## 4 Results and Discussion
### Different Latitudes Area Results
#### 4.2.3 High-Latitude Area Results  
In order to verify the results for the high-latitude area, the positioning accuracy and convergence time of SF PPP in static and dynamic modes during MS and NMS periods were analyzed.  
It was concluded in Figure 10 that at the 95% level, TIC1 and TIC2 still did not converge in the kinematic mode in the MS period, but TIC1 converged in the NMS period. Although the number of stations distributed in the high latitude band was less than the low latitude band, TIC1 converged in the NMS period, indicating that the occurrence of magnetic storms had a greater impact on the convergence time of SF PPP. The effect of the magnetic storms on the convergence time was also demonstrated in Figure 11, and the convergence time of TIC1 in the NMS period was shorter than that of TIC2 during the MS period in the static mode. As shown in Table 8, adding tropospheric constraints shortened the convergence time of TIC2 in the MS period by 13.2% and 20.4% in the horizontal and vertical components, respectively, in the kinematic mode and at the 68% level which was comparable to TIC1. Compared to TIC1 the percentage of convergence time in the static mode was shorted to 10.8%, 9.3%, 40.9%, and 18.8% at the 95% level and horizontal component, the 68% level and horizontal component, the 95% level and vertical component, and at the 68% level and vertical component, respectively. Up to 51.6% and 97.7% reduction occurred in the horizontal and vertical components, respectively, in the kinematic mode and at the 68% level, which for TIC1 in the NMS period was comparable to the MS period. The TIC1 in the static mode, which in the NMS period was comparable to the MS period, had a shorter convergence time at the 95% level and horizontal component, the 68% level and horizontal component, the 95% level and vertical component, and at the 68% level and vertical component, which shortened times 40.0%, 32.6%, 30.0%, and 96.9%, respectively.  
It can be seen from Table 9 that during the MS period, the RMS value of TIC2 was smaller than that of TIC1. Under TIC1, the RMS value of the MS period was greater than that of the NMS period. This showed that in the high latitude region, not do only the tropospheric constraints have an influence on the convergence time, but they also affect the positioning accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{4}{c}{**Kinematic SF PPP (m)**} & \multicolumn{4}{c}{**Static SF PPP (m)**} \\ \cline{2-9}  & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** \\ \hline TIC1\_MS & 0.396 & 0.186 & 0.395 & 0.059 & 0.171 & 0.078 & 0.162 & 0.025 \\ TIC2\_MS & 0.386 & 0.184 & 0.387 & 0.079 & 0.164 & 0.077 & 0.129 & 0.038 \\ TIC1\_NMS & 0.354 & 0.172 & 0.371 & 0.064 & 0.156 & 0.072 & 0.151 & 0.025 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The RMS of GPS static and kinematic SF PPP in MS and NMS of TIC1 or TIC2.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{4}{c}{**Kinematic SF PPP (min)**} & \multicolumn{4}{c}{**Static SF PPP (min)**} \\ \cline{2-9}  & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** \\ \hline TIC1\_MS & – & 45.5 & – & 22.0 & 32.5 & 21.5 & 55.0 & 16.0 \\ TIC2\_MS & – & 39.5 & – & 17.5 & 29.0 & 19.5 & 32.5 & 13.0 \\ TIC1\_NMS & 50.0 & 22.0 & 93.5 & 0.5 & 19.5 & 14.5 & 38.5 & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The convergence times of GPS static and kinematic SF PPP in MS and NMS of TIC1 or TIC2.  
Figure 11: The GPS static SF PPP convergence performance in different constraint schemes during the MS and NMS periods.  
Figure 10: The GPS kinematic SF PPP convergence performance in different constraint schemes during the MS and NMS periods.