The number of Moon missions is increasing, but to facilitate these missions, an improved approach for lunar navigation is required. The proposed strategy is to deploy a constellation in Polar or Equatorial Medium Earth Orbits (PECMEO) based on GNSS technology, which can be utilised as universal lunar navigation system: the Lunar Positioning System (LPS). The system will provide navigation for lunar missions on a more autonomous base and without limitations on the number of receivers. However, for the nine LPS navigation satellites to provide accurate positioning for lunar objects, it is crucial that the positions of the satellites themselves are estimated with high accuracy. This is because the ephemeris error of navigation satellites is a dominant factor in the position error of lunar objects. This thesis investigates the achievable position estimation accuracy for the LPS. The estimation is based on observations provided by GNSS constellations, but also by precise inter-satellite ranging within the constellation to enhance the position knowledge of the satellites significantly. This research focuses on the feasible position estimation of the LPS satellites and, specifically, what improvements can be achieved by including ISL. In order to correctly perform the estimation for the ISL systems, modified least-squares algorithms have been developed suitable for observations linked to multiple satellites and the simultaneous position estimation. The average 3-dimensional position error is 7.84 cm if no ISL is used. When ISL is added to the estimation, the average 3-dimensional position error reduces to 1.80 cm. Therefore, it is shown that significant improvements can be achieved for the positioning of the LPS satellites by using ISL. With the achieved accuracy and the prospected improvements in the solution, LPS is shown to be a viable system for lunar navigation.

Many low earth satellites use GNSS for orbit determination, both for operational purposes and post-facto scientific orbits. Using GNSS systems for Lunar navigation proves difficult, however, due to the signals being weak and having limited coverage. This thesis investigates, through numerical simulation, the usage of a constellation of Polar or Equatorial Medium Earth Orbit (PECMEO) satellites for Lunar navigation. The system is proposed as alternative for orbit determination using ground-based observations, making navigation of the spacecraft more autonomous, without limitations on the number of receivers. A navigation constellation of 9 satellites at an orbital radius of 14 000 km is designed by minimizing the Geometric Dilution of Precision (GDOP). The resulting Pareto front of optimum solutions consists of two distinct groups of constellations. Firstly, constellation with lower mean GDOP and higher maximum GDOP have two orbits approximately orthogonal to the ecliptic plane, while the third orbit is in the ecliptic plane. Meanwhile, a second group of solutions with slightly higher mean GDOP, but significantly lower maximum GDOP are found for constellation with one plane approximately orthogonal to the ecliptic plane, while the remaining two planes have an inclination of near 45 degrees. One of the latter group of solutions has been chosen for the system for its lower maximum GDOP. The effect of omitting observations passing through the ionosphere is investigated to determine if there is a need to obtain observations at multiple frequencies to allow for ionospheric corrections. Omitting those observations results in a slightly increased GDOP right before and after a satellite passes behind Earth, of up to 56.4%. However, only 13.9% of the samples are effected, making the overall effect rather small. The positioning accuracy of the system is assessed by simulating pseudorange and carrier phase observations, and solving these with point position and kinematic least squares methods. Two main error contributions on the solutions are caused by observation noise and navigation satellite ephemerides errors. A solution for observations without ephemeris error, a mean 3-dimensional position error of 3.3m is obtained. A solution for noiseless observations yields a mean 3-dimensional position error of 26.8m. Finally, the solution obtained from observations with all simulated errors results in a mean 3-dimensional position error of 27.0m, to which the ephemeris errors are thus the main contributors, despite optimistic assumptions on their magnitude. The observed accuracy shows that the system is a viable navigation method for Lunar spacecraft.