## 2 Simulation Setup and Estimation
### Satellite Constellations and Ground Station Network  
We selected the Galileo MEO satellite constellation--the satellite properties are based on the first-generation Galileo satellites--as a typical GNSS satellite constellation and expanded the constellation by either four GEO or IGSO satellites. Analogous to the scheme of the GETRIS concept, we globally distributed the GSO satellites around the Earth [2,3]. An overview of the three satellite types used in this work is given in Table 1. We analyzed the results for the MEO-only, MEO+IGSO and MEO+GEO constellations. As the ground station network used for the L-band and OTUVL measurements consists of 16 ground stations (see Figure 1), the GSO satellites had a different total number of visible ground stations. This allowed for an analysis of the necessary ground station visibility as well.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Satellite Types** & **MEO** & **IGSO** & **GEO** \\ \hline Number of satellites in constellations & 24 & 4 & 4 \\ \hline \multirow{6}{*}{Constellation details} & \multirow{6}{*}{Walker constellation (\(56^{\circ}\): \(24/3/1\)).} & Equatorial passes of the & \multirow{2}{*}{Placed at the geographical \(10^{\circ}\), \(100^{\circ}\), \(190^{\circ}\) and \(280^{\circ}\) to obtain a homogeneous distribution around the Earth; inclination \(52^{\circ}\). With respect to the Earth-centered inertial frame, all GEO satellites are on the same orbital plane.} & \multirow{2}{*}{Placed at the geographical \(10^{\circ}\), \(100^{\circ}\), \(190^{\circ}\) and \(280^{\circ}\) to obtain a homogeneous distribution around the Earth. With respect to the Earth-centered inertial frame, all GEO satellites are on the same orbital plane.} & \multirow{2}{*}{Monopared \(280^{\circ}\) to obtain a homogeneous distribution around the Earth. With respect to the Earth-centered inertial frame, all IGSO satellites are on the same orbital plane.} & \multirow{2}{*}{Monopared \(280^{\circ}\) to obtain a homogeneous distribution around the Earth.  
Our analysis was based on a period of 10 days, the Galileo MEO repeat cycle. We processed 24 h observations, and the results were taken from one-day arcs. All satellites were each equipped with one clock, to which all the observations types refer to. For the first analysis, we emulated a PHM clock on each satellite. The PHM clocks were simulated with white frequency noise at the level of 1 \(\times\) 10\({}^{-12}\) and random walk at the level of 3.9 \(\times\) 10\({}^{-16}\) when integrating over one second. A quadratic phase drift was not simulated. For comparison, we performed further simulations with the ACES clocks, carried by all satellites in the constellation, representing a high-stability clock. We simulated the AHM of the ACES clock with flicker phase noise at the level of 1.4 \(\times\) 10\({}^{-13}\), white frequency noise at the level of 3 \(\times\) 10\({}^{-14}\) and flicker frequency noise at the level of 1.35 \(\times\) 10\({}^{-15}\), when integrating over one second. PHARAO was simulated with white frequency noise at the level of 1 \(\times\) 10\({}^{-13}\) when integrating over one second. The ACES clock noise is composed in such a way that the lowest noise always dominates. As PHARAO is a frequency standard, the ACES clock is expected to have no quadratic phase drift. We are aware that high-stability clock types such as the ACES clock will not be used as a standard GNSS satellite clock in the near future. Nevertheless, in this work we want to analyze the benefit when using the ACES clocks for GSO and MEO satellites.