## 3 Results
### Satellite Clock Validation  
In order to assess the influence of different code bias extraction models on the stability of satellite clocks after the start of estimation, the satellite clocks are compared with the IGS final products. In this assessment, the RMS and standard deviation (STD) values for each satellite are calculated. The RMS values reflect the deviation degree of estimated clocks relative to the IGS, and the STD values represent the quality and stability of clocks.  
Figure 8 shows the RMS and STD values of clock estimates compared with the IGS final products on DOY 031. Obviously, the RMS and STD values of the Undifferenced model are more consistent with the Undifferenced-RCB model, and the Undifferenced-SCB is closer to the Undifferenced-SRCB model, which indicates that the RCBs do not damage the quality of satellite clocks. Additionally, the mean RMS and STD values of the clock estimates displayed in Figure 8 are given in Table 3, which also confirms the above conclusion.  
Figure 6: Time series of RCBs extracted by Undifferenced-RCB model on DOY 031.  
Figure 7: Time series of RCBs extracted by Undifferenced-SRCB model on DOY 031.  
It can also be seen from Figure 8 and Table 3 that if the SCBs are extracted during the clock estimation process, the STD values of the satellite clocks decrease, but the RMS values increase at the same time, which means that the quality and stability of the satellite clocks are improved and the relative biases between the estimated and IGS clocks become larger. Obviously, the SCBs contained in IGS clocks are responsible for the increase in the RMS. It is worth noting that, the stability of IGS clocks is not destroyed by time-varying SCBs; therefore, those SCBs are likely to be driven into the code residuals such as Equation (2). Then, we can infer that the reason for the instability of clocks estimated using the Undifferenced model is that the time-varying SCBs are assimilated by the satellite clocks. Moreover, it is a time-consuming process to drive the time-varying SCBs into the code residuals; therefore, we extract SCBs directly to accelerate the convergence and stabilization of clocks.  
Considering that SCBs are the main factors that damage the stability of satellite clocks, then only the Undifferenced and Undifferenced-SCB are compared in the following. Figure 9 shows the biases of estimated satellite clocks with respect to the IGS final clocks. Compared with the Undifferenced model, the satellite clocks without SCBs have a faster convergence speed and are more stable. In particular, the satellite clock bias of the Undifferenced model, represented by the blue line, is changed by about 0.5 ns from the 12 h to the 20 h, but it is not the case in the Undifferenced-SCB model. The accuracy of the satellite clocks estimated using the above two models in one week is shown in Table 4. As expected,  
Figure 8: RMS and STD values of clock estimates compared with the IGS final products on DOY 031. The mean values are also plotted near the right edge of each panel. G01 is the reference satellite.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **RMS (ns)** & **STD (ns)** \\ \hline Undifferenced & 0.73 & 0.15 \\ Undifferenced-SCB & 1.24 & 0.06 \\ Undifferenced-RCB & 0.72 & 0.15 \\ Undifferenced-SRCB & 1.33 & 0.08 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The mean RMS and STD of clock estimates by different models when compared to the IGS final products on DOY 031.  
the RMS of the Undifferenced-SCB model is larger than that of the Undifferenced model. After SCBs' extraction, the mean STD of the clocks decreases from 0.15 to 0.07 ns.