# Comparison Analysis on the Accuracy of Galileo PPP Using Different Frequency Combinations in Europe
## 2 Methods
### Accuracy of Multi-Frequency Galileo Kinematic PPP  
Long convergence time is the key factor affecting the application of PPP, therefore, the contribution of multi-GNSS and multi-frequency observations to PPP convergence and accuracy improvement were assessed in the kinematic mode. Instead of calculating the convergence time using the criterion when a horizontal positioning accuracy achieves 10 cm, a positioning convergence ratio (PCR) was used to describe the accuracy improvement in different session lengths. The PCR from the starting epoch \(t_{0}\) to epoch \(t_{0}+\Delta t\) is defined as:  
\[PCR(t_{0})=\frac{nConv(t_{0},t_{0}+\Delta t)}{nTotal(t_{0},t_{0}+\Delta t)} \tag{4}\]  
where \(nConv\) represents the number of epochs that a horizontal positioning accuracy is less than 10 cm, and \(nTotal\) represents the total number of epochs in the session. The PPP was processed in a 1-h session, and the PCR was calculated every 5 min, i.e., \(\Delta t=5\) min. Using the observations from ten successive days with 30 s interval, \(nTotal\) for PCR calculations were generally 2400.  
Figure 9 presents the PCR at different sessions when using single- and multi-GNSS observations. The \(x\)-axis indicates different sessions, where \"S05\" represents a statistical period from minute 0 to minute 5, and \"S10\" represents the statistical period from the minute 5 to the minute 10, and so on. It was observed that the GPS, Galileo, and BDS single constellation PPP could not achieve 100% PPP convergence accuracy, even after a 30 min convergence period, of which BDS showed poor convergence performance, followed by the GPS and Galileo constellation. Figure 10 shows the series of the positioning errors at the north, east, and up direction for GPS and Galileo kinematic PPP on station OVE6. The Galileo-only PPP showed minor errors at the convergence period. When comparing the multi-constellation combinations, the GPS + BDS performed better than that of GPS + GLONASS constellations, whereas the GPS + Galileo constellations showed the best performance. Besides, it was observed that the multi-GNSS combinations could not outperform the GPS + Galileo dual-frequency combinations, which was due to the fact that the observations at the IGS stations showed good geometry and quality. Overall, 100% convergence could be achieved after 30 min when the Galileo constellations were used.  
Figure 9: PCR for different GNSS combinations using the ionosphere-free combinations.  
Figure 11 shows the site-specific PCR at session \"S10\" and \"S20\" for GPS + GAL dual-frequency combinations. The data for different receiver types are separated by the red vertical line. It is observed that the stations equipped with the \"JAVAD TRE_3 DELTA\" receivers showed better performance than that of the \"TRIMBLE NETR9\" receiver; the PCR can be improved by 30% and 14% for \"S10\" and \"S20,\" respectively. Overall, an average of 80% PCR can be achieved after 20 min and 97% can be achieved after 30 min.  
Figure 12 presents the accuracy comparison for different Galileo frequency combinations. Overall, multi-frequency combinations cannot bring improvements to the convergence of kinematic PPP. So, more efforts should focus on using multi-frequency observations to achieve fast ambiguity resolution. Specially, the convergence performance for the E1/E7 combinations were worse than the other models, which is similar to the results of static PPP in Figure 5.  
Figure 10: The positioning error series from GPS and GAL dual-frequency PPP on station OVE6.