## 4 Characteristics of the BDS Satellite Clock
### Frequency Stability  
The overlapping Hadamard deviation was applied to the frequency stability calculation. The phase data of a single day were used to calculate the stability of 10,000 s, and the phase data of 15 consecutive days were used to calculate the stability of a day. The average indicators obtained for each month are shown in Figure 10.  
Figure 9: Frequency accuracy of BDS Satellites.  
The average frequency stability for 10,000 s of BDS-2 satellite atomic clocks is \(7.53\times 10^{-14}\), where C16 shows the best performance, reaching 2.88 \(\times\) 10\({}^{-14}\), and satellite atomic clocks with a later launch time usually show performance superior to those with an earlier orbit. The average index of the BDS-3 satellite atomic clock is 2.48 \(\times\) 10\({}^{-14}\), which is stable and maintained at a high level, and the performance has been significantly improved with time. In general, the frequency stability of BDS-2 satellite atomic clocks fluctuates significantly; a few satellite atomic clocks such as C02, C04, and C06 even have indicators inferior to \(9.0\times 10^{-13}\) in some months. In contrast, the frequency stability of the BDS-3 satellite atomic clock fluctuates slightly, basically within the order of 10\({}^{-14}\).  
The average frequency daily stability of BDS-2 satellite atomic clocks is \(6.57\times 10^{-14}\); there are great distinctions between different clocks. A few satellite atomic clocks such as C09, C11, and C16 could reach the target superior to 2.0 \(\times\) 10\({}^{-14}\), while the daily stability of C02, C04, and C06 is even inferior to their frequency stability for 10,000 s. This indicates that the long-term stability of satellite atomic clocks operating for more than 11 years will be significantly reduced, and the clock offset data solution strategy will also have an impact on the stability analysis. The daily frequency stability of BDS-3 satellite atomic clocks reached \(1.19\times 10^{-14}\) on average; the stability of all clocks is reliable, with an index superior to \(9.0\times 10^{-14}\) for every month. In terms of clock type, the daily stability of some BDS-3 RAFS has reached the level of 10\({}^{-15}\), and almost all PHMs have reached this accuracy.  
In general, the frequency stability of BDS-3 satellite atomic clocks with a smaller fluctuation range is significantly superior to that of BDS-2, especially when the smoothing  
Figure 10: Sequence diagram of frequency daily stability.  
time becomes longer. Dynamic changes indicate that the value of overlapping Hadamard variance shows a downward trend, especially for clocks launched at the later stage of BDS-3. In the first test month, the stability indicators of BDS-2 were mostly concentrated in the interval of 2-7 \(\times\) 10\({}^{-14}\), and then rose to 1-4 \(\times\) 10\({}^{-14}\) after 6 months; the corresponding indicators of BDS-3 are 2 \(\times\) 10\({}^{-14}\) and 3-8 \(\times\) 10\({}^{-15}\), respectively. Obviously, after the BDS was officially commissioned, it went through a period of testing and performance improvement for about half a year, so that the stability of the satellite atomic clock became better over time. As of 2021, the performance of BDS satellite atomic clocks has begun to be at a stable high level, mainly benefitting from the contributions of inter-satellite link measurements for the precise orbits and clock determinations of BDS-3 satellites [30; 31].