## 6 Conclusions  
In this study, the necessary for long-term characterization of the BDS-3 satellite clock was described, the clock offset model and the calculation of the main indicators were introduced, and a systematic long-term characterization scheme for the satellite clock was designed. The characteristics of 35 BDS satellites atomic clocks were analyzed based on 620 days of precision clock aberration data provided by GFZ since July 2020. The MAD-based outlier detection method was applied to ensure the quality of the clock aberration data, and then the fitting residuals of the clock aberration model and the corresponding  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**System** & **PRN** & \begin{tabular}{c} **Drift** \\ **Rate** \\ **(\(10^{-18}\))** \\ \end{tabular} & \begin{tabular}{c} **Daily** \\ **Drift** \\ **(\(10^{-14}\))** \\ \end{tabular} & \begin{tabular}{c} **Accuracy** \\ **(\(10^{-14}\))** \\ \end{tabular} & \begin{tabular}{c} **Stability** \\ **Stability** \\ **(\(10^{-14}\))** \\ \end{tabular} & \begin{tabular}{c} **Basiduals** \\ **(ns)** \\ \end{tabular} & \begin{tabular}{c} **Cycle 1** \\ **(h)** \\ \end{tabular} & \
\begin{tabular}{c} **Cycle 2** \\ **(h)** \\ \end{tabular} &
\begin{tabular}{c} **Cycle 3** \\ **(h)** \\ \end{tabular} \\ \hline \multirow{9}{*}{BDS-2} & C01 & 2.46 & 17.62 & 3.69 & 9.07 & 3.42 & 0.47 & 12.08 & 24.00 & 8.02 \\  & C02 &  
spectral characteristics were calculated. Long-term dynamic indices such as frequency drift rate, frequency accuracy, and frequency stability were derived, respectively.  
The analysis shows that the BDS-3 satellite atomic clock offset contains cyclic terms that are closely related to orbital operations, with the main cyclic term typically approaching the orbital operation duration or 1/2. The frequency drift rate and frequency accuracy of the BDS-3 satellite atomic clocks are generally an order of magnitude superior to those of BDS-2, and the frequency stability is about half an order of magnitude higher. Detailed changes in a number of long-term metrics have been discussed, notably the fitting residuals and the cyclic characteristics in the frequency drift rate of about half a year, and the significant improvement in frequency stability since BDS-3 was officially commissioned. The main findings can provide a reference for technical research on GNSS system operation monitoring, satellite atomic clock offset forecasting, and GNSS time scale algorithms.  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments, analyzed the data, and wrote the paper; [PERSON] and [PERSON] helped in the discussion and revision; [PERSON] completed the software code part to analyze the data. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (No. 41804076 and 61503404).  
The datasets analyzed in this study are managed by IGS.  
All authors gratefully acknowledge Deutsches geoforschungs zentrum and IGS for providing the data, mainly including clock and precise orbit determination data.  
The authors declare no conflict of interest.