## 4 Characteristics of the BDS Satellite Clock
### Frequency Drift Rate  
The frequency drift rate of the BDS satellite clock was calculated by Equation (6), and the average RMS value of the drift rate sequence was determined. Figure 7 shows the drift rate calculated by all satellite atomic clocks day by day; some detailed dynamic changes can also be observed.  
Figure 7: _Cont_.  
Figure 7: _Cont._  
Intuitively, the drift rate of a BDS-2 satellite atomic clock is generally in the order of \(10^{-18}\), while BDS-3 reaches the order of \(10^{-19}\). The C04 satellite with a long running time has the worst drift rate of 1.82 \(\times\)\(10^{-17}\), which is due to the high drift rate caused by the ageing of the equipment of the satellite atomic clock after long-term operation. Comparison between different orbits shows that MEO satellite atomic clocks have the optimal drift rate; comparison between different clock types shows that PHM with the smooth trend has a better drift rate than RAFS. In addition, if there are some points with a relatively high drift rate (such as C30) in the overall drift change curve, there will be fluctuation points at the corresponding position of the frequency map that protrude, which may be due to the high drift rate.  
Figure 7: Drift rate of BDS satellite clocks.  
the calculating error of the satellite clock offset or the switching between the primary and standby atomic clocks.  
It is worth noting that the frequency drift of all GEO satellite clocks has the characteristics of oscillation and fluctuation; in addition, the frequency drift change of all IGSO satellite clocks is similar to the triangular wave law, with the cycle of half a year, which may be due to the slow change of frequency drift caused by the earth's movement. The daily frequency drift rate of the BDS satellite clock was calculated by Equation (6), and the average RMS value of the daily drift rate sequence was determined. Figure 8 shows the daily drift rate calculated by all satellite atomic clocks; some detailed dynamic changes could also be observed intuitively.  
Figure 8: _Cont._  
Figure 8 shows that the daily drift rate shows similar characteristics to the drift rate in the same sampling period, and the relatively large fluctuation points in the drift rate graph are also reflected in the statistical graph of the daily drift rate. It is easy to find that the magnitude of PHM is better than the RAFS in terms of the performance of the daily drift rate, which also confirms that the PHM has superior long-term function. According to all the satellite data, the drift rate of each satellite clock does not show an obvious divergence trend after the long-term operation of the satellite, which proves that the phase and frequency adjustment and calibration operations after comparison with the time reference of the ground station are effective in restraining the drift speed of the satellite clock, especially for the \(\sim 10^{-11}\) years.  
Figure 8: Daily drift rate of BDS satellite clocks.  
the RAFS with a large long-term drift index. At present, although the drift rate index of BDS-2 satellite clocks is relatively inferior to BDS-3, its operation state is stable.