# Clock Ensemble Algorithm Test in the Establishment of Space-Based Time Reference
## 3 Experimental Analysis
### Frequency Stability of the Timescales Generated by the Three Algorithms
This is because, for a clock set composed of clocks with good short-term stability and clocks with good long-term stability, the natural Kalman algorithm always tends to optimize the long-term stability without considering the short-term stability. The reduced Kalman algorithm, on the other hand, can synthesize the performance of clocks with varying performance to produce a result with greater stability over the entire sampling time range. However, in this experiment, the clock is primarily hydrogen clocks, and no clock with good short-term stability is available for optimization. As a result, when compared to the natural Kalman algorithm, the reduced Kalman algorithm only slightly \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time Series** & **Allan Deviation** & **Allan Deviation** \\  & **(\(\tau\) = 300 s)** & **(\(\tau\) = 86,400 s)** \\ \hline TA\_A & 7.50 \(\times\) 10\({}^{-14}\) & 5.93 \(\times\) 10\({}^{-15}\) \\ TA\_B & 1.10 \(\times\) 10\({}^{-13}\) & 9.10 \(\times\) 10\({}^{-15}\) \\ TA\_C & 3.06 \(\times\) 10\({}^{-13}\) & 1.12 \(\times\) 10\({}^{-14}\) \\ TA\_D & 2.68 \(\times\) 10\({}^{-14}\) & 5.27 \(\times\) 10\({}^{-15}\) \\ TA\_A\_TA\_B & 1.35 \(\times\) 10\({}^{-13}\) & 1.08 \(\times\) 10\({}^{-14}\) \\ TA\_A\_TA\_C & 3.15 \(\times\) 10\({}^{-13}\) & 1.24 \(\times\) 10\({}^{-14}\) \\ TA\_A\_TA\_D & 8.02 \(\times\) 10\({}^{-14}\) & 8.37 \(\times\) 10\({}^{-15}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Allan deviation of each group (RKT). Figure 3: Allan deviations of RKT. improves short-term stability while having little effect on medium and long-term stability. In addition, as mentioned above, the obvious slopes of 1 and \(-\)1 can be seen in Figure 3, indicating that the generated timescales still have WFM and RWFM. For the TKT algorithm, the four groups of time deviation need to be reconstructed using the first-stage filtering to obtain the reconstructed time deviation and then generate timescales according to different weights. The weights are also proportional to the inverse of the Allan deviation with a sampling interval of 86,400 s. The overlapping Allan deviation of the reconstructed time deviation is shown in Figure 4. The 86,400 s frequency stability of the reconstructed time deviation and the unreconstructed time deviation is given in Figure 5, and the values are shown in the table below. In the figure, blue represents the Allan deviation of the unreconstructed time deviation, and red represents the Allan deviation of the reconstructed time deviation. The sampling interval is 86,400 s. It can be seen that the short-term frequency stability of the reconstructed time deviation has been greatly improved, and the Allan deviation with a sampling interval of 86,400 s is improved by 0.1 to 1 order of magnitude. Figure 4: Allan deviations of reconstructed time deviation. Figure 5: Allan deviation of reconstructed and unreconstructed time deviation. Red represents the reconstructed time deviation; blue represents the unreconstructed time deviation. The sampling interval is 86,400 s.  
1 disappears and becomes a continuation of the part with slope \(-1\). This means that the generated time scale is only RWFM, without WFM. This is consistent with the algorithm introduction in Section 2.4. In addition, for the current three kinds of onboard clocks, no matter which clock ensemble algorithm is chosen, as expected, the hydrogen clock is more stable than the rubidium clock, and the rubidium clock is more stable than the cesium clock. Therefore, hydrogen clocks are a better choice when higher frequency stability is needed to establish space-based time references. The frequency stability of the timescale is an approach to the value of commonly used timescales on the ground [52; 53]. For the NKT algorithm, the generated timescale fully considers the short-term stability performance of each satellite clock. The clock with better short-term stability will have more weight.