## 3 SF-PPP Performance Analysis of Multi-GNSS Stations
### Positioning Performance Analysis of Geodetic Receivers  
The data from 40 global MGEX stations were processed using the GRAPHIC and uncombined SF-PPP approaches. Their weekly coordinate solutions from the IGS SINEX file were regarded as references to assess positional errors. To investigate the SF-PPP convergence, the RMS values of positioning errors every 5 min were also calculated. Three stations at different latitudes were selected for illustration. As seen in Figure 2, the positioning errors and RMS values of GRAPHIC and uncombined models at the (a) MAL2 (low latitude), (b) JFNG (middle latitude), and (c) KIR0 (high latitude) stations on 26 October 2020 are presented. For each station, the left panels depict the time series of the positioning errors in the east (E), north (N), and up (U) components for the whole day period, respectively, while the right panels illustrate the RMS values every 5 min in each component for the first 4 h. Both the GRAPHIC and uncombined approaches achieved sub-meter positioning accuracy for these three stations. For the east and north components, the positioning precision reached at 0.1 m level, and 0.2 m for the vertical component. The MAL2 showed larger variations than the other two stations in all three components, which should be because the ionosphere activity was higher at low latitudes. The GRAPHIC and uncombined approaches exhibited different positioning convergence speeds. Comparatively, the uncombined model approach showed generally faster convergence than GRAPHIC, and its variations were much more stable. During the first 15 min, positioning errors of GRAPHIC SF-PPP even reached several meters, especially in the up direction, while the uncombined model was less than about 0.5 m and 1 m in the horizontal and vertical directions, respectively. This should be mainly attributed to the code and carrier phase combination in GRAPHIC approach being much noisier than the carrier phase observations in the uncombined approach. To compare the overall convergence performance, the convergence times for all the 40 MGEX stations for the whole week were calculated. The convergence criteria were set as the positioning errors in the E, N, and U directions keeping less than 0.3 m, 0.3 m, and 0.5 m, respectively, for at least 10 min. In Figure 3, the distribution diagram of convergence time is depicted. It can be observed that the uncombined SF-PPP converged faster than GRAPHIC. For the results of the uncombined model, there was 55% for the east solutions, 40% for the north solutions, and 10% for the up solutions, which could converge within 5 min. In contrast, there were few solutions of the GRAPHIC model that could converge within 5 min. \begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Processing Strategies** \\ \hline Navigation constellation & GPS/Galileo/BDS \\ Observations & Raw observations or GRAPHIC combinations \\ Frequency choices & L1/E1/B1I \\ Processing mode & Kinematic \\ Cutoff elevation angle & 10\({}^{\circ}\) \\ Satellite orbit and clock & Fixed to precise products (WUM) [36] \\ Differential clock offset & MGEX DCB products (CAS) \\ PCO/PCV & Corrected by IGS ANTEX files (igs14.atx) \\ Receiver clock offset & Estimated as a random walk process \\ ISB & Estimated as a random walk process \\ Troposphere & Hydrostatic delay calculated by GPT [37] and GMF \\ Ambiguity & Estimated as a random walk process \\ Station displacement & Solid earth tide, ocean tide, pole tide [39] \\ Relativistic time delay & Corrected \\ Phase windup & Corrected \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Strategies for SF-PPP. Figure 2: Positioning errors (left panel) and RMS values of errors every 5 min (right panel) in the first 4 h during the test period of SF-PPP solutions at the (**a**) MAL2, (**b**) JFNG, and (**c**) KIR0 stations.