Relative Navigation in Asteroid Missions Using Dual Quaternion Filtering

Abstract

Ben-Gurion University of the Negev, POB 653, 84105, Beer Sheva, Israel 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 landmarks 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 to the conventional filter. The errors feature similar steady-state levels in both filters.

Variational Bayesian adaptive high‐degree cubature Huber‐based filter for vision‐aided inertial navigation on asteroid missions

“…The position of the landmarks is denoted by , which is known in the frame. The measurement equation of the visual sensor can be expressed as follows [6, 20]: where is the position of the spacecraft in the frame, and denotes the attitude matrix from frame to frame .…”

“…The VNS can provide position and attitude information that is consistent and accurate [5], but the data update rate is slow due to the image processing computational costs. Therefore, the vision‐aided INS (VAINS), which uses complementary inertial and visual navigation information, is increasingly being used for the asteroid missions [6, 7]. Li et al utilised the pixels of three selected landmarks to correct an INS drift error [4], and Trawny et al confirmed the validity of the vision‐aided inertial navigation [8].…”

Multiple-Step Randomly Delayed Adaptive Robust Filter With Application to INS/VNS Integrated Navigation on Asteroid Missions

“…where d p is the delay probability given in Table 1. The contaminated Gaussian measurement noise was drawn from the distribution given in (7), with the following covariances of the ideal Gaussian distribution and the perturbing Gaussian distribution [5]:…”

“…The most extensively used nonlinear filter for INS/VNS integrated navigation is the extended Kalman filter (EKF) [4], [5]. However, the performance of the EKF will be severely degraded for a system with strong nonlinearities because the EKF is based on first-order linearization [6].…”

Vision-Based Relative Navigation Using Dual Quaternion for Spacecraft Proximity Operations

“…Many of those approaches employ dual inertia operator to estimate angular and linear velocity under the assumption of known mass moment of inertia information of spacecraft [12,13]. Dual quaternionbased relative navigation-applied extended Kalman filter (EKF) is introduced in asteroid circumnavigation considering gravity field and integrated navigation sensor system [14]. In addition, extended and unscented Kalman filter (UKF) using dual quaternion-based twistor parameters are proposed for relative navigation between two spacecraft [15,16].…”