# Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias
## 4 Impact of the Timing Group Delay Bias
### Signal-In-Space Range Error Assessment  
The algorithm used for SISRE assessment was introduced in Section 2. To assess the SISRE performance with the current BDS constellation, the half-year data from DOY 001-180 in 2019 was used. During the SISRE assessment, the data sampling was set at 15 min, and the threshold of gross outlier rejection was set at 10 m.  
Table 7 summarizes the overall SISRE performance from Schemes 1-4 at B1I, B3I, and B1I/B3I. From the comparison, it can be concluded that:  
1. The SISRE performance of BDS-3 is better than that of BDS-2 in all the schemes. This was expected, as more stable satellite clocks and inter-satellite link techniques are employed in BDS-3 satellites [20; 21]. 2. Significant SISRE improvement can be observed after the TGD bias correction. Among the three correction schemes, the satellite-dependent TGD bias calibrated from precise products shows the  
Figure 6: Relationship between the TGD bias from precise products and the network solution. The red dashed lines plot their relationship after linear fitting and R\({}^{2}\) is the correlation coefficient. \(dtgd_{0}\) 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. best improvement, with an overall SISRE improvement from 0.71, 0.81, and 1.40 m to 0.64, 0.66, and 0.64 m at B1I, B3I, and B1I/B3I frequencies, whereas the improvement of the TGD bias from the network solution is slightly lower. This is due to the fact that the TGD bias from the precise product directly removes the systematic bias of each satellite during SISRE assessment. For the TGD bias only considering the systematic bias between BDS-2 and BDS-3, although a noticeable improvement can also be observed, it is still not comparable with the satellite-dependent TGD bias correction, especially at the B1I/B3I frequency. This is a result of the amplification of the TGD error after the ionosphere-free combination. 3. For Scheme 2, the SISRE performance at each frequency is similar, which indicates that after the TGD bias correction, the accuracy of the TGD is close to that of the DCB. It is promising to see that the SISRE of BDS-3 is within 0.5 m, which agrees with the results presented by [PERSON] et al. [14] and fulfills the target of SISRE accuracy standard of the BDS [22]. For a detailed observation of the SISRE improvement for each satellite after TGD bias correction, Figure 7 depicts the 6-month SISRE result of each BDS satellite at B1I, B3I, and B1I/B3I from Schemes 1-3. Note that as the overall performance of Scheme 4 is close to that of Scheme 2, it is not compared in Figure 7. From the comparison, it was found that after the satellite-dependent TGD bias correction, the SISRE for all satellites and all frequencies improved at a different level. If we only consider the TGD bias between BDS-2 and BDS-3, the SISRE for some satellites would become even larger. This proves that it is better to correct the TGD bias by each individual satellite. Meanwhile, we can see that, different from the discordant SISRE values of BDS-2 satellites, the SISRE of BDS-3 after the satellite-dependent TGD bias correction is at a more consistent level, except for that at C35-C37. This may be attributed to the fact that both Trimble and Septentrio receivers cannot track the B3I signal of C35-C37, which may lead to a lower accuracy of the precise product for these satellites.