# An Analysis of Satellite Multichannel Differential Code Bias for BeiDou SPP and PPP
## 4 Time-Varying Characteristics of DCB and OSB on BDS Satellites
### Stability of DCB and OSB Obtained from the CAS
In general, the stability of DCBs and the combined OSB values of BDS-2 are equivalent. The mean STD of the C2I-C7I DCBs of the IGSO satellites is 0.12 ns, slightly better than the 0.13 ns of the MEO satellites and the 0.18 ns of the GEO satellites. The mean STD of the C2I-C6I DCBs of the IGSO satellites is 2.28 ns, larger than the 0.43 ns of the MEO satellites and the 0.44 ns of the GEO satellites. The BDS-3 DCBs are more stable than the corresponding values computed with the OSBs. The BDS-3 DCBs of the IGSO satellites are obviously more stable than those of the MEO satellites, with mean STDs of 0.42 ns and 0.84 ns on average, respectively. The better stability of DCBs for the IGSO satellites is due to the longer observation arcs and wider geographic coverage [28]. The observables of the MEO satellites are more prone to being affected by elevation-dependent bias than those of the GEO and IGSO satellites, leading to less stability in the solution results. Figure 4: Time series of CAS BDS-3 OSBs from July in 2020 to June in 2021. Figure 3: Time series of CAS BDS-2 OSBs from July in 2020 to June in 2021. As can be seen from Table 5, the BDS-2 DCBs of C2I-C7I and the BDS-3 DCBs of C1X-C5X are stable, with mean STDs of 0.14 ns and 0.15 ns, respectively. The BDS-3 DCBs of C1P-C5P and C1P-C6I have larger fluctuations, with mean STDs of 1.53 ns and 1.55 ns. The annual means of C2I-C7I, C1X-C5X, C1P-C5P, C1X-C6I, C1P-C6I, C1X-C7Z, and C1X-C8X DCBs are close to zero, and this is mainly attributed to the constraint of the \"zero mean\" benchmark in the estimation of DCB parameters. The annual means of C1P-C5P and C1P-C6I DCBs deviate from the zero-mean values due to the addition of new satellites to C1P and C5P in 2021. The mean values and STDs of C2I-C7I and C2I-C6I DCBs and the combined OSB values of BDS-2 are highly consistent. Among the combined OSB values of BDS-3, C1X-C5X has the smallest fluctuation and C1P-C6I has the largest fluctuation, with mean STDs of 0.22 and 2.16 ns, respectively. The mean difference between the DCBs and combined OSB values for each channel is 0.18 ns, and the mean STD is 0.23 ns. The mean values and STDs of the raw BDS OSBs for each satellite and each signal are given in Figure 6 and Table 6. The mean values are positive for BDS-3 OSBs and mostly negative for BDS-2 OBSs. The differences between the means of C2I and C7I OSBs for BDS-2 and C1X, C5X, C6I, C7Z, and C8X OSBs for BDS-3 are all no more than 0.01 ns. The STD of BDS-3 OSBs after removing some of the more volatile satellites is less than that of BDS-2 OSBs and generally fluctuates between 1 and 4 ns. Figure 5: Mean values and STDs of DCBs and combined OSB values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**System**} & \multirow{2}{*}{**Signal**} & \multicolumn{2}{c}{**DCB**} & \multicolumn{2}{c}{**Combined OSB**} & \multicolumn{1}{c}{**Note**} \\ \cline{3-6}  & & **Mean (ns)** & **STD (ns)** & **Mean (ns)** & **STD (ns)** & **(Rejection Rate)** \\ \hline \multirow{2}{*}{BDS-2} & C2I–C7I & 0 & 0.15 & 0 & 0.14 & 0 \\  & C2I–C6I & 7.73 & 1.30 & 7.73 & 1.30 & 0 \\ \hline \multirow{6}{*}{BDS-3} & C2I–C6I & \(-4.29\) & 0.61 & \(-4.59\) & 1.14 & OSB:11.11\% \\  & C1X–C5X & 0 & 0.15 & 0 & 0.22 & 0 \\  & C1P–C5P & \(-0.31\) & 1.53 & \(-0.31\) & 1.41 & 0 \\ \cline{1-1}  & C1X–C6I & 0 & 0.20 & 0 & 0.55 & 0 \\ \cline{1-1}  & C1P–C6I & \(-0.80\) & 1.55 & \(-2.15\) & 2.16 & OSB:18.51\% \\ \cline{1-1}  & C1X–C7Z & 0 & 0.45 & 0.02 & 0.84 & 0 \\ \cline{1-1}  & C1X–C8X & 0 & 1.11 & 0.01 & 1.34 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean values and STDs of DCBs and combined OSB values for each signal channel. We further analyzed the short-term stability of DCBs and OSBs on a monthly basis. Figures 7-9 show the monthly STDs of the BDS DCBs. The bars in different colors represent the monthly stability of DCB in different months. The mean monthly STDs of C2I-C7I DCBs for the GEO, MEO, and IGSO satellites are 0.10, 1.17, and 0.08 ns, while those of C2I-C6I DCBs are 0.22, 3.04, and 9.40 ns, respectively.