Monocular-vision-based spacecraft relative state estimation under dual number algebra

Abstract

This paper develops a relative state estimation method for two spacecraft based on monocular vision measurement, where the leader spacecraft of three-dimensional shape is observed by a calibrated camera fixed on the follower spacecraft. The two-dimensional image of the leader spacecraft with multiple geometric features is obtained by the camera. Multiple geometric features including points, lines and circles are described under dual number algebra, and the observation models are proposed based on the geometric projection relationships of these features. By the proposed method, the geometric features appeared on the leader spacecraft can be employed to estimate the relative state between the two spacecraft. Another contribution of this paper is to develop a six-degree-of-freedom relative motion dynamics using dual number. The dynamics model describes the relative motion between arbitrary points on the spacecraft, and both the kinematically and dynamically coupling effects are considered. Based on the derived process model and observation model, an extended Kalman filter is presented to estimate the relative state between the two spacecraft. In addition, an unscented Kalman filter is also developed to avoid complicated calculation of derivations. Finally, numerical simulations are performed to evaluate the proposed EKF and UKF approaches based on multiple geometric feature measurement. Simulation results verify the effectiveness of the proposed method, and show that by using EKF or UKF technique, the relative translation and rotation estimation errors converge rapidly with the desired high estimation accuracy. Comparison simulations are made with the situations using less feature measurement, which demonstrate that employing multiple feature measurement provides superior estimation performance than methods with less feature measurement.