## 4 Conclusions  
In this simulation study, we analyzed the impact of optical dual one-way measurements--Optical Inter-Satellite Links (OISL) and ground-space-oriented Optical Two-Way Links (OTWL)--in addition to L-band measurements for clock estimation. We analyzed the capabilities for a pure Medium Earth Orbit (MEO) constellation as well as the MEO+IGSO (Inclined Geosynchronous Orbits) and MEO+GEO (Geostationary Orbit) constellations by the mean error of the estimated clocks, the standard deviation and the Allan deviation. Furthermore, we predicted the estimated clocks and analyzed the capabilities for predictions up to one day. All scenarios were computed for two different clock types: Passive Hydrogen Maser (PHM) and Atomic Clock Ensemble in Space (ACES). While the PHM clock represents a current standard clock type, the ACES clock is an example of a future high-stability clock. We want to indicate that this work is a simulation study. Generally, the complexity of physical reality cannot be fully emulated in a simulation environment. Therefore, all the results discussed in this study are to be regarded as indicative and are not absolute performance results. With real data in the future, the presented results may be confirmed or need further tuning. As we estimated a range bias and a clock synchronization bias for each transmitter and receiver, which led to a rank-deficient normal equation matrix, we had to introduce constraints in the case of the OTWL observations. In the analysis, we had to use hard constraints for the clock synchronization biases at the level of measurement precision of 1 mm. This allowed to achieve the clock error of the estimated clocks that need a time and ranging reference in space to be implemented. Five times looser constraints already led to 7-10 times worse clock errors. In the case of the L-band+OISL scenario, the clock error is mainly dominated by the remaining mean errors of the estimated clocks. A collocated use of the L-band and OTWL in scenarios showed that the mean error of the estimated clocks can be estimated to a great extent. The L-band+OTWL scenario shows a smaller mean error of the estimated clocks on average than the L-band+OISL scenario by far. This is due to the direct relation of OTWL to the reference station, which allows for reducing the systematic effects from the L-band measurements. While the L-band-only and L-band+OTWL scenarios show a variation in the mean error for the different satellites, scenarios including the OISL measurements help to compensate for this discrepancy. This is the benefit of OISL: not only do all MEO satellites achieve about the same mean errors of the estimated clocks but also IGSO or GEO satellites do when included in the constellation. Achieving around 3 mm of the mean error of the estimated clocks on average, the L-band+OTWL+OISL scenario gives the best results by far, combining the advantages of OTWL and OISL. We could show that the L-band, OTWL and OISL are complementary. Moreover, all scenarios that include optical observations achieve the standard deviations of the estimated clocks at the mm level for the MEO, IGSO and GEO satellites. Hence, concerning positioning accuracy, the clock error from the L-band+OTWL+OISL scenario is at a similar level as the orbit error, with 1-3 mm being achievable for the L-band+OTWL+OISL scenario (compare with [17]). The use of a high-stability clock does not give an improvement for the clock estimation as long as the clocks are estimated epoch-wise. Clock modeling in the estimation procedure helps to gain from a higher frequency stability, but this is not shown in this work. Furthermore, a common troposphere estimation for the L-band and OTWL might improve the results. As the Allan deviation analysis shows, the potential of clock estimation is limited by the use of the PHM clocks for the scenarios using combinations of observation techniques. The use of the ACES clocks offers the possibility of the further improvement of the frequency stability of the estimated clocks.