## 3 Results
### Results of the Estimated Clocks
#### 3.2.1 Mean Error of the Estimated Clocks
However, due to the varying number of visible ground stations for each of the four IGSO satellites and, hence, the varying numbers of L-band observations, the scatter between the minimum and maximum values of the mean error of the estimated clock is much larger in the L-band-only scenario than for the MEO satellites. For L-band-only the best realization is at around 2 cm and the worst at around 70 cm. Although the number of OTWL observations varies with the number of visible ground stations for each IGSO, no significant degradation of the mean error of the estimated clocks shows up for the L-band+OTWL scenario, when analyzing the different realizations, compared to the results achieved for the MEO satellites. The same behavior is noticeable for the L-band+OISL scenario. However, the L-band+OTWL+OISL scenario shows about 1 cm worse mean errors of the estimated clocks for some realizations for the IGSO satellites. When averaging the mean errors of the estimated clocks per satellite over 10 days (see Figure 5), it is noticeable for the L-band+OTWL and L-band+OTWL+OISL scenarios that one IGSO satellite has a larger mean error of the estimated clock than the other IGSO satellite or all the MEO satellites. Figure 4: Analysis of the mean error of the estimated clocks, averaged for the 24 MEO satellites in the MEO-only constellation. The plot shows the mean error 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+GEO constellation, the L-band-only scenario achieves worse mean errors of the estimated clocks for the MEO satellites, compared to the MEO-only constellation. The degradation in the L-band-only scenario is at around 3 cm for the mean and the 95% values and 9 cm for the maximum value. For the scenarios with combinations of observation techniques, the mean errors of the estimated clocks are similar to the results from the MEO-only constellation. For the GEO satellites, the coverage by the ground stations largely affects the results of the L-band-only and L-band+OTWL scenarios. While each IGSO satellite has visibility of at least four ground stations, some GEO satellites see less: GEO-1 sees two stations, GEO-2 sees five stations, GEO-3 sees one station, and GEO-4 sees three stations. Due to this, the normal equation matrix in the estimation is singular for some GEO satellites in the L-band-only and L-band+OTWL scenarios, as we estimate the orbit parameters in parallel to the clock parameters. Therefore, we have to exclude GEO-1, -3 and -4 from the L-band-only analysis. Due to the additional two-way observations in the L-band+OTWL scenario, the clocks can be synchronized with only three ground stations when estimating the orbit and clock parameters in parallel. Hence, we only exclude GEO-1 and -3 for the L-band+OTWL scenario. The mean clock errors of the estimated clocks, averaged over 10 days, are shown in Figure 6. For the GEO satellites, similar mean errors of the estimated clocks can be achieved compared to the MEO satellites, for all scenarios. For MEO, IGSO and GEO satellites, the main outcome is that the OISL measurements homogenize the mean errors of the estimated clocks for all satellites, which is especially noticeable when averaging the results per satellite over several days. This is expected from OISL and underlines the advantage of having steady clock synchronizations between satellites at different altitudes. Although the OTWL observations in addition to the L-band measurements cannot synchronize satellite clocks to each other, the overall mean error of the estimated clocks is much smaller compared to the L-band+OISL scenario, as OTWL has a direct relation to the reference clock and, hence, helps to reduce the L-band's systematic errors. The L-band+OTWL+OISL scenario combines the advantages of OISL and OTWL.