Nowadays, several space agencies are emphasizing the interest for the human return to the Moon. This renaissance in lunar exploration involves both the public and private sectors and will offer new opportunities for science across a multitude of disciplines from planetary geology to astronomy and astrobiology. Precise data concerning the position of rovers on the Moon surface will become of vital importance for future missions and an autonomous navigation system capable of real-time absolute positioning on the Moon will be crucial for the future of the Moon exploration. For this reasons, the paper proposes the deployment of an autonomous navigation system based on a small constellation of satellites in orbit around the Moon. It will allow complex and simultaneous missions on the Moon surface with a minimal control from Earth. This work proposes the design of minimal constellation optimized for the South Pole that today seems the most interesting part of the Moon. This Lunar Positioning System (LPS) will be based on the same concept of the classical GNSS: the user will compute its position by the use of ranging signals coming from the satellites. In the paper, a first evaluation of the system was done in terms of: (a) constellation geometry (service availability and continuity and dilution of precision) and (b) final positioning accuracy. Two different constellations with four satellites were evaluated and compared. Moreover, to evaluate final user position accuracy, the main pseudorage error contributions are modeled and different configurations are considered. Good performances in terms of service availability, continuity and DOP are obtained: availability up to 58% and continuity up to 840 minutes were obtained in the simulation. Concerning the final user positioning error, it mostly depends on the satellite position error, and it is below 200 meters RMS. Exploiting the differential approach with the classical lander-rover configuration, the final rover position error can be reduced to 3 meters RMS also for very long baseline.