# Clock Ensemble Algorithm Test in the Establishment of Space-Based Time Reference
## 4 Satellite Clock Bias Prediction
### Satellite Clock Bias Prediction  
In this paper, we fit the clock bias data sets, i.e., the bias between the satellite clock phase and the timescale, every hour with a moving window in the length of 12 h, and predict for the next 12 h at every fitting. The clock bias in the prediction arc is treated as a true value. We calculate the residual root mean square (RMS) to evaluate the prediction accuracy. The clock bias calculated with three clock ensemble algorithms is analyzed. Take time clock data from 10 June 2021 as an example. Figure 8 displays the deviations in residuals between each satellite's prediction results and the true values. The solid line in the figure represents the hydrogen clock and the cesium clock, which are fitted by a first-order polynomial model. The dotted line represents the rubidium clock, which is fitted by a quadratic polynomial model. Figure 8: \(Cont\). The prediction residual, shown in Figure 8, with durations ranging from 1 h to 12 h of the NKT algorithm and RKT algorithm, is within 0.4 ns\(\sim\)1 ns, and the general trend is rather consistent. The prediction residual of the TKT algorithm increases linearly from 0.01 ns to 0.3 ns. In terms of orders of magnitude, the prediction accuracy of the TKT algorithm is about 1-2 orders of magnitude higher than that of the NKT algorithm and RKT algorithm, and the shorter the prediction duration, the greater the difference in the prediction accuracy. To focus on the different prediction periods, we calculated the RMS of the prediction residuals of each satellite clock of three timescales with 1, 6, and 12 h and depicted their statistical results in Figure 9. In the histogram, from left to right, each cluster represents the RMS of 1, 6, and 12 h prediction residuals of the NKT algorithm, RKT algorithm, and TKT algorithm, respectively. The specific values are listed in the table below the figure. To make the TKT prediction result distinguishable, the figure adapts the upper limit of the y-axis to fit the magnitude of other satellite clocks, which makes the RMS of G08 not fully exhibited. The RMS of the prediction residual of the NKT algorithm is very close to that of the RKT algorithm, both of which are much larger than that of the TKT algorithm, no matter how long the prediction duration is. For the 16 satellites, the RMS of the prediction residual of the Galileo system is smaller than that of the BDS, and the BDS is smaller than that of the GPS. To generate a timescale, the satellite clock we used in GPS is a rubidium clock, which leads to inferior accuracy and stability to the hydrogen clock. This makes it intelligible why the prediction accuracy of the timescale generated with GPS satellite clocks is the worst. Yet it cannot explain the disparity between Galileo and BDS. Since they both employ hydrogen maser frequency standards that are approximate in accuracy and stability, there must be other factors polluting the satellite clock bias data. The clock bias series of GFZ is calculated with the methods of orbit determination and time synchronization (ODTS). As one of the estimated parameters, the clock bias has strong correlations with other parameters, such as orbit elements. Thus, the estimated error of clock bias not only comes from the measurement noise of the clock bias itself but also blends with the orbit error. It implies that the orbital dynamics modeling error for the Galileo system is smaller than that of BDS. Figure 8: The residuals between the prediction result and the true value of each satellite clock. (**a**) The prediction residual with NKT; (**b**) Prediction residual with RKT; (**c**) Prediction residual with TKT. Although both systems consist mainly of hydrogen clocks, Galileo's prediction accuracy is still better than BDS's. In addition, we compared the RMS of the residual of the three algorithms. With the extension of the prediction duration, the RMS of the prediction residual of the NKT algorithm and RKT algorithm will raise, but the growth trend is relatively slow and occasionally will decrease.