*3.4. Model Deviation and Residual Analysis*

In addition to the observation noise, some non-modeled errors (e.g., IFCB) were reflected in the post-test residuals of the observation equations, and the time series of the post-test residuals of corrected IFCB and uncorrected IFCB third-frequency phases for the ASCG stations of the GPS, BDS-3, and Galileo are presented in Figure 7. As expected, the GPS without the corrected IFCB exhibited a significant systematic bias effect in the L5 phase residuals, while the IFCB-corrected L5 eliminated this bias effect. Contrary to the GPS, for the BDS-3 and Galileo, the residuals did not show any influence of IFCB, further demonstrating that the IFCB can be neglected for the BDS-3 and Galileo. Meanwhile, to

further analyze the effect of IFCB on the GPS L5 phase residuals, the root mean square error of the L5 phase residuals of the GPS at 21 stations for 7 days is given in Table 5. The standard deviation of the L5 phase residuals of the GPS before and after the IFCB correction was 1.18 cm and 0.41 cm, respectively, with a 65.12% reduction. Accordingly, it was concluded that after correcting the IFCB, the effect of apparent systematic bias in the L5 residuals of the GPS can be eliminated, and thus, the rejection in the positioning solution process due to excessive residuals can be avoided.

**Figure 7.** Post-check residual time series of GPS, BDS-3, and Galileo (corrected and uncorrected IFCB) third-frequency phase for ASCG stations (DOY 65, 2022).


**Table 5.** Root mean square error of GPS L5 phase residuals for 21 stations in 7 days (RMS, unit: cm).
