## 2 Algorithm
### Design Parameters  
The spatial position of two satellites is one of the most important design parameters that directly impact the rover position accuracy. It is known that in order to acquire an accurate user position, a small DOP value is required, and accordingly, the distance between two satellites has to be large. In comparison, in order to keep both satellites in the rover's view for a long time, a short distance between two satellites is preferable. As a result, these two requirements conflict with each other, and both impacts must be carefully considered to find the best compromise point in the satellite trajectory selection. Figure 2 shows availability, which is the percentage of time at which both satellites are in the rover's view to total mission time, and the Total GDOP value at several orbit conditions: circular orbits with four different satellite altitudes (300 km, 600 km, 900 km, 2100 km) and five different orbital phase differences \(\Delta\Omega\) between two satellites (5 deg, 15 deg, 25 deg, 35 deg). Rover/lander positions were fixed to the south-pole (-90 deg, 90 deg), and satellite orbital inclination was fixed to 110 deg without losing the generality of the discussion. As seen in Figure 2, availability and Total GDOP have a negative correlation. At the same time, there are some good compromise points, such as \"altitude 300 km/phase difference 15 deg,\" where both availability and Total GDOP have moderate values. The value of availability is also an important factor to consider for rover operation. In the case of two low lunar orbiters, the value of availability is limited up to around 15%. However, we think that this value is compatible with a mission that requires a higher availability value for long-range exploration: essentially, the rover can rely on its inertial navigation system (INS) when pseudorange-based navigation is not available and can retrieve the precise position once the pseudorange-based navigation is back in service. In order to keep the position error within 100 m all the time, the design margin should be considered in a way such that the navigation accuracy of the dual-satellite pseudorange navigation has a sufficient margin to 100 m, which is used to compensate for the position error induced by INS-based navigation during the time that dual-satellite pseudorange navigation is not available. Another consideration is the required power for RF communication between satellites and the rover/lander. In general, the higher the orbit altitudes, the more power that is required by RF communication, and the free-space path loss increases proportionally to the square of the distance between the satellites and the rover/lander. In order to reduce the system burden for RF power on the satellite side as well as on the rover and lander side, a lower orbit, such as 300 km, is preferable. Furthermore, for a long-period mission, orbit perturbation should also be considered. As a result of cis-lunar perturbation, some important orbital parameters, such as altitude and phase difference, are subject to change over time. In this study, the main focus is on algorithm verification and performance evaluation under specific conditions. Therefore, the selection of satellite trajectories used in the next section was not optimal, although it was good enough to maintain the phase difference between 15.0 deg and 17.5 deg over the course of the simulation period. Additionally, it is well-known that there are several stable orbit families that repeat ground tracks on the Moon, known as repeat ground track (RGT) orbits. For example, [PERSON] successfully proved that stable or near-stable families of solutions exist for a full range of average inclinations and altitudes, making them suitable for  
Figure 2: Availability and Total GDOP under different orbital conditions: circular orbits with four different satellite altitudes (300 km **(a)**, 600 km **(b)**, 900 km **(c)**, 2100 km **(d)**) and five different orbital phase differences \(\Delta\Omega\) between two satellites (5 deg, 15 deg, 25 deg, 35 deg).