An adaptive GNSS-based reduced dynamic approach for real time autonomous navigation from the Earth to the Moon

In this research study we describe our last effort in further improving the achievable Global Navigation Satellite System (GNSS) based navigation performance in an Earth-Moon Transfer Orbit (MTO). The GNSS-based orbital filter we implemented previously with a dynamic approach, is modified by adopting a reduced-dynamics approach, which, with a certain accuracy, compensates for the dynamic model errors using a process noise model that weights observational and dynamical errors. Empirical accelerations are estimated as part of the state vector in a Kalman filter, adopting a deterministic forces model. Unlike the implementations reported in the existing literature, typically for orbit determination in Low Earth Orbit (LEO), here, in order to correctly weight observational and dynamical errors in the full trajectory from the Earth to the Moon, characterized by very variable signals and geometry conditions, an adaptive tuning of the filter is adopted. The observational and dynamical errors are predicted as function of different parameters, i.e., the estimated carrier-to-noise-ratio of the signals at the receiver position, the tracking loops setting, the kinematic state of the receiver and the combination of orbital forces modelled at different altitudes. The implemented orbital filter together with the developed receiver are designed in order to provide real-time autonomous on-board navigation on the way from the Earth to the Moon. Following a description of the simulation models and assumptions and of the existing orbit determination approaches, the paper focusses on the implementation of the proposed adaptive reduced-dynamic orbital filter and finally presents its performance in a MTO.