## 3 Results
### Results of the Estimated Clocks
#### 3.2.1 Mean Error of the Estimated Clocks  
In this section, we analyze the mean error of the estimated clocks (true--estimated) for the different scenarios. The results shown in this section refer to simulations with the PHM clocks, but almost the same results are achieved for the ACES clocks. This is expected when estimating clocks epoch-wise. The advantage of a more stable clock is then only exploited in the prediction. For the L-band-only scenario, a substantial mean error of the estimated clocks is noticeable (see Figure 3). Due to the epoch-wise clock estimation, errors from other sources--e.g., remaining orbit errors, errors due to a wrong bias estimation and dominant troposphere errors--are shifted to the clock. The optical observations support the L-band and prevent these errors from going into the clock. OISL does not allow for errors to be put into individual satellite clocks, as all satellite clocks are strongly connected. This is the huge benefit of OISL, as all satellites are synchronized with each other. The results for the clock errors are mostly given in centimeters to relate to the positioning error, which is analyzed in this work. Hence, the scenarios including OISL show the same mean error of the estimated clocks for all satellites for each daily solution, but the mean errors are still substantial. The reason is that OISL has no direct relation to the reference station on the ground, which only allows to uniformly distribute the clock synchronization biases for an average error. For the L-band-only or L-band+OTWL scenarios, the mean error of the estimated clocks varies for each satellite. However, for the scenarios including OTWL measurements, the estimated clock synchronization bias compensates for the systematic errors to a great extent. The reason is that OTWL has a direct relation to the reference station, and OTWL forces the solution toward the optical troposphere error--no model parameters are estimated for the optical troposphere delays, which are at the level of some millimeters. In the L-band+OTWL+OISL scenario, both the arguments of OISL and OTWL apply together. Figure 3: Total error of the estimated clocks for the different combinations of observation techniques and for the 10 days of the simulation period. Each color represents a different clock. Analogous to Section 3.1, we compute the mean error of the estimated clocks per satellite and per day of the simulation period, arranging the realizations in ascending order and extract the minimum, the 5%, the mean (average), the 95% and the maximum absolute values of all realizations. Figure 4 compares the mean error of the estimated clocks for the L-band-only, L-band+OTWL, L-band+OISL and L-band+OTWL+OISL scenarios in the MEO-only constellation. On average, the L-band-only scenario achieves a mean error of the estimated clocks of around 21 cm. The scatter of the mean error of the estimated clocks for the different realizations is substantial. For the L-band+OISL scenario, the average error reduces to around 18 cm. The minimum error is at 15 cm, and the maximum error is at around 21 cm. The scatter is from the daily variation in the estimated clock synchronization biases, as all satellites achieve an almost identical mean error of the estimated clocks per daily solution (see Figure 3). The L-band+OTWL scenario achieves an average error of 0.8 cm and 3.8 cm at the maximum. The L-band+OTWL+OISL scenario achieves the best results with an average error of 0.3 cm and a maximum error of 0.7 cm. For additional IGSO satellites in the constellation, no significant changes in the mean errors of the estimated clocks are noticeable for the MEO satellites for all the scenarios compared to the MEO-only constellation. For IGSO satellites, the mean errors of the estimated clocks behave similarly overall to the MEO satellites.