# Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias
## 1 Introduction
For BDS-3, [PERSON] et al. [10] assessed the broadcast orbit and clock accuracy by comparing with precise orbit and clocks and found a nonzero mean bias of BDS-3 clocks. However, no explanation of how the clock bias comes about was given. Besides, these researches only focused on the overall datum bias between BDS-2 and BDS-3 or assumed that the satellite-dependent bias is from the clock error. Does the bias also disperse on BDS-2 satellites? Is the bias satellite-dependent bias also frequency dependent? A detailed analysis of these issues should be further investigated. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**System**} & \multicolumn{6}{c}{**Frequency (MHz)**} \\ \cline{2-9}  & **1575.42** & **1561.098** & **1227.60** & **1176.45** & **1207.14** & **1191.795** & **1268.52** & **1278.75** \\ \hline GPS & L1 & & L2 & L5 & & & \\ Galileo & E1 & & & E5a & E5b & E5 & & E6 \\ BDS-2 & & B1I & & & B2I & & B3I & \\ BDS-3 & B1c & B1I & & B2a & B2b & & B3I & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Open signals of GPS, Galileo, and BeiDou navigation satellite system (BDS). The bias between the DCB and TGD affects the performance of signal-in-space range error (SISRE) and user positioning [11]. [PERSON] et al. [12] evaluated the BDS SISRE using the TGD and DCB. During a 12-month comparison in the period of 2013-2014, the BDS SISRE showed a better consistency with an RMS of 1.1 m after DCB correction as compared to 1.5 m using TGD correction. The accuracy of the TGD also decreases the precision of single point positioning (SPP) compared with the DCB [13]. With the update of the BDS TGD after July 2017, the BDS SISRE was reported to be around 0.81 m after TGD or DCB correction, which indicates a similar accuracy and good agreement between TGD and DCB [8]. For the SISRE performance of BDS-3, [PERSON] et al. [14] first reported an average value of 0.44 m using 4 days' worth of data from eight BDS-3 satellites by comparing the broadcast ephemeris and precise results from the International GNSS Monitoring and Assessment System (iGMAS). A comprehensive comparison with 2 months' worth of data from the 18 BDS-3 satellites showed that the SISRE of BDS-3 was 0.71 m after TGD correction and 0.57 m after DCB correction [15]. Therefore, except for the apparent TGD bias between BDS-2 and BDS-3, a dispersion bias of the TGD among BDS-3 satellites was also indicated. The motivation of this contribution was to investigate and calibrate the satellite-dependent TGD bias with the current BDS constellation. Other than [PERSON] et al. [9] and [PERSON] et al. [10], we calibrate the satellite-dependent bias for BDS-2 and BDS-3 and attribute this bias to a TGD bias, which is frequency dependent and validated by orbit and clock comparison and network solution. The paper is organized as follows. First, the TGD bias is calibrated by comparing the difference between the BDS broadcast ephemeris and MGEX precise products. To further confirm the existence of the bias, raw observation data from 87 MGEX stations are used for the calibration of the bias. The contribution of the calibrated TGD bias is then applied to the SISRE assessment and single point positioning (SPP). Finally, some conclusions and discussions are presented.