Asteroid Gravity Field Estimation by a Satellite Constellation

Abstract

Asteroid missions stand at the forefront of space exploration endeavours. These face a number of challenges, with safe navigation being one of the main issues. The irregular nature of these bodies creates highly perturbed gravity fields that, if modelled incorrectly, can be a danger to the safe navigation of the spacecraft. Therefore, improving the gravity field modelling of asteroids is of key importance.

This research aims to improve the gravity field estimation of asteroids through the use of a satellite constellation consisting of a mothership and a set of CubeSats. In particular, it focuses on the modelling and estimation of the gravity field with spherical harmonics (SH), which makes the research only applicable to the navigation of the spacecraft outside of the Brillouin sphere.

The system design is based on a CubeSat constellation orbiting the asteroid that relays measurements back to a mothership that estimates its state and gravity field through an Unscented Kalman Filter (UKF). The research is centered around 433 Eros asteroid for the model implementation, being an irregular body with known characteristics from the Near-Shoemaker mission.

An end-to-end simulation environment is implemented for the system research. This allows for simulating the orbits of the satellites in a real-world environment considering SH gravity field up to degree and order 15, the perturbation effect of the Sun point mass, and the solar radiation pressure. Additionally, it includes a realistic polyhedral shape of the asteroid including its landmarks. The asteroid model is used together with the modelling of the satellite sensors to estimate the measurements that can be obtained in a realistic scenario including sensor errors, visibility, and communications constraints. Furthermore, the simulation environment contains a UKF filter capable of conducting the gravity-field estimates from the measured states of the constellation satellites.

The research conducts a thorough sensitivity analysis of the scenario evaluating how the constellation design impacts the estimates obtained. This analysis evaluates a number of filter designs, and determines that better performance is achieved when the design models the dynamics of several satellites at the same time. This is followed by an analysis of variance, conducted to obtain a better understanding of the constellation characteristics' effects on the filter estimates.


From the results obtained, a design synthesis is conducted to test the system implemented with an optimised constellation design. Furthermore, the filter design is re-evaluated and improved through the addition of better covariance matrix tuning and the addition of a degree-by-degree estimation procedure that allows to reduce computational load, a main constraint of the system. The results obtained show that the model is capable of accurately estimating the gravity field spherical harmonic coefficients with an error lower than 15% when the filter is tuned properly for SH up to degree and order nine. Additional verification of its applicability has been conducted by testing the system with extreme case asteroids, which show that the system requires a thruster and control system for the satellites to be capable of maintaining stable orbits around the asteroids when these have extremely irregular gravity fields.