Autonomous navigation for Mars probes using only satellite-to-satellite tracking measurements by singularity-avoiding orbit elements

This paper proposes a novel autonomous navigation method for Mars-orbiting probes. Satellite-to-satellite tracking (SST) between two probes is generally deemed to involve autonomous measurements with no dependence on any external observation sites on the Earth. For the conventional two-body dynamic model, it is well known that the orbit states cannot be estimated by merely using such SST measurements. Considering the effects of third-body gravitation perturbation and the weak Mars tesseral harmonics perturbation, autonomous navigation with SST measurements alone becomes weakly observable and may be achieved by some nonlinear filtering techniques. Two significant improvements are made to mitigate the nonlinearity brought by the dynamic models. First, singularity-avoiding orbit elements are selected to represent the dynamic models in order to reduce the intensity of the nonlinearity which cannot be overcome by the traditional position-velocity state expression. Second, the unscented Kalman filter method is effectively utilised to avoid the linearised errors calculated by its extended Kalman filter counterpart which may exceed the tesseral harmonics perturbation. A constellation, consisting of one low-orbit probe and one high-orbit probe, is designed to realise the autonomous orbit determination of both participating Mars probes. A reliable navigation solution is successfully obtained by Monte Carlo simulation runs. It shows that the errors of the semimajor axes of the two Mars probes are less than 10 m and the position errors are less than 1 km.