Recent years have seen an increased need for a lunar navigation service to support the large volume of missions planned for the coming decade. Supplying lunar navigation from the Earth suffers from limitations deriving from the long distance to the Moon. Thus, it must rely on a constellation of lunar navigation satellites. This thesis addresses the Orbit Determination (OD) of the satellites of a Lunar Navigation System (LNS) using range and Doppler observations from terrestrial stations. It provides a recommendation for the values of the design parameters of the OD system of a LNS to achieve the required OD accuracy and evaluates the impact of non-design factors such as the constellation's geometry and the observational noise. The parameters of the orbit propagation and the length of the estimation arc are identified as drivers of the OD accuracy. The relation between OD errors and navigation performance is also assessed.