## 4 Results and Analysis
### Results of the Simulation Data Set  
In this subsection, the simulation data are utilized to validate how our approach performs when data interruption occurs. In Figure 5, each panel shows three types of time series of clock offset estimation with a time resolution of 10 min data interruption on BRUX. Other stations perform a similar feature; hence, we will no longer display them in detail. Furthermore, the clock difference in the time series of scheme 1 and scheme 2, with respect to the results of the complete data with the between-epoch constraint model, is displayed in Figure 6 for a data interruption of 10 min. Combining Figures 5 and 6 results in two findings. For one thing, as we noted earlier, the clock offset will re-converge, especially for scheme 1, when the data interruption occurs. Obviously, the results from the complete data show some fluctuation (see Figure 6), as evidenced by the fact that the ambiguity parameters cannot instantaneously yield stable results, although we have constrained 20 consecutive epochs. Additionally, compared with the results from scheme 1, scheme 2 shows no obvious jump when the data interruption occurs. This can be explained by the fact that a prior clock offset is constrained by the prediction results. For a better quantification, we calculated the RMS of the two schemes using the corresponding time series of the complete data as a reference; the results are presented in Table 4. Note that we have deleted the gross errors before calculating the RMS values. The maximum RMS values for scheme 1 are 0.52 ns for all stations with 10-, 30-, 60-, and 90-min data interruptions, while the corresponding maximum RMS values are 0.19, 0.18, 0.20, 0.23 and 0.26 ns for scheme 2. The improvement percentage of scheme 2 shows that the average RMS values of all stations are significantly reduced, i.e., by 66.03% from 0.43 to 0.14 ns, by 64.91% from 0.44 to 0.15 ns, by 57.47% from 0.43 to 0.18 ns, and by 51.67% from 0.44 to 0.21 ns for 10-, 30-, 60-, and 90-min data interruptions, respectively. This implies that scheme 1 is not as good as our approach. We surmise this may be attributed to two reasons. First, the between-epoch constraint model will reduce the noise of the clock offset. Second, our approach does not produce jumps that may accelerate clock offset convergence. Figure 4: Prediction error of the adaptive clock prediction model at station BRUX at 10, 30, 60 and 90 min. Figure 5: Clock offset time series for scheme 1 (**blue**) and scheme 2 (**red**) when a data interruption of 10 min occurs; the yellow colour represents the solutions of the complete data using the between-epoch constraint model; the bottom figure is a partial amplification of the top figure. Figure 6: Clock difference time series using scheme 1 (**blue**) and scheme 2 (**red**) with respect to the results of the complete data using the between-epoch constraint model when a data interruption of 10 min occurs; the bottom figure is a partial amplification of the top figure. The Allan deviation (ADEV) is employed to obtain the frequency stability [8; 28], which is also utilized to further assess the performance of RT-PPP solutions, using five kinds of precise products. In this contribution, Stable32 software ([[http://www.wriley.com/](http://www.wriley.com/)]([http://www.wriley.com/](http://www.wriley.com/))) is applied to calculate ADEV. Note that the gross error of all RT-PPP solutions is eliminated before computing ADEV by using Stable32 software (Hamilton Technical Services, Beaufort, SC, USA). With the different lengths of the missing observations and two scenarios, Figures 7 and 8 demonstrate the effects of the Allan deviation based on six stations. Many similarities can be found from the figures. From 10 to 90 min, regardless of the length of the observation interruption, the results from all the selected stations indicate that scheme 2 is more stable than scheme 1. The magnitude of the improvement at the six stations is very similar. This is because the same random-walk model is constrained by the atomic clock.