# Evaluation of BDS-2 and BDS-3 Satellite Atomic Clock Products and Their Effects on Positioning
## 4 BDS-2/BDS-3 Clock Stabilities and Detum Discrepancy
### BDS-2/BDS-3 Clock Stabilities
It is interesting to note that the majority of BDS-3 Rb and PHM clocks have virtually identical performance from averaging intervals between 30 and 10,000 s, but the ADEV for BDS-3 Rb clocks slightly increase compared with most BDS-3 PHM clocks for averaging intervals greater than 10,000 s. The PHM clocks for BDS-3 C38-C44 also show worse stability than other BDS-3 satellite PHM clocks for averaging intervals beyond about 7000 s in the two sets of results, probably owing to the lack of tracking stations. Nevertheless, the performance of BDS-2 Rb clocks exhibits significant disparity up to averaging intervals of 10,000 s and has no relevance to the satellite type. Between 500 and 2000 s, the satellite C10 and C11 show an increased ADEV compared with other BDS-2 satellites in both plots. For the averaging interval of 30,600 s, the BDS-2 Rb clocks show an Allan deviation between 2.0 and 4.5 \(\times\) 10\({}^{-14}\), compared with 1.4--3.1 \(\times\) 10\({}^{-14}\) and 1.1--2.9 \(\times\) 10\({}^{-14}\) for BDS-3 Rb and PHM clocks, respectively. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**System** & **PRN** & **Type** & **Manuf** & **Clock Type** \\ \hline \multirow{3}{*}{BDS-2} & C01 C02 C03 C04 C05 & GEO & CASC & Rb \\  & C06 C07 C08 C09 C10 C13 C16 & IGSO & CASC & Rb \\  & C11 C12 C14 & MEO & CASC & Rb \\ \hline \multirow{6}{*}{BDS-3} & C19 C20 C21 C22 C23 C24 & \multirow{2}{*}{MEO} & CASC & Rb \\  & C32 C33 C36 C37 C45 C46 & & & \\ \cline{1-1}  & C41 C42 & MEO & CASC & PHM \\ \cline{1-1}  & C38 C39 C40 & IGSO & CASC & PHM \\ \cline{1-1}  & C59 C60 C61(Testing) & GEO & CASC & PHM \\ \cline{1-1}  & C25 C26 C27 C28 C29 C30 & & & \\ \cline{1-1}  & C34 C35 C43 C44 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: BDS-2 and BDS-3 satellites information. Over averaging intervals from 30 to 30,600 s, the decreasing range in ADEV for IIF-Rb is 23.8--1.5 \(\times\) 10\({}^{-14}\), and 18.1--0.7 \(\times\) 10\({}^{-14}\) for FOC-PHM. It is easy to find that the BDS-3 Rb and PHM clocks show better performance compared with the IIF-Rb clock in most cases from Figure 2. Moreover, the comparison of ADEV shows that the BDS-3 Rb and PHM clocks seem to be competitive with the FOC-PHM clock for averaging intervals less than 1000, but they do not reach the performance of FOC-PHM clock for longer intervals. The plots in Figure 3 depict long-term overlapping Allan deviation for the same satellites with broadcast ephemeris (BRDC). Prior to calculating ADEV, the clock offset data were calculated from broadcast ephemeris by a second-order polynomial and stacked to 1-week periods. Then, the results derived from 1-week data for averaging intervals beyond 7200 s were averaged and shown. Inevitably, the performance of broadcast ephemeris is poorer compared with precise products in Allan deviation at the same averaging interval. The ADEV differences for BDS-3 PHM clocks are greatly small, while they are relatively large for BDS-2 and BDS-3 Rb clocks. Additionally, BDS-3 Rb clocks have a similar ADEV performance to that of BDS-3 PHM clocks for averaging intervals less than 20,000 s but show an increased Allan deviation for longer averaging intervals. However, it is interesting  
Figure 2: Overlapping Allan deviation of clock for each BDS satellite, all GPS Block IIF satellites and all Galileo FOC satellites. Average values for the period from 28 November 2019 to 31 December 2020 (MJD 58815-59214) using GFZ (**top**) and WHU (**bottom**) precise products are shown. For comparison, results of BDS-2 Rb, BDS-3 Rb, BDS-3 PHM, IIF-Rb and FOC–PHM clocks are depicted in blue, green, red, purple and cyan, respectively. to note that the ADEV of C41 and C42 PHM clocks exhibits the same trend as that of BDS-3 Rb clocks, while C19, C45 and C46 Rb clocks are similar to BDS-3 PHM clocks in ADEV. At an averaging interval of 227,490 s, the median value of ADEV for BDS-2 Rb, BDS-3 Rb and BDS-3 PHM clocks is 7.5 \(\times\) 10\({}^{-14}\), 1.8 \(\times\) 10\({}^{-13}\) and 8.3 \(\times\) 10\({}^{-15}\), respectively.