## 3 Results
### Results of the Estimated Clocks
#### 3.2.2 Standard Deviation of the Estimated Clocks  
In this section, we analyze the standard deviation of the estimated clocks. The results shown in this section refer to the simulations with the PHM clocks but are analogous to the mean errors of the estimated clocks; the estimation results are similar when using the ACES clocks.  
For the MEO satellites, the standard deviations of the estimated clocks are similar for the MEO-only and MEO+IGSO constellations. The results according to 240 realizations is shown in Figure 7 as an example for the MEO+IGSO constellation. The L-band-only scenario still has cm level standard deviations and a remarkable discrepancy between the minimum (around 2.7 cm) and maximum (around 18 cm) values. On the other hand, the standard deviations of the estimated clocks are at the mm level for the scenarios that include optical links (see also Figure 3). In addition, when the daily standard deviations per satellite are averaged over 10 days, the scatter of the results between the satellites is negligibly small with mean values of around 4-7 mm. The L-band-only scenario has a maximum scatter of about 4 cm and a mean of around 8 cm.  
Figure 6: Analysis of the mean error of the estimated clocks by computing the mean per satellite per day and then averaging over the 10 days of the simulation period per satellite. Each blue bar is related to one of the 24 MEO; the red bars relate to the GEO satellites in the MEO+GEO constellation.  
Figure 7: Analysis of the standard deviation of the estimated clocks for the 24 MEO satellites in the MEO+IGSO constellation. The plot shows the standard deviation of the estimated clocks as a function of the type of observables used. The minimum, mean (average) and maximum values as well as the values bounding the 5% or 95% of the results are reported.  
For the MEO satellites in the MEO+GEO constellation, the daily results for the standard deviation of the estimated clocks are similar to the results of the MEO-only and MEO+IGSO constellations for the scenarios that include optical links. The L-band-only scenario shows worse results. Compared to the MEO-only and MEO+IGSO constellations, the degradation factor is around 1.8 for the mean value and around 2.7 for the 95% and the maximum value. The reason for the degradation in the L-band-only scenario is the correlation between the troposphere (visible in the estimated parameters of the tropospheric wet zenith delay) and clock parameters, as the final MEO orbit errors are rather smaller when adding the GEO satellites to the constellation (compare [17]).  
Analyzing the scenarios with GSO satellites in the constellation, in the L-band-only scenario the best realization (minimum value) for the IGSO satellites is at around 5.7 cm, while the worst (maximum value) is at around 44 cm. Averaged over 10 days, the best IGSO achieves a standard deviation of the estimated clocks of around 15 cm and around 32 cm for the worst. The GEO satellite with good ground station coverage achieves around 26 cm for the best realization and around 114 cm for the worst. Averaged over 10 days, the standard deviation is at around 58 cm. Hence, the IGSO satellites achieve smaller standard deviations of the estimated clocks than the GEO satellites when having only L-band measurements. However, this can be traced back to the total number of visible ground stations.  
For the scenarios with optical links included, the standard deviations of the estimated clocks for all IGSO satellites in the MEO+IGSO constellation as well as for all GEO satellites in the MEO+GEO constellation are at a similar level as for the MEO satellites. Hence, the optical links stabilize the clock errors of the MEO as well as the GSO satellites overall, to a great extent.