# Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias
## 1 Introduction  
With the continuous launch of new satellites since 2017, the BeiDou navigation satellite system (BDS) was announced to provide global service from the end of 2018. Consisting of 15 BDS-2 and 18 BDS-3 satellites by the end of June 2019, the BDS is able to provide global positioning, navigation, and timing (PNT) services with a positioning accuracy within 10 m (95%) in the horizontal and vertical components [1]. The BDS-2 satellites transmit public signals at frequencies of B1I, B2I, and B3I, while B1I, B1c, B2a, B2b, and B3I signals are transmitted on BDS-3 satellites [2]. The B1I, B2I, and B3I signals are centralizedat the frequencies of 1561.098, 1207.140, and 1268.52 MHz, while the B1c and B2a signals share the same frequency with L1(GPS)/E1(Galileo) and L5(GPS)/E5a(Galileo), which enables the compatibility and interoperability among these systems. The detailed frequency of the open signals for GPS, Galileo, and BDS are listed in Table 1.  
For BDS, the satellite clock in the broadcast ephemeris is referred to the B3I signal, whereas the post-processed precise clock provided by the International GNSS Service (IGS) is usually based on an ionosphere-free combination. To correct the hardware delay difference on different frequencies or different frequency combinations, the timing group delay (TGD) transmitted in the broadcast ephemeris or the post-processed differential code bias (DCB) is adopted, namely TGD\({}_{1}\) and TGD\({}_{2}\), which describes the TGD corrections from B3I to B1I and B2I frequencies, respectively. By tracking the regional monitoring stations in China, the BDS provides TGD with a stability of better than 1 ns [3]. Meanwhile, for the post-processed DCB provided by the multi-GNSS experiment (MGEX), it exhibits a precision of 0.36 ns with a monthly stability of 0.17 ns with the contribution of more globally distributed MGEX stations [4]. Although both the BDS DCB and TGD exhibit good stability, there still exists a bias between the BDS TGD and DCB. A notable scatter of \(\pm\)1.5 ns for TGD\({}_{1}\) and \(\pm\)3 ns for TGD\({}_{2}\) was observed by [PERSON] et al. [5], which far exceeds the uncertainty of the TGD estimation. Even for the BDS DCBs generated by different MGEX analysis centers, there also is a bias of 0.3-0.4 ns at different satellites [4]. This may be a result of the different selection of the tracking network and corresponding receivers in TGD/DCB estimation [5]. As pointed out by [PERSON] and [PERSON] [6], the inconsistent code bias of different receivers will lead to inconsistency in DCB estimation, even if all receivers are configured to use their standard correlators. According to [PERSON] [7], multiple parallel narrow correlation techniques are adopted at BDS monitoring stations, which is different from the commonly used wide correlators in commercial receivers such as Trimble and Septentrio. This may explain the significant bias between the BDS TGD and DCB. Starting from July 2017, the wide correlated pseudo-range observations were adopted in the BDS TGD estimation [8]. An apparent improvement in the consistency of the TGD and DCB was observed for BDS-2 after TGD update, with a root mean square (RMS) difference of 0.29 ns in TGD\({}_{1}\) and 0.25 ns in TGD\({}_{2}\), respectively. With the availability of BDS-3 satellites, the corresponding DCB was also generated at the Chinese Academy of Science (CAS) and the German Aerospace Center (DLR). [PERSON] et al. [9] analyzed the accuracy of broadcast group delay of GPS, Galileo, and BDS by comparing with DCB products from the CAS. It was shown that the overall agreement was at the level of 0.05-0.45 ns for GPS, while for Galileo, the agreement of 0.3-0.4 ns was obtained, which is acceptable considering the accuracy of DCB products. However, when comparing the DCB and TGD\({}_{1}\) of BDS-3 satellites in January 2019, a datum deviation of 3.8 ns between BDS-2 and BDS-3 was found. [PERSON] et al. [9] inferred that independent receivers are employed at the monitoring stations for BDS-2 and BDS-3.