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.