## 4 Results and Discussion
### Different Magnetic Storm Results  
This section analyzes the effects of SF PPP on convergence time and positioning accuracy during magnetic and non-magnetic storm periods, and under different constraints, as well as in static and dynamic modes. It can be concluded from Figures 4 and 5 that the convergence time in the vertical component was shorter than the horizontal component under the same environment and constraints, except for the kinematic positioning in the MS period and the static positioning in the NMS period of the TIC1 in the 95% level. In the MS period, when the tropospheric constraints were increased, the convergence time was reduced, except in the vertical component at the 68% level. The convergence time in the MS period was longer than the NMS period of the TIC1. Table 2 shows that for the TIC2 at the 95% level, the convergence time in the kinematic mode was shortened by 10.6% in the horizontal component and 34.2% in the vertical component in the MS period when compared to the TIC1. In the static mode, the convergence time was improved from 53.5 to 47.5 min (11.2%) in the horizontal component and by 36.2% from 47.0 to 30.0 min in the vertical component. At the 68% level, the convergence time was shortened by 12.3% and 3.5% in the horizontal component of the TIC2 in the kinematic and static modes, respectively, which were comparable to the TIC1 in the MS period. However, the convergence time of TIC2 in the vertical component was 0.5 min longer than TIC1. The convergence time of TIC1 in the NMS period will be further analyzed. When compared to the MS period, the convergence time in the horizontal and vertical components was shortened by 34.9% and 41.8%, respectively, in the kinematic mode and at the 95% level in the NMS period. While in the static mode and at the 95% level, the convergence time was 24.3% and 12.8%, respectively. When compared to the MS period, in the horizontal component and at the 68% level, the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Kp**} & \multicolumn{2}{c}{**Kp in**} & \multirow{2}{*}{**G-Scale**} & \multicolumn{2}{c}{**Auroral**} & \multirow{2}{*}{**Kp} & \multicolumn{2}{c}{**Kp in**} & \multirow{2}{*}{**G-Scale**} & \multirow{2}{*}{**Auroral Activity**} \\  & & & & & & & & \\
0 & 0.00 & G0 & Quiet & 5– & 4.67 & G1 & Minor storm \\
0+ & 0.33 & G0 & Quiet & 5 & 5.00 & G1 & Minor storm \\
1– & 0.67 & G0 & Quiet & 5+ & 5.33 & G1 & Minor storm \\
1 & 1.00 & G0 & Quiet & 6– & 5.67 & G2 & Moderate storm \\
1+ & 1.33 & G0 & Quiet & 6 & 6.00 & G2 & Moderate storm \\
2– & 1.67 & G0 & Quiet & 6+ & 6.33 & G2 & Moderate storm \\
2 & 2.00 & G0 & Quiet & 7– & 6.67 & G3 & Strong storm \\
2+ & 2.33 & G0 & Quiet & 7 & 7.00 & G3 & Strong storm \\
3– & 2.67 & G0 & Unsettled & 7+ & 7.33 & G3 & Strong storm \\
3 & 3.00 & G0 & Unsettled & 8– & 7.67 & G4 & Severe storm \\
3+ & 3.33 & G0 & Unsettled & 8– & 8.00 & G4 & Severe storm \\
4– & 3.67 & G0 & Active & 8+ & 8.33 & G4 & Severe storm \\
4 & 4.00 & G0 & Active & 9– & 8.67 & G5 & Extreme storm \\
4+ & 4.33 & G0 & Active & 9 & 9.00 & G5 & Extreme storm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The values of the Kp-index. TIC1 at the NMS period shortened the convergence time by 29.8% and 19.3% in the kinematic mode and static mode, respectively. However, their convergence time was equal to 0 in the vertical component. Figure 4: The GPS kinematic SF PPP convergence performance in different constraint schemes during the MS and NMS periods. Figure 5: The GPS static SF PPP convergence performance in different constraint schemes during the MS and NMS periods. In order to compare the final positioning accuracy in the case of the MS and NMS periods, the root mean square (RMS) error in the horizontal and vertical components as well as in the static and kinematic mode were estimated. The RMS error was based on the statistics of the last 15 min of the position solution error [17].