF satellite were corrected with the PCO and PCV of only L2, because the PCO and PCV of the L5 frequency were not available. GPS L1 and L2 were corrected using PCO and PCV information on their respective frequency, and GPS Block III satellite L5 was corrected using PCO and PCV information on L5 frequency. BDS and Galileo satellites were corrected by PCO and PCV at their respective frequencies. In addition, since the frequencies between L2 and L5 are closer, the receiver PCO and PCV of L2 were used to correct the L5. The coordinates in the SINEX file of the IGS were used as the reference coordinates of each station, and the filtering was considered to be converged when the positioning deviations in the three directions of east (E), north (N), and up (U) of the coordinates were less than

10 cm in 30 consecutive epochs. Next, the positioning deviations after the solution filtering were selected for the statistical positioning accuracy.

**Figure 1.** MGEX stations used in the experiment. The blue dots represent the stations used to estimate IFCB, and the red dots represent the stations used for PPP validation.


**Table 2.** Triple-frequency PPP positioning processing strategy.

#### *3.2. Time-Varying Feature Analysis of IFCB*

3.2.1. Intraday Time-Varying Characteristics Analysis of IFCB

Figures 2 and 3 show the IFCB time series and the IFCB amplitude for each satellite, respectively. It can be seen that the single-day amplitude of GPS Block IIF satellites was large among all, and the amplitude size was between 10 and 20 cm, which is evidently a non-negligible error for PPP. Alternatively, the single-day amplitudes of GPS Block III and BDS-3 satellites were in the range of 1 to 3 cm, and those of the Galileo satellites were below 2 cm. Meanwhile, the standard deviation of IFCB for Block III satellites of the BDS-3, Galileo, and GPS was about 1.5 mm for a single epoch, which was almost unaffected by the IFCB. Therefore, it was necessary to focus on the variation in IFCB of only GPS Block IIF satellites, and analyze the corresponding impact of IFCB on multi-frequency positioning in terms of both positioning performance and residuals; see Sections 3.3 and 3.4. Since IFCB is considered as a temperature-dependent inter-frequency hardware bias, the different IFCB characteristics of the GPS, BDS-3, and Galileo may be caused by the different designs and payloads of the satellites. However, the IFCBs for GPS Block III and Block IIF satellites

express different characteristics and require more information from inside and outside the GPS satellites, for their comprehensive analysis and determination.

**Figure 2.** IFCB time series plot for GPS, BDS-3, and Galileo, where each color represents a satellite (DOY 65, 2022).

**Figure 3.** IFCB amplitudes of GPS, BDS-3, and Galileo satellites (DOY 65, 2022).

3.2.2. Inter-Day Variation Characteristics of IFCB

Figure 4 shows the IFCB time series plot for DOY 43 to 71 in 2022. The IFCB of the GPS Block IIF satellite varied between −15 cm and 15 cm, and exhibited a clear repetitive feature. Meanwhile, the IFCB of Galileo satellites still exhibited relatively small magnitudes, and the large errors in the IFCB of the BDS-3 in some periods were caused by the small number of observable BDS-3 B2a frequency stations present, which indicates that although the IFCB can maintain a good stability and periodicity in most cases, there still exist serious errors in some periods that need further improvement. Montenbruck and Li et al. [13,25,26] found that the IFCB of the GPS Block IIF satellite had 12 and 6 h periods, where the 12 h period is

due to the satellite receiving the same amount of sunlight and the 6 h period is due to the satellite having the same amount of heat at two orbital positions around 6 h. Since IFCB has a 6 h and 12 h periodicity expression, it can be further expressed that the IFCB exhibits a 24 h periodicity, and Figure 4 also shows a characteristic single-day periodicity of IFCB. The single-day periodicity of IFCB further assisted in the analysis of the short-term stability of IFCB provided in Section 3.5.

**Figure 4.** IFCB time series plot consisting of G01, G24, G30, C21, and E01 (DOY 43–71, 2022).
