Ellipsoidal estimation of motion parameters of a non-cooperative space vehicle from visual information

The use of near-Earth space is currently complicated by presence of space debris objects in Earth’s orbit, which include spent stages of launch vehicles, inoperative satellites, and other large and small artificial objects. One approach to solving the problem of space debris involves docking and capturing a non-cooperative space object or spacecraft (target) with a so-called service spacecraft (chaser) for further actions to repair, refuel or change its orbit. Rendezvous and docking are complicated by the rotation of uncontrolled space objects caused by various factors. To perform this task, it is necessary to know the parameters of the orbital, rotational and relative motion of the target. The parameters of the orbital motion of such objects are usually known quite accurately from measurements from the Earth. This paper examines the case of a tumbling non-cooperative target located in an elliptical orbit. It is assumed that the target relative position and orientation are measured by the computer vision system (CVS) of the chaser. In this case, the position and orientation of the graphical reference frame (GRF) associated with the known 3-D graphical model of the target are determined relative to the reference frame associated with the chaser. The specific type of CVS is not considered. It is assumed that the chaser can carry out some maneuvers near the target and all parameters of the chaser angular motion are known. Thus, the attitude of the GRF relative to inertial reference frame (IRF) can be determined. The measured parameters are not enough to ensure safe rendezvous and docking with the target. To complete this task, it is necessary to determine all kinematic and dynamic parameters of the relative motion between the spacecraft. The rest of the required parameters are estimated. Orientation and rotation parameterization is done using quaternions. The angular motion equation of the target is considered in the GRF. This makes the angular velocity estimation faster and the inertia tensor estimation more stable. Stochastic characteristics of measurement errors are considered to be unknown and are not used. The only information about the errors is the bounds of their values. To determine the relative motion parameters, we use a new dynamic set-membership filter with ellipsoidal estimates. The filter can be successfully implemented on low-power on-board processors. The properties of the proposed algorithm are demonstrated using numerical simulation. The results obtained are expected to be used in the development of a navigation system for the rendezvous and docking, developed by a group of Ukrainian space industry enterprises under the leadership of the LLC “Kurs-orbital” (https://kursorbital.com/).