## 2 Background
### Characteristics of a Space DGNSS Scenario  
#### 2.2.1 Measurements Errors  
When transitioning to a lunar GNSS scenario, the pseudorange model described in Equation (3) can be simplified. This section explains the main differences between a terrestrial and a lunar GNSS scenario as well as the potential obstacles for DGNSS ranging in space with respect to the GNSS measurements considered in this study. **Atmospheric delays**  
The typical atmospheric delays considered in GNSS navigation, being the tropospheric and ionospheric delays, and represented by \(d_{atm,k}\) in Equation (3) become less of a concern as most of the GNSS signals received at lunar altitudes did not propagate through these layers. This is due to the GNSS constellations' altitude being significantly higher than the upper limit of the Earth's ionosphere combined with the fact that the lunar GNSS users are located even higher than the GNSS constellations themselves. As a consequence, a GNSS user located in space and above the GNSS constellations typically receives GNSS signals transmitted by satellites on the other side of the Earth relative to the user's location as well as from the side. However, it will not be able to track signals from the closest transmitting satellites, as GNSS antenna patterns are pointing toward the center of the Earth. This becomes obvious when looking at Figure 2, where the ionosphere and its upper limit are depicted in orange. This has already been thoroughly analyzed and discussed in [42], which analyzes the off-boresight angles histogram of the Galileo and GPS signals which are actually tracked by a GNSS receiver simulated in the lunar Gateway orbit. It shows that over a one-week simulated period of a GNSS receiver in lunar orbit, more than 80% of the signals tracked by this lunar receiver originate from the side lobes of the transmitting satellites' antenna. Concerning the main lobe, over the 8.3\({}^{\circ}\) of angle aperture not covered by the Earth's body, only 2\({}^{\circ}\) are covered by the ionosphere, as depicted in Figure 2. A mask can hence be applied to discard the few satellites of which the signals actually crossed the ionosphere by setting a conservative upper ionosphere's limit such as 1000 km as considered in [56]. They will, therefore, be omitted in the following analyses. **Signal In Space Error (SISE)**  
For a GNSS receiver in lunar orbit, the \(C/N_{0}\) of the signals tracked are low and highly variable [41]. This implies a reduced capacity of the receiver to demodulate the navigation message as demonstrated in [42], which shows a significant reduction in the visibility of a GNSS receiver in lunar orbit when the navigation message can not be demodulated versus when it can be. More specifically, the analyses performed in [42] showed that the GPS L1 signal ephemerides can be demodulated for only 5 to 40% of the time over the one-week simulated period of a GNSS receiver in lunar orbit. Hence, given the potential capacity overload of the ground network of deep space antennas, the receiver must be capable of using ephemerides demodulated in the past, i.e., with an older age of data. As a consequence, this might increase the GNSS satellite orbit residual errors significantly with respect to terrestrial applications. These are characterized by SISE that is defined as the difference of the satellite position and time as broadcast by the navigation message and the true satellite position and time, projected on the user-satellite direction [57]. In Equation (3), they are hidden in the unmodeled errors term \(e_{i,k}^{s}\). They remain under 1 m for ground applications as stated in [49]. In [57], the characterization of the SISE 95% was performed for GPS over 4 years in the nominal range of the navigation message age of data (<3 h). However, outside of this nominal range, as explained in [58], the globally averaged SISE orbit degrades gracefully over time and is specified to remain below a 95 th-percentile value of 388 m throughout a two-week period.