## 3 Results
### Kinematic PPP Validation  
Although extracting SCBs can improve the quality and stability of satellite clocks at the beginning of estimation, if these biases are not considered in PPP, the positioning accuracy will be seriously damaged. Unfortunately, as discussed in Section 3.2, SCBs are contaminated by code noises; therefore, they cannot be used as the corrections in PPP. In this study, we increase the noises of code observations to realize the application of satellite clocks without SCBs in PPP. Here, we define Ratio as the prior noise ratio of the code observations and the phase observations. Generally, the Ratio is set to 100, which means that if the prior noise of the phase observations is 0.003 m, then the noise of the code observations is 0.3 m. The observation data on DOY 031 of 57 stations distributed in Figure 1 are used for PPP with different ratio values. The positioning accuracy and convergence time are investigated to determine the appropriate Ratio. Figure 10 shows the statistical results, where the positioning error is a three-dimensional error and the convergence time is defined as the \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**DOY**} & \multicolumn{2}{c}{**Undifferenced Model**} & \multicolumn{2}{c}{**Undifferenced-SCB Model**} \\ \cline{2-5}  & **RMS (ns)** & **STD (ns)** & **RMS (ns)** & **STD (ns)** \\ \hline
031 & 0.73 & 0.15 & 1.24 & 0.06 \\
032 & 0.69 & 0.14 & 0.85 & 0.07 \\
033 & 0.71 & 0.14 & 0.82 & 0.09 \\
034 & 0.73 & 0.15 & 1.12 & 0.07 \\
035 & 0.70 & 0.15 & 0.85 & 0.08 \\
036 & 0.70 & 0.15 & 1.13 & 0.08 \\
037 & 0.71 & 0.14 & 0.75 & 0.06 \\ Mean & 0.71 & 0.15 & 0.97 & 0.07 \\ \hline \end{tabular}
\end{table} 
Table 4: The RMS and STD of clock estimates using different models when compared to the IGS final products from DOY 031 to 037. Figure 9: Time series of the clock biases with respect to the IGS final products on DOY 031. Different colors correspond to different satellites, and mean values are removed. time required to attain a three-dimensional positioning error less than 15 cm and keep at least for 10 epochs [32]. The positioning accuracy is poor when the Ratio is 100; therefore, it is not plotted in the figure. It can be seen from Figure 10 that with the increase in the Ratio, the positioning accuracy is improved, and the convergence time is reduced. When the Ratio is greater than 700, the positioning performance is not significantly improved. In addition, large observation noises are not conducive to the convergence of PPP. Therefore, we set the Ratio to 700 when the satellite clocks estimated using the Undifferentiated-SCB model are applied to carry out PPP experiments, and set the Ratio to 100 when the satellite clocks estimated using the Undifferentiated model or the IGS final clocks are used. Then, the above three kinds of clocks are used in PPP to evaluate the effectiveness of Undifferentiated-SCB clocks. It should be noted that in order to prove the advantage of the Undifferentiated-SCB model at the beginning of the estimation, satellite clocks estimated using the Undifferentiated and Undifferentiated-SCB models used in PPP do not converge in advance; therefore, the PPP solutions obtained by using the IGS clocks should have obvious positioning performance advantages. Figure 11 shows the time series of the positioning errors for station ABPO as an example. Obviously, compared with the Undifferentiated solution, the Undifferentiated-SCB offers a better positioning and convergence performance. Moreover, Figure 12 shows the RMS of the positioning errors with IGS solutions in contrast to those with the Undifferentiated and Undifferentiated-SCB solutions for each station from DOY 031 to 037. Each dot in the figure represents one station. There is no doubt that IGS solutions have the most effective performance. In addition, the positioning performance of the Undifferentiated-SCB solutions is closer to the IGS than that of the Undifferentiated solutions.