## 2 Materials and Methods  
### Overview of Previous Research  
Prior to further establishment of long-time robotic and human missions on the Moon, a consistent system for precise landing, navigation, and positioning is needed to accommodate continuous and safe work. At present, the navigation of objects located on the Lunar surface is controlled by Earth-based deep space network antennas [15]. Current investigation on navigation methodologies is based on technologies and working principles related to imaging, celestial (\"star sensors\"), inertial, and GNSS-like systems. They are introduced in following paragraphs. There are several propositions based on imaging concepts using a camera as a navigating tool. Vision-based navigation is a technique suggested by major space agencies, aiming to achieve 200 m accurate autonomous landing [16]. So called pin-point Lunar landing uses an optical navigation system based on tracking features on the images by measuring an angular rate and a velocity vector of the spacecraft. Another possibility is to identify those features using a geo-referenced database to determine the position of the spacecraft. Using this technique, the position and velocity estimation accuracy of a spacecraft reaches approximately 10 m at 0.05 m/s. It was noticed that illumination conditions represent main issues for this optical Lunar navigation system [16]. For path planning and rover control, the successor of Yutu-1, Chang'e-4 Yutu-2 rover, used an upgraded version of an autonomous navigation system called visual Simultaneous Localization and Mapping (SLAM), which is based on tracking rover moves detected as a part of an image by a photogrammetric computer [17]. ESA, as a collaborative member on the Luna-27 mission, is developing the PILOT system as a main navigation system for the landers. The system compares the images of terrain landmarks taken by a camera and landmarks pre-stored in a database on the spacecraft to perform optical recognition of the crater's landmarks for soft landing [18]. In the absence of satellite navigation systems, another navigation approach is possible, using star sensors supported by inclinometers. The Strapdown Inertial Navigation System (SINS) is a method based on a combination of two operational steps, approximate and fine navigation. The coarse positioning is used for initial alignment providing a real-time solution where all navigation errors were calculated and compensated in real time by SINS. Error corrections in SINS are done by the star sensors. Results from simulation have shown that this method can achieve high precision for rovers' autonomous navigation [19; 20]. For autonomous navigation, using only inertial navigation is not efficient due to growth of imperfections of inertial sensors which can provide relatively precise autonomy only for very short time. For that reason, a combination of inertial navigation with celestial navigation was suggested in [19; 20]. The simulation presented in [19; 21] applied the SINS method for the autonomous navigation of the rovers. In this model, starlight imaging was used, where the star sensor determines the altitude of the vehicle. The tilt angle between the horizontal plane and a vehicle is measured by a dual-axis inclinometer. Apart from the star sensor and inclinometer, attention was also paid to the utilization of precise clocks to provide real-time data and to synchronize data between two sub-segments of the compound navigation system. Misalignment of the star sensor and inclinometer can cause a significant positioning error. To avoid this systematic influence, the QUaternion ESTimator (QUEST) calibration method is introduced. This model can provide continuous measurements for only a few minutes, providing autonomous positioning accuracy from 20 m to 70 m in distance. To support robotic missions, a constellation of the small satellites is considered as a technology that could resolve the navigation issue.