## 5 Summary Analysis  
For further comparative analysis and detailed discussion, the main indicators of each satellite atomic clock are listed in Table 2, and the corresponding main features of each stage are analyzed as follows:  
1. Data quality. The MAD-based method is effective in processing a large number of satellite atomic clock offset data. The error rate of the original data of satellites launched by BDS-2 in the early stage was unacceptable, which reflects that the operating life would be exhausted. Similarly, the data efficiency of satellite clocks launched in the later stage was low, which was caused by the commissioning phase and would be improved when entering the stable operation stage.
2. Fitting residuals and periodic characteristics. The daily fitting residual of the BDS-2 satellite clock is within the range of 0.25-0.6 ns, while that of BDS-3 is in the range of 0.1-0.2 ns. The daily fitting residual is processed by FFT, and the main period terms of the satellite atomic clock obtained are close to 1 time or 1/2 of its orbital period. Specifically, 24 h and 12 h for Geo and IGSO and 12.92 h and 6.46 h for MEO, where the main period term of the orbital period is related to the influence of diurnal variation and solar light pressure, or it is related to the periodic change of the distance between the satellite and the earth during the elliptical orbit of the satellite (one circle around the earth must undergo two semi major axis and semi minor axis changes). In addition, the fitting residuals of the atomic clocks of GEO and IGSO satellites show a periodic variation law of about half a year, which may be related to the earth's revolution.
3. Frequency drift rate. The early BDS-2 satellite atomic clock has a large drift rate due to long service life, with more frequency modulation points and phase modulation points. The drift rate of RAFS launched at the later stage is at the same level as that of BDS-3, and the drift rate of PHM is optimal, whose phase change tends to be linear over the whole sampling period. In addition, the drift rates of GEO and IGSO showed a significant periodic term variation trend of about half a year, which was similar to the variation characteristics of the fitting residuals.
4. Frequency accuracy. The frequency accuracy of the BDS-2 atomic clock is at the 10\({}^{-11}\) level, while that of BDS-3 is at the 10\({}^{-12}\) level. The PHM has better continuity and a smaller fluctuation range. The change of frequency accuracy within the sampling time tends to be linear, and is superior to that of RAFS.
5. Frequency stability. The stability of the BDS-2 satellite clock is half an order of magnitude inferior to that of BDS-3. In particular, the five satellites C01-C05, which have been in service for a long time, not only have a low overall frequency stability, but also have greater fluctuations than other satellite clocks. Among the three satellites with different orbits, MEO has the optimal frequency stability, followed by IGSO, whilst GEO has the worst performance. The average daily frequency stability of BDS-3 satellite atomic clocks was 1.19 \(\times\) 10\({}^{-14}\) over the whole test period, and increasing to 3-8 \(\times\) 10\({}^{-15}\) with the stable operation of the system.  
The analysis in this paper, combined with existing research results, shows the PHMs of Galileo at the present stage have the best performance, and the performance of BDS-3 is also at the first-class level, close to GPS. Meanwhile, there is still room for further improvement [14].