## 2 Simulation Setup and Estimation
### Simulated Obervation Techniques  
The simulated observation types for the study are the common GNSS L-band as well as optical ranging and time transfer measurements: OISL, as a dual one-way satellite-to-satellite measurement concept, and OTWL, as the dual one-way ground-to satellite counterpart. An overview of the different links and their simulation procedures is given in Table 2.  
Figure 1: Ground station network used in this study.  
In our simulations, it is assumed that each satellite is equipped with one terminal to perform OTWL measurements in the L-band+OTWL scenario. For OTWL, a ground station can, thus, connect with one satellite per epoch. In the following epoch, the ground station tracks the nearest available satellite by its elevation and azimuth to avoid long-distance telescope movements. The OTWL scheduling algorithm is optimized to avoid a ground station connecting with the same satellite in consecutive epochs. The minimum OTWL measurement elevation, as seen from the ground stations, is 30\({}^{\circ}\). A more detailed description of the OTWL scheduling algorithm is given in [16].  
Furthermore, we assumed that each satellite is equipped with one terminal to perform OISL measurements in the L-band+OISL scenario. The scheduling was an any-to-any scenario. The connectivity scheme was adapted from [27]. In the case of MEO+IGSO and MEO+GEO constellations, the IGSO or GEO satellites were integrated alongside the MEO satellites in the any-to-any link connectivity scheme, such that no GSO satellite connects to another GSO satellite in successive epochs.  
For the L-band+OTWL+OISL scenario, the satellites were assumed to be equipped with two optical terminals: one to exclusively perform OISL measurements and the other to exclusively perform OTWL measurements.  
In this study, we combined the three observation techniques in several ways, such as the L-band+OTWL, L-band+OISL and L-band+OTWL+OISL scenarios, and compared the results to the L-band-only scenario. We also performed the optical-only measurement technique scenario OTWL+OISL; however, in this scenario the clocks are singular [17]. Therefore, we do not consider the OTWL+OISL scenario in this work. Furthermore, we neglect relativistic effects on the clocks. No full recovery of the relativistic influences of the orbit may further disturb clock synchronization.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Measurement Techniques** & **L-Band** & **OTWL** & **OISL** \\ \hline Simulation & \begin{tabular}{c} Two-frequency code and \\ phase measurements in E1 \\ and E5a. \\ \end{tabular} & Dual one-way range measurements and clock \\ \end{tabular} \\ \hline Simulation details & \begin{tabular}{c} Ionosphere free \\ linear combination. \\ \end{tabular} & \
\begin{tabular}{c} Scheduling according to [16]: \\ one OTWL terminal per \\ satellite; a ground station \\ can connect to one satellite \\ per epoch; long distance \\ telescope movements for the \\ ground stations are avoided \\ when switching to the next \\ satellite; minimum \\ observation elevation is 30\({}^{\circ}\), \\ seen from ground stations. \\ \end{tabular} &
\begin{tabular}{c} Scheduling adapted from the \\ connectivity scheme by [27]. \\ Any-to-any scenario with \\ bidirectional links. One OISL \\ terminal per satellite. \\ \end{tabular} \\ \hline Sampling rate in seconds & 60 & 60 & 60 \\ \hline Number of used satellites & 24 MEO satellites, optionally 4 additional IGSO or GEO satellites. \\ \hline Number of used ground stations & 16 & 16 & - \\ \hline Number of simulated \\ measurements per day: & 408,740, in code and phase. & 43,400 & 32,290 \\ MEO-only constellation & & \\ \hline Number of simulated \\ measurements per day: & 482,830/478,900, \\ MEO+ICSO/GEO constellation & & in code and phase. & 45,040/44,950 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulated measurement techniques.