# Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias
## 4 Impact of the Timing Group Delay Bias
### Single Point Positioning  
To assess the effect of the TGD bias on SPP, one-week data from DOY 134 to 140 at 97 MGEX stations were selected. In addition, for the independent assessment of the data, among the 97 stations, 33 of them were new stations, different from the stations used in the network solution. The distribution of the stations is depicted in Figure 8.  
For the processing of SPP, the broadcast ephemeris was adopted. The troposphere delay is corrected by the GPT2w and VMF models [18]. The ionosphere delay is corrected by the BDS Klobuchar model [1] for single-frequency data or eliminated by the ionosphere-free combination for dual-frequency data. Therefore, the parameters to be estimated are the station coordinates and the receiver clock at each epoch. For the assessment of the SPP performance, the reference station coordinates were obtained from the IGS daily solutions. Table 8 summarizes the statistical results of the three-dimensional (3D) positioning RMS for the four schemes at B1I, B3I, and B1I/B3I frequencies, along with the corresponding improvement of Schemes 2-4 in comparison with Scheme 1. We can draw the following conclusions from Table 8:  
Figure 8: Ninety-seven MGEX stations for single point positioning (SPP), including the same 64 stations (red dots) in the network solution and 33 new stations (green dots). Figure 7: The BDS SISRE at B1I (**a**), B3I (**b**), and B1I/B3I (**c**) frequencies for different schemes. The BDS-2 and BDS-3 satellites are separated by the dashed line. Among the results in the frequencies of B1I, B3I, and B1I/B3I, the SPP result at B1I/B3I exhibits the worst precision, which may due to the amplification of the observation noise and TGD errors after ionosphere-free combination. However, the SPP performance at B1I/B3I also improves to the maximum extent after TGD bias correction. For B1I or B3I frequencies, the improvement is not that significant. 2. Among the three schemes with TGD bias correction, the satellite-dependent TGD bias from precise products shows the best improvements of 5.6%, 8.4%, and 21.6% at B1I, B3I, and B1I/B3I frequencies. The satellite-dependent TGD bias correction from the network solution is at a similar level. Therefore, it is not recommended to only consider the TGD bias between BDS-2 and BDS-3. For a spatial observation of the impact of the satellite-dependent TGD bias in SPP, the station-dependent SPP results comparing Schemes 1 and 2 at the B1I/B3I frequency are shown in Figure 9. We can clearly see that positioning improvement outside the East Asia region is more evident. One reason for this phenomenon is that with the decrease of visible satellites [15], the contribution of the TGD bias correction becomes more significant. The other reason may due to the more scattered TGD bias of BDS-3 satellites, as indicated in Figure 6.  
Furthermore, for a more specific observation of the contribution of the satellite-dependent TGD bias correction, we took one of the stations, MCHL (Mitchell, 26.36\({}^{\circ}\)S, 148.15\({}^{\circ}\)E), as an example. Figure 10 compares the horizontal and vertical positioning error of SPP at B1I and B1I/B3I frequencies, comparing Schemes 1 and 2. As can be seen, the positioning error was less scattered after TGD bias correction, with a decrease from 1.75 to 1.31 m in the horizontal and from 3.06 to 2.48 m in the vertical for B1I/B3I. Similar improvements can also be found for B1I. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Frequency** & **S1 (m)** & **S2 (m)** & **S3 (m)** & **S4 (m)** & **Impr2-1** & **Impr3-1** & **Impr4-1** \\ \hline B1I & 2.69 & 2.54 & 2.67 & 2.57 & 5.6\% & 0.8\% & 4.7\% \\ B3I & 3.62 & 3.32 & 3.54 & 3.35 & 8.4\% & 2.4\% & 7.5\% \\ B1I/B3I & 5.10 & 4.00 & 4.27 & 4.04 & 21.6\% & 16.3\% & 20.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: RMS and improvement of the BDS SPP for different schemes. Impr\({}_{yi}\) indicates the positioning improvement (\(Impr_{j-i}=\big{(}RMS_{Si}-RMS_{Sj}\big{)}/RMS_{Si}\)).