## 5 Performance Assessment of BDS-3 Satellite Clocks
### Discussion  
In order to analyze the specific characteristic of stability during the whole averaging time, Figure 13 gives the HDEV of one continuous arc for BDS-2 satellites. It can be seen that there are significant periodic signals at the time of about 2 cycles per revolution (cpr) with 12 h, while this phenomenon is not obvious for BDS-3, GPS, and Galileo satellites, as shown in Figures 14 and 15. The stability of C16 is significantly better than other BDS-2 IGSO satellites, and the launch date of C16 was on 2018/07/09. From Figures 13 and 14, we see the stability of BDS RAFS has a significant improvement from BDS-2 to BDS-3, and the BDS PHM presents the best clock stability. Figure 15 shows the stability of E07 and E08 is relatively worse than other Galileo satellites, with the average values being \(0.76\times 10^{-14}\) and \(1.91\times 10^{-14}\) for the averaging time of 86,400 s. The average value of other Galileo satellites is \(4.67\times 10^{-15}\). In general, the stability at the averaging time of 86,400 s for BDS-3 PHM, GPS IIF RAFS, and Galileo PHM satellites is comparable. Figure 14: HDEV of the differenced frequency data for BDS-3 MEO RAFS and GPS IIF RAFS satellites with respect to KOUR station. Figure 13: HDEV of the differenced frequency data for BDS-2 satellites with respect to KOUR station. The volume and weight of BDS-3 RAFS clocks are smaller than those of BDS-2. Besides, the very-high precision spaceborne RAFS was first carried on C36 and C37 satellites, which is the key for providing decimeter-magnitude positioning accuracy. From the results, it can be seen that the clock performance of the two satellites is basically comparable to other BDS-3 RAFS satellites, in spite of the 10,000 s and 1 d stability being slightly better. It should be noted that the number of visible stations (used in POD of XRS product) for C35, C36, and C37 satellites, with about a dozen stations, is fewer than other BDS-3 satellites with at least 30 visible stations. This may be also the reason that the clock STD of the three satellites between XRS and WUM products is bigger than other BDS-3 satellites. The clock performance between BDS-3 RAFS and GPS IIF RAFS has respective advantages in different aspects. The 10,000 s stability of BDS-3 RAFS is better than GPS, but for other indexes, the clock performance of GPS is superior. More importantly, for the first time, there are eight BDS-3 satellites carrying PHM in the construction of BDS. Compared to RAFS, the key technical indexes (i.e., the frequency accuracy, drift rate, and stability) are superior, which has a significant influence on users' positioning and timing accuracy, prediction performance, and autonomous navigation. The PHM includes a physical and electronics package and the working mechanism is different from RAFS. The specific work procedure can be found in [20]. The above results show the excellent performance of the PHM clock in terms of the three indexes, especially the frequency drift rate of PHM, which is basically two orders of magnitude smaller than RAFS satellites. On the whole, the clock performance of BDS-3 PHM is comparable to Galileo satellites, except C34 and C35 have large drift rates and the 10,000 s stability of BDS-3 is slightly worse than Galileo satellites. Generally, when processing the stability analysis in the time domain, the reference frequency standard should be one-third smaller than that of the tested atomic clocks. The stability of 10,000 s and 86,400 s is \(8.93\times 10^{-15}\) and \(1.85\times 10^{-15}\), respectively, for the differenced values between receiver clocks of MGUE and KOUR with both attached to high-precision AHM. The threefold value of \(8.93\times 10^{-15}\) is \(2.68\times 10^{-14}\), which is basically comparable to the 10,000 s stability of BDS-3 PHM with the value \(2.32\times 10^{-14}\). The threefold value of \(1.85\times 10^{-15}\) is \(5.55\times 10^{-14}\), which is basically comparable to the 10,000 s stability of BDS-3 PHM with the value \(5.28\times 10^{-14}\).