## 4 Results and Validation
### Assessment of Homogeneous Receivers  
We first check the quality of the WL and NL UPD products, which are critical for PPP ambiguity resolution. This can be done by examining the a posteriori residuals of the float WL and NL ambiguities. Figure 3 shows a statistical histogram of these residuals. The figure shows that for the WL ambiguity, 95.8% of residuals are within 0.15 cycles of the nearest integer for the GPS, whereas only 83.7% are within 0.15 cycles for GLONASS. However, 94.2% of GLONASS WL residuals are within 0.25 cycles, which satisfies the WL ambiguity resolution. For the NL ambiguity, more than 95% of residuals are within 0.1 cycles for GPS and GLONASS, and more than 98% are within 0.15 cycles for both. The proposed WL IFCB calibration method only relies on the NL UPD, which has the same high quality as that of the GPS, so the lower quality of GLONASS WL UPD will not affect the proposed IFCB calibration method. The quality of the IFCB estimates can be checked by examining residuals of the WL and NL ambiguities in the estimation. Figure 4 shows a statistical histogram of these residuals. For some satellites, there is only one ambiguity and the WL residual is thus zero; we deleted the WL residuals for these satellites. The figure shows that for the NL ambiguity, 77.3% of residuals are within 0.1 cycles and 97.0% are within 0.2 cycles, which means that 97.0% of all GLONASS ambiguities were used for WL IFCB estimation. For the WL ambiguity, 96.2% and 99.9% of residuals are within 0.1 and 0.2 cycles, respectively. The WL residuals are smaller than the NL residuals because of the much longer WL wavelengths (-0.84 m). These statistics confirm that the IFCB estimates are of good quality. To assess the stability of IFCB estimates, we selected four representative stations distributed evenly across the network. Figure 5 portrays time series of their WL IFCB estimates because they are critical for WL ambiguity fixing. It is seen that estimates of the WL IFCB are relatively stable, and values for different days agree with each other to better than 0.05 cycles (root-mean-square or RMS value). The IFCB can, therefore, be calibrated at update intervals of several days or even longer. Thus, in the following analysis, the IFCB estimates on the first day were used for PPP-IAR. Figure 4: Distribution of a posteriori residuals of the WL and NL float ambiguities when performing GLONASS WL inter-frequency code bias (IFCB) calibration. Receivers with homogeneous type are used as rover sites. Figure 3: Distribution of a posteriori residuals of the wide-lane (WL) (**a**,**b**) and narrow-lane (NL) (**c**,**d**) float ambiguities for Global Positioning System (GPS) and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) ((**a**,**c**) to (**b**,**d**)) in uncalibrated phase delay (UPD) estimation with reference stations. To further validate the quality of the IFCB corrections, we processed GPS + GLONASS daily static PPP-IAR for each rover station. We attempted to fix ambiguities with a tracking arc longer than 30 min by rounding with the criterion of 0.2 cycles. Figure 6 shows the average daily fixing percentage for each station. For all stations, the fixing percentage is over 97.1% and 95.3% for the GPS and GLONASS, respectively, with averages 99.4% and 98.9%. Upon applying the IFCB corrections, the average fixing percentage for GLONASS improves to 99.3%. For GLONASS, 32 stations show improvement. Among the degraded stations, two stations have degradations of 3.9% and 1.0%, whereas the others have degradation within 0.4%. To comprehensively analyze the efficiency of the IFCB calibration method, we performed kinematic PPP-IAR for all hourly observations of the 40 rover stations using three models, i.e., GPS-only PPP, combined GPS + GLONASS PPP without IFCB calibration, and combined GPS + GLONASS PPP with IFCB calibration. Figure 5: Stability of daily WL IFCB estimates of all 24 GLONASS satellites for four representative stations. Different color represents different satellites.