## 3 Results and Analysis
### Data Processing and Analysis
#### 3.2.1 The Static RT PPP with Different Data Processing Methods  
Figure 4a shows the positioning errors of static RT PPP with dual-frequency for stations ANRK on DOY 045, 2018. We can see that the result of three data processing methods is very similar when the filter converges to stable values. But there is great difference in convergence time with different processing methods. As seen from the blue curves, the convergence time of GPS/GALILEO RT PPP is about 116 min. After the ionospheric products are introduced for positioning with priori variance, it is clear that the convergence time can be reduced distinctly, especially in the UP direction. Compared with the priori variance method, the weights calculated by using new method are more reliable, and thus, convergence time can be further reduced; it only takes 26 min to achieve vertical accuracy of better than 0.1 m. The number of visible GPS/GALILEO satellites is shown in Figure 4b, together with the PDOP (position dilution of precision). The average number of visible GPS and GALILEO satellites are 9.3 and 5.4, respectively, leading to an average PDOP of 1.7. Figure 4c shows the weight factors of ionospheric constraints for different processing methods. The weight factors solutions vary in a range of 2.0 to 8.0 by using the new method. Since the priori variance for the ionospheric constraints does not correspond to reality, the weight factors of the new method are larger than that of a priori variance when the filter is not convergent; this is the reason why the convergence performance can be improved by using the new method. To test the effectiveness of the new method in static single-frequency RT PPP, an experiment was conducted for station METG on DOY 051, 2018. Figure 4d shows the time series of single-frequency RT PPP positioning errors. The convergence performance of the without-constraints method is the worst of the three methods, especially in the East and Up direction, and its convergence time is up to 106 min. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Setting** \\ \hline Observations & Raw pseudo range and phase observations \\ Frequency & GPS: L1/L2; GALILEO: E1/E5 \\ Estimator & Extended Kalman filter \\ Elevation cutoff & 10\({}^{\circ}\) \\ Sampling offset & 30 s \\ Observations weight & Elevation dependent weighting; 0.01 m and 1 m for GPS/GALILEO \\  & phase and pseudo range observables in zenith direction; \\ Phase window & Phase polarization effects applied [21] \\ Attitude law & Nominal attitude for GPS and GALILEO \\ Station displacement & Solid Earth tides, ocean tide loading and pole tides [22] \\ A priori Troposphere delay & Saastamoinen model and Niell mapping function [23] \\ Zenith wet tropospheric delay & Estimated as random walk (\(1\times 10^{-8}\)m\({}^{2}\)/s) \\ Ionosphere & Estimated as random walk processes (\(1\times 10^{-6}\)m\({}^{2}\)/s); \\ Station coordinate & Estimated as constant/white noise (\(60^{2}\) m\({}^{2}\)) in static/kinematic modes \\ Receiver clock & Estimated as white noise for each GNSS system \\ Satellite antenna PCO and PCV & PCV and PCO values for GPS/GALILEO were corrected with igs14.atx; \\ Receiver antenna PCO and PCV & Corrected by igs14.atx; \\ Phase ambiguities & Float solution [24; 25] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Strategies for RT GPS/GALILEO PPP. When ionospheric products are introduced as a pseudo-observable to constrain ionosphere delay in RT PPP, the convergence time can be reduced greatly. Using the new method, the convergence time is further reduced to 37 min and the positioning solutions are more precise than those of a priori variance. Figure 4f provides the weight factors for different processing methods. Due to the small weight factors calculated by the new method during the process of filter convergence, the contribution of ionospheric constraints is proper, and thus, convergence time can be reduced.