## 3 Results
### Clock Prediction  
In this section, we analyze the possibilities for the prediction of clocks when using the different combinations of observation techniques. The prediction is performed for up to one day. The PHM clocks we use in this work are simulated from the noise taken from an Allan deviation (see the true clocks shown in Figure 8). We did not simulate a quadratic phase drift for the PHM clocks. We are aware that in reality the PHM also shows a quadratic phase drift, but for short prediction periods of up to about one day the effect of a quadratic phase drift is barely noticeable, as tested in a pre-analysis using the true clocks. On the other hand, the ACES clock is expected to have no quadratic phase drift, as PHARAO is a frequency standard. Hence, our clock prediction model reduces to a linear fitting model of the estimation interval of one day. We optimize the fit length for each scenario to achieve the overall best prediction results. For each scenario, we compute the 95 the percentile from all realizations at different prediction times. As a comparative value, we also include the prediction results related to the true clocks. This value can also be seen as the best possible clock prediction value. Figure 9 shows the 95% prediction values for the MEO satellites in the MEO-only constellation when using the PHM clocks in the simulation. Similar results can be achieved for the MEO satellites in the MEO+IGSO or MEO+GEO constellations. For the L-band-only scenario, a fit length of 12 h gives the best results, while the scenarios including  
Figure 8: Allan deviation using PHM (**left**) and ACES (**right**) clocks in the simulation study. Results are for the MEO satellite with respect to the different combinations of observation techniques. The black dots refer to the true PHM and ACES clocks. optical observation techniques as well as the true clocks achieved the best results for a fit length of 6 h.  
After 20 min of prediction, the values are mainly dominated by the remaining mean errors of the estimated clocks. With the L-band+OISL scenario, around 51-55% of improvement was noticeable compared to the L-band-only scenario. The L-band+OTWL and L-band+OTWL+OISL scenarios achieve the best results by far, with an improvement of around 93-94% with respect to the L-band-only scenario and of around 84-88% in relation to the L-band+OISL scenario. The L-band+OTWL+OISL scenario is almost at the level of the true clock prediction errors. This is noticeable for all the prediction times shown and again underlines that the PHM is limiting the potential of the L-band+OTWL and L-band+OTWL+OISL scenarios for the clocks' prediction. For longer prediction times, the percentage discrepancy between the different scenarios decreases. After a prediction of 8-12 h, the linear fitting starts to dominate the clock prediction errors. At a prediction time of one day, the L-band-only scenario achieves around 124 cm. The improvement when using the L-band+OISL scenario is at around 15% in relation to the L-band-only scenario. With a clock error of around 97 cm, the L-band+OTWL and L-band+OTWL+OISL scenarios improve by 22% compared to the L-band-only scenario. For GSO satellites, the results concerning the L-band-only and L-band+OTWL scenarios are highly dependent on the number of ground stations each of the satellites can see. For the L-band-only scenario, the results are statistically not reliable. Furthermore, in the case of the L-band+OTWL scenario, there is a huge spread in the clock error of the prediction that does not give a reliable analysis foundation. Therefore, we only analyze the scenarios including OISL measurements, as those deliver more balanced prediction errors for the clocks and a better statistic. Almost the same results for the clock prediction are obtained for the IGSO and GEO satellites. The results are also quite similar to those of the MEO satellites for short prediction times.