Abstract
This work presents a precise analytical model to reconstruct the line-of-sight vector to a target satellite over time, as required by angles-only relative navigation systems for application to rendezvous missions. The model includes the effects of the geopotential, featuring: the analytical propagation in the mean relative orbital elements (up to second-order expansion), the analytical two-way osculating/mean orbital elements’ conversion (second-order in J2 and up to a given degree and order of the geopotential), and a second-order mapping from the perturbed osculating elements’ set to the local orbital frame. Performances are assessed against the line-of-sight reconstructed out of the precise GPS-based positioning products of the PRISMA mission. The line-of-sight modelled over a far-range one day long scenario can be fitted against the true one presenting residuals of the order of ten arc-seconds, which is below the typical sensor noise at far-range.
Highlights
Angles-only navigation plays a relevant role to treat the problem of space debris in the Low Earth Orbit (LEO) region
In-flight demonstrations of such approach are provided by ARGON (Advanced Rendezvous Demonstration using Global Positioning System and Optical Navigation) D’Amico et al (2013) and AVANTI (Gaias and Ardaens, 2018), where the manoeuvres executed to perform the rendezvous supported the convergence of the relative navigation solution
Given its orbital scenario, PRISMA is extremely representative for future missions exploiting LOS navigation in LEO, considering the weak effect of the differential aerodynamic drag (Gaias et al, 2015)
Summary
Angles-only navigation plays a relevant role to treat the problem of space debris in the Low Earth Orbit (LEO) region. The proposed analytical line-of-sight modelling is based on three functional components, namely: the relative mean orbit propagation, the mean/osculating orbital elements’ conversion, and the mapping from osculating elements to the moving orbital frame This methodology is valid for large relative orbits in the region where the main perturbation is the non-homogeneous distribution of the Earth mass (i.e., the typical LEO environment where active debris removal is required in place of the natural orbit decay). At the same time it improves the Gim and Alfriend (2003) and Yang et al (2018) relative motion models, either in order and/or in considered perturbations, while preserving the compact formulation deriving from the parametrisation in ROEs. The two-way conversion between osculating and mean orbital elements is carried out through an analytical and compact algorithm that combines a second-order Lie-based approach to cancel the J 2 effect, to the Kaula’s linear method for the remaining terms of the geopotential (Gaias et al, 2019).
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