# Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias
## 3 BeiDou Timing Group Delay Bias from Network Solution
### Estimated Results  
Following the network-based TGD bias estimation method, we derived the weekly bias of each satellite. Figure 5 depicts the estimated bias at B1I, B3I, and B1I/B3I respectively. Compared with the results presented in Figure 3, we can see that the biases from both methods are quite similar. The average STDs of all satellites were 0.80, 0.77, and 1.00 ns at B1I, B3I, and B1I/B3I, which is slightly higher than that obtained from the precise products. This was expected, as carrier phase observations are used in the precise orbit determination, and the DCB products are not affected by errors from the broadcast ephemeris and troposphere [4; 5]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Receiver** & **Types or Version** & **Number** & **Note** \\ \hline \multirow{2}{*}{Javad} & TRE\_3 & \multirow{2}{*}{22} & \multirow{2}{*}{Track all BDS satellites} \\  & TRE\_3 DELTA & & \\ \multirow{2}{*}{Trimble} & ALLOY & & \\  & NETR9 & & \\ \multirow{2}{*}{Septentrio} & POLARXSTR & \multirow{2}{*}{33} & \multirow{2}{*}{Cannot track B3I signal of C16, C23–C27, C29–C30, C35–C37} \\ \multirow{2}{*}{Septentrio} & POLARX5 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Receiver information of the selected MGEX stations. Figure 4: The \(87\) selected multi-GNSS experiment (MGEX) stations in the network solution. Figure 5: Estimated bias at B1I (**a**), B3I (**b**), and B1I/B3I (**c**) frequencies. The error bar stands for the standard deviation at each station. The BDS-2 and BDS-3 satellites are separated by the dashed line. Similarly, \(dtgd_{0}\) and \(dtgd_{1}\) for each satellite can be determined based on Equation (5). The calibrated TGD biases are listed in Table 5, in which we can see that the biases are slightly different from the results obtained from precise products. For a better comparison of the two methods, Table 6 compares the difference and Figure 6 gives the relationship of the TGD bias from precise products and the network solution. It is shown that the two sets of the TGD bias have a linear correlation with the coefficients of 0.821 and 0.985. Most of the absolute values are within 1 ns, especially for \(dtgd_{1}\). However, as the slope of the linear fitting function is not close to 1.0, the absolute values of the two methods do not match perfectly. This may be a result of the difference between the receivers and processing strategy of the two methods. Additionally, it was shown that, compared with \(dtgd_{0}\), the systematic bias of \(dtgd_{1}\) between BDS-2 and BDS-3 is more significant and the \(dtgd_{1}\) of BDS-3 is more scattered compared with that of BDS-2, which was also proven in the method using the precise products. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**PRN** & \(dtgd_{0}\) & \(dtgd_{1}\) & **PRN** & \(dtgd_{0}\) & \(dtgd_{1}\) & **PRN** & \(dtgd_{0}\) & \(dtgd_{1}\) \\ \hline
1 & 0.72 & \(-\)0.60 & 12 & \(-\)0.36 & \(-\)0.20 & 26 & \(-\)0.19 & 0.31 \\
2 & 0.54 & \(-\)0.27 & 13 & \(-\)0.26 & \(-\)0.22 & 27 & \(-\)0.19 & 0.14 \\
3 & 0.25 & \(-\)0.27 & 14 & \(-\)1.07 & 0.12 & 28 & 0.06 & 0.01 \\
4 & \(-\)0.06 & \(-\)0.57 & 16 & 0.58 & 0.00 & 29 & \(-\)0.11 & 0.02 \\
5 & \(-\)0.39 & \(-\)0.16 & 19 & \(-\)0.36 & 0.20 & 30 & \(-\)0.32 & 0.20 \\
6 & 0.45 & \(-\)0.18 & 20 & \(-\)0.74 & 0.28 & 32 & \(-\)0.10 & 0.22 \\
7 & 1.10 & \(-\)0.35 & 21 & \(-\)0.04 & 0.00 & 33 & \(-\)0.33 & 0.14 \\
8 & 0.86 & \(-\)0.29 & 22 & \(-\)0.08 & 0.08 & 34 & 0.12 & \(-\)0.09 \\
9 & 1.11 & \(-\)0.28 & 23 & \(-\)1.25 & 0.42 & 35 & \(-\)1.06 & 0.18 \\
10 & 1.49 & \(-\)0.36 & 24 & \(-\)0.31 & 0.40 & 36 & \(-\)0.37 & 0.25 \\
11 & 1.05 & 0.02 & 25 & \(-\)1.13 & 0.60 & 37 & 0.38 & 0.29 \\ \hline \end{tabular}
\end{table} 
Table 6: Difference of TGD bias from precise products and the network solution (in ns). \(dtgd_{0}\) means the TGD bias at B3I frequency, and \(dtgd_{1}\) is the residual TGD bias of TGD\({}_{1}\). The average difference for all satellites was removed.