## 3 Experimental Data Set and Analysis
### Single-Frequency PPP with the Constraints  
In this section, we analyse the effects of single-frequency GPS on unconstrained, troposphere-constrained, ionosphere-constrained, and their dual constrains on convergence time. Table 5 summarizes the four constraint schemes. Figures 8 and 9 show the percentage statistics of the effects of different constraint methods on the convergence time of GPS. It can be concluded from these two figures that in the horizontal component, the convergence time of the TIC3 has the largest percentage in the same range, and the TIC1 has less influence on the convergence time. In the vertical component, the percentage of convergence time of the TIC3 in the same range is still the largest, but the influence of TIC1 on the convergence time is higher than the percentage of TIC2 in a certain range. On the whole, the convergence performance of TIC0 is worse in both components when not using GIM products or tropospheric products as constraints. The convergence performance is improved as compared to TIC0 after considering TIC1 or (and) TIC2 in GPS SF PPP processing. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Interpolation Method** & **Static (sec)** & **Kinematic (sec)** \\ \hline NENE & 6.905 & 6.821 \\ BILI & 6.550 & 6.512 \\ BICU & 6.775 & 6.797 \\ JUNK & 6.429 & 6.474 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation time of FLRS station in SF PPP in different interpolation schemes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{4}{c}{**Static SF PPP (min)**} & \multicolumn{4}{c}{**Kinematic SF PPP (min)**} \\ \cline{2-9}  & **H(95\%)** & **H(68\%)** & **V(95\%)** & **V(68\%)** & **H(95\%)** & **H(68\%)** & **V(95\%)** & **V(68\%)** \\ \hline NENE & 3.21 & 15.10 & 17.20 & 40.60 & 18.45 & 77.34 & 78.46 & 134.10 \\ BILI & 3.14 & 14.40 & 15.18 & 32.81 & 16.10 & 73.00 & 68.95 & 131.50 \\ JUNK & 3.87 & 17.55 & 19.44 & 42.92 & 19.00 & 78.30 & 79.44 & 134.60 \\ BICU & 3.42 & 15.70 & 17.68 & 41.30 & 19.30 & 78.30 & 79.01 & 134.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average convergence time of GPS static and kinematic SF PPP in different interpolation schemes. \begin{table}
\begin{tabular}{c c} \hline \hline
**Abbreviation** & **Item** \\ \hline TIC0 & Standard single-frequency PPP model \\ TIC1 & Toposphere-constrained single-frequency PPP model \\ TIC2 & Ionosphere-constrained single-frequency PPP model \\ TIC3 & Toposphere- and ionosphere-constrained single-frequency PPP model \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The four constraint schemes. Figure 8: The percentage of GPS static SF PPP convergence performance in different constrain schemes (horizontal component (left panel) and vertical component (right panel)). Figure 9: The percentage of GPS kinematic SF PPP convergence performance in different constrain schemes (horizontal component (left panel) and vertical component (right panel)). At the same time, Table 6 shows that TIC1 performs a notably better than TIC0 in the vertical component and marginally better than TIC0 in the horizontal component. TIC2 performs notably better than TIC0 and TIC1 in the horizontal component, while, in the vertical component, TIC2 is better than TIC0 and worse than TIC1 only in 68% level static mode. TIC3 performs best among the handling schemes. Compared with TIC0, the average convergence time of TIC1 at the 95% level is improved from 27.17 to 26.07 min (4.0%) in horizontal and by from 23.21 to 18.17 min (21.7%) in the vertical components. At the 68% level, the convergence time in the horizontal component reduced by 4.3% from 42.11 to 40.29 min and by 28.8% from 39.34 to 27.98 min in the vertical component. However, in kinematic mode, the average convergence time of TIC1 is not much higher than that of TIC0, with a maximum increase of 11.7% and a minimum increase of 2.1%. TIC2 has a larger boost when compared with TIC0.