## 3 Experimental Data Set and Analysis
### The Effect of Interpolation Method on Ionosphere-constrained GPS Single-frequency PPP  
For the convenience of description, Table 2 shows the abbreviations, according to the four interpolation methods that were introduced above. For GIM grid products, this study discuss the \begin{table}
\begin{tabular}{c c} \hline
**Item.** & **Models/Strategies** \\ \hline Constellation & GPS \\ Data span & 1–30 Sep 2017 \\ Observations & GPS raw code and phase observations \\ Frequency selection & L1 \\ Sampling rate & 30 s \\ Satellite cut-off elevation & 7\({}^{\circ}\) \\ Positioning mode & Static/kinematic (simulated kinematic) \\ Estimator & Kalman filter \\ Satellite orbit and clock & Final by IGS orbit and clock products \\ Weighing strategy & A priori precision of 0.003 and 0.3 m for raw phase and code [35] \\ Satellite DCB & Correct using CODE Differential Code Bias (DCB) products \\ Ionospheric delay & Klobuchar model [39] (priori) or GIM products from IGS (constrains) \\ Ionospheric noise & Random walk [10] \\ Tropospheric delay & Saastamoinen model [40] (priori) or products from IGS (constrains) \\ Tide displacement & Solid Earth, pole and ocean tide were corrected [41] \\ Sagnac effect & Corrected model [42] \\ Relativistic effect & Corrected model [43] \\ Satellite and receiver antenna & Phase Center Offset (PCO) and Variations (PCVs) values from igs14.atx \\ Reference coordinates & IGS SINEX files \\ Phase ambiguities & Float values \\ \hline \end{tabular}
\end{table} 
Table 1: Models and strategies used in single-frequency Precise Point Positioning (SF PPP). Figure 4: The flowchart of our study procedure. convergence time of the four interpolation methods under ionosphere-constrained and the average time of calculation of 78 stations. Figures 5 and 6 show the percentage of convergence time. From these two pictures, whether in the 95% or 68% level, and whether it is static mode or kinematic mode, the convergence time is less than 10 min, the percentage of the BILI method calculation result is slightly lower than the other three methods, and in the subsequent convergence time less than 20 min, 30 min, etc., the percentage of BILI method calculation results has been higher than the other three methods, as shown in the green histogram. That is to say, the convergence time of the BILI interpolation method is the shortest when compared to the other three methods. Figure 7 shows the statistical results of the root mean square (RMS) error in the horizontal and vertical components in the static and kinematic mode, respectively. The RMS errors are based on the statistics of the last 15 min of the position solution error [44]. In the static mode, the percentage of BILI method calculations exceeds 40% in the horizontal and vertical components when the RMS is less than 5 cm, and the other three methods are lower than 40% and, in the subsequent statistical stages, the percentage of the BILI method is higher than the other three methods to reach 100%. In the kinematic mode, the percentage of BILI method calculation results in the horizontal component is 60% when the RMS is less than 15 cm, and the other three methods are lower than this value; while, in the vertical component, the BILI method exceeds 40%, and  
The average convergence time (removed the data that the convergence time is equal to 180 min, that is, the data that does not convergence within three hours) is shown in Table 3, as compared to the JUNK method with the longest average convergence time, the average convergence time of BILI method  
Figure 6: The percentage of GPS SF PPP convergence time in different interpolation schemes in the kinematic mode (horizontal component (left panel) and vertical component (right panel)). Figure 7: The percentage of GPS SF PPP root mean square (RMS) in different ranges in the static and kinematic mode.