Improving the performance of lunar satellite navigation systems by exploiting inter-satellite distance information

This paper evaluates a method to improve the accuracy of a lunar satellite-based navigation system for two different localization techniques, the One-Way ranging and the Two-Way ranging. The method integrates into the navigation solution the measurement corresponding to the inter-satellite distance in addition to the existing measurement. The additional measurement comes directly from the ephemerides, and no additional equipment is required for the satellite’s payload. In this way, it introduces additional constraints to the system of navigation equations: two satellites and the user shall always lay on a triangle, and the cosine law can be used to relate the distance between a couple of satellites and the distances between the satellites and the users. This constraint has a regularization effect that reduces the ill-conditioning of the system of equations, in particular for the cases in which the number of satellites is reduced or not optimized, as can happen in the preliminary deployment of a lunar navigation system. The effectiveness of the method was evaluated through simulations that take into account all the main system measurement errors, both via a theoretical Cramer-Rao Lower Bound (CRLB) computation and via Monte Carlo runs exploiting a Weighted Least Square (WLS) positioning algorithm.