###### Abstract  
In view of the upcoming missions to obtain resources from the lunar surface, it is essential to have highly-accurate navigation systems to locate surface vehicles in shadowed regions. In response, we propose a dual-satellite lunar navigation system that is based on a multi-epoch double-differenced pseudorange observations (MDPO) algorithm. We used multi-epoch observations in a new way that reduces the number of navigation satellites required. In addition, the double-differenced pseudorange is used in order to eliminate the bias effects of the satellite and user clocks that conventional dual-satellite navigation algorithms did not fully take into account. Furthermore, a pre-known lunar digital elevation model is used to reduce the number of observations. The theoretical behavior of the MDPO algorithm was confirmed by simulation and the results indicate that user position accuracy can be several tens of meters with 95% probability (2 drms) within a one-minute observation. GNSS; navigation; microsatellite; nanosatellite; moon; lunar rover; interplanetary missions +
Footnote †: journal:  
0000-0002-4091-558X][PERSON] 0000-0002-0002-0002-3886][PERSON] 0000-0002-0002-3886-2288][PERSON] 0000-0002-0002-3886-2288][PERSON] 0000-0002-0002-3886-2288][PERSON] 0000-0002-0002-3886-2288][PERSON] 0000-0002-0002-3886-2288][PERSON] 0000-0002-3886-2288][PERSON] 0000-0002-3886-2288][PERSON] 0000-0002-3886-2288][PERSON] 0000-0002-3886-2288][PERSON] 0000-0002-3886-2288][PERSON] 0000-0002-3886-2288][PERSON] 0000-0002-3886-22888][PERSON] 0000-0002-3886-22888][PERSON] 0000-0002-3886-22888][PERSON] 0000-0002-3886-22888][PERSON] 0000-0002-3886-22888][PERSON] 0000-0002-3886-22888][PERSON] 0000-0002-3886-228888][PERSON] 0000-0002-3886-22 missions. In summary, our target in this study is a low-cost micro-sized lunar navigation satellite system that can provide precise locations, i.e., within 100 m, for multiple small rovers. To date, navigation technologies for the shadowed regions have been studied extensively. One study investigated the use of rovers with visual sensor-based navigation using a stereo camera with artificial light to explore the PSRs [3; 4]. However, considering that a huge amount of power (calculated to be 864 W based on [3; 4]) is required to provide sufficient light to illuminate a broad and continuous area, this approach is limited to large-scale rovers, i.e., rovers that weigh several hundred kilograms. Another study was conducted that considered the use of another type of visual sensor-based navigation, i.e., laser triangulation systems, on rovers to identify terrain profiles in the shadowed regions [3]. A laser triangulation system effectively uses its own light source by limiting the sensing area, and its power consumption can be reduced to a few watts by carefully selecting short distances, i.e., a few meters [3]. However, such applications have an inherent problem in that they cannot determine distances if the lunar surface is flat and repetitive and if there are no landmarks that can be used to assess distances [5]. Therefore, given the uncertainty of lunar terrains, there is significant risk associated with using visual sensor-based methods that have limited sensing ranges. Another study investigated a combination of the rover's inertia accelerometers and star tracker measurements for navigating rovers on the lunar surface [6]. In order to achieve 100-m position accuracy with this method, theoretically, 11.8-arcsecond user attitude determination is required, which is not feasible in the presence of sensor alignment errors. Another recent study introduced the idea of deploying orbiters in Halo orbits to establish a lunar global navigation satellite system (Lunar GNSS) analogous to Earth GNSS [7; 8].