Relative Navigation in Asteroid Missions Using Dual Quaternion Filtering

Abstract

This paper investigates the efficacy of dual quaternion filtering in the realm of asteroid missions. The main contribution is the development of a dual quaternion relative navigation filter applied to asteroid circumnavigation. The simulated target asteroid is Kleopatra, a dog-bone-shaped asteroid featuring a low-potential highly perturbed gravity field. The spacecraft is equipped with a navigation camera and a laser ranger for position sensing and a star tracker and rate gyroscope for attitude sensing. The paper innovates in the methods for landmark identification within a camera field of view, true range and ranging errors determination, and spacecraft gravity-gradient torque modeling. For the sake of comparison, a navigation filter based on a conventional pose representation using Cartesian coordinates position and attitude quaternion is developed and tested under the same conditions. The dual quaternion filter succeeds in estimating the relative pose with high accuracy, as well as the gyroscope drift and the asteroid angular rates. The latter depends on the frequency and geometry of the landmarks lines of sight detected within the camera field of view. Significant gains in the transients of the estimation errors are achieved by the dual quaternion filter when compared with the conventional filter. The errors feature similar steady-state levels in both filters.