## 2 Materials and Methods
### Overview of Previous Research
It was suggested that the satellites might be placed into halo orbits in Earth-Moon libration points or LaGrange points [22; 23]. An extension of the GLONASS navigation system is proposed in [24] to modify the satellites using additional narrow-beam antennas directed to the Moon. It would be implemented in the form of a constellation of six navigation satellites located in near-circular orbits at ~100,000 km height in two perpendicular planes with an inclination of 90\({}^{\circ}\). Standard Satellite Navigation Equipment (SNE), a transmitter/receiver, and modified software for Moon usage would be integrated onboard a Lunar orbiting spacecraft and objects based on the Lunar surface. Simulation of this conceptual design has shown that position and velocity of the spacecraft can reach 15 m (1\(\sigma\)) in position and 0.02 m/s in velocity. For the objects based on the Lunar surface, it was highlighted that instantaneous navigation solutions can be provided only if the geodetic map with high precision is memorized in the SNE. Under this condition, if the objects are in the visible Lunar disk, the navigation accuracy is 10 m (1\(\sigma\)). While objects move away from the center, the accuracy degrades (e.g., for 60\({}^{\circ}\) deviations from the disk, errors can reach 20 m to 100 m). It was concluded that the proposed method cannot be used for navigating the objects on the far side of the Moon [24]. Yet another example is a GPS-based local area positioning system developed by the Aerospace Robotics Laboratory (ARL) at Stanford University for the planet Mars. The ground-located pseudosatellites replace the space-located satellite constellation with the goal of providing similar performance to GNSS on the Earth. Enabling localization is directed by a Self-Calibrating Pseudolite Array (SCPA). A network of transceivers is a way to expand the coverage of the system. The mathematical model of positioning the transceivers, which will both transmit and receive GNSS-like signals, used SCPA [25]. Field tests were performed using a prototype of NASA Aims K-9 Mars rover achieving code- and carrier-level positioning less than 3.7 m and 8.8 cm, respectively [26; 27]. In the case of open-pit mining, ARL at Stanford University developed a guidance system for transport and operational vehicles based on pseudo-assisted Carrier-Phase Differential GPS. With this system, a narrow angle of open sky above the pit and a small number of visible satellites will be mitigated by six or eight pseudolites placed around the rim. This system will augment the existing GPS constellation and ensure the availability of navigation anywhere inside the pit [27; 28]. NASA envisaged the Artemis program to develop a special receiver which will be able to receive signals from the Global Positioning System (GPS). This receiver is based on the same working principles as receivers used for high-altitude navigation in Magnetospheric Multiscale mission (MMS) and Geostationary Operational Environmental Satellites (GOES) in combination with the GPS processing power of NavCube receivers [29]. To this day, there is no satellite navigation system which will help spacecraft to be navigated autonomously to the Moon. This is only supported by constant controlling from the Earth, which will be extremely complicated when multiple missions are shuttling and maneuvering backwards and forwards. Dozens of missions to the Moon are planned and some of them already started, with initial executions such as NASA's Artemis 1 and ispace's HAKUTO-R Missions 1 [30; 31]. Experiences gained via the Artemis 1 mission, where the capabilities of the Orion's systems were tested, showed that loss of communication with spacecraft can happen easily at the moment when the vehicle is located behind the Moon. Moving through space, the Earth is the only point of reference when a returning ping signal will provide the position of the spacecraft. If there is an obstacle between them, there will be plenty of blind spots and high risk of a complete loss of communication.