## 3 Results
### Simulated Configuration Setups  
Analysis and results in this research are performed on the Shackleton Crater; thus, DEM [48] is trimmed to match the area of interest. To simulate various LRNTS configuration setups, a number of points are digitized over the Shackleton DEM in order to obtain their 3D approximate positions. The points locations are not directed by any special rule, but rather spread around the crater. In Figure 4, the Shackleton Crater DEM is represented both as a false-color palette and a 300 m equidistance contour map overlapped with the possible locations of LRNTS transceiver nodes (marked as white triangles with their locally assigned IDs). The optimization of LRNTS treats locations and number of transceivers that would assure the best positioning performance within the crater. The optimal configuration of the LRNTS network should provide:  
* enough measurands (i.e., number of transceiver nodes) for self-calibration of the system;
* signal coverage throughout (or, if not possible, for the majority of) the crater's interior;  
Figure 4: Candidate places for LRNTS transceivers. * reliable signal transmission by minimizing multipath effects. The locations of the transceivers should allow the undisturbed mutual transmitting and receiving of navigation messages between all transceivers. The same goes for spreading the signals towards the crater bottom, where the surveying of construction sites will be done. The signals with lower elevation angles (closer to the ground) can experience multipath effects, since the transceivers are placed on the ground, not in space. Further analysis of Shackleton topography is performed by creating a slope map. The frequency histogram (Figure 5) of the Shackleton slope map shows that the majority of the crater is at cca 50\({}^{\circ}\) slope, which should be taken into account for future LRNTS utilization plans in order to avoid possible multipath effects during the transmission of transceivers' signals. The histogram values in Figure 5 are expressed in pixels. In addition to the careful planning of LRNTS transceivers' distribution in the sense of accuracy, the number and location of the transceivers should be optimized for the availability of the signals as well. Assuming future use of GNSS receivers for in-crater positioning, permanent visibility of at least four transceivers must be assured. Furthermore, for economic reasons, the total number of the transceiver nodes should be minimized. Although a receiver can solve its position by collecting observations from only four satellites, experiences from terrestrial GNSS positioning show that, in realistic scenarios, it is not enough because of temporal obstacles that violate visibility of the sky. In the case of ground-based transceivers, that problem could arise as well. In addition, there is a practical maximum of the number of satellites where there is no significant increase in accuracy or reliability. Therefore, the selection of the number of transceivers per configuration and their locations is carried out by examining user experiences in terrestrial GNSS positioning. First simulations involve 24 different configurations, from 5 to 24 transceivers. As stated before, the only criterion for choosing locations for the transceivers was their approximate uniform distribution along the crater. The positioning by four transceivers could be violated in the case of obstacles or a poor configuration. Therefore, we put 5 as a minimum for the number of LRNTS transceivers and 24 as a maximum, although the maximal number of the transceivers is theoretically not limited. However, increasing the number of LRNTS transceivers does not increase accuracy and reliability linearly. We have randomly chosen 33 different configurations. Among them, 12 are presented in this paper. Others are rejected because of their bad numerical figures. The setups involve between 6 and 11 LRNTS transceivers.