Satellite Attitude Determination from Terrestrial/Planetary Landmarks

Abstract

Attitude Determination (AD) or specifying orientation relative to a known reference frame plays a crucial role in meeting the mission specific pointing goals of a satellite. Attitude sensors provide measurements of known directional references such as celestial bodies (Sun, Earth, planets, stars) or beacon signals in body fixed frame of the satellite. Similarly, distinctive features or landmarks on Earth, Moon or a planet also serve as references for AD. Depending on the pose (position, orientation) and intrinsic parameters (the focal length, principal point o set) of the sensor/camera, the pattern of landmarks in the sensed image gets distorted due to perspective projection for a given viewing geometry. On the other hand, it is possible to extract pose of a camera, if a sufficient number of landmarks are observed in the captured scene. Although there is a considerable volume of literature on image-based motion estimation for autonomous navigation, only a few deal with the specific problem of attitude determination through landmark detection. This thesis addresses three-axis attitude determination of a satellite from identified landmarks in an image acquired by an onboard camera where the line-of-sight vectors connecting the landmarks to the centre of perspective of the camera serve as the directional references. The central idea behind the proposed AD scheme is: the angle between two landmarks, as viewed from the camera, depends on the relative position of the camera due to the finite distance between the camera and a particular landmark. This relative distance keeps varying throughout the orbit (except for a truly geostationary satellite). While the look direction from camera to a given landmark depends on the current attitude and the position of the camera, inter-landmark angle, as viewed from the camera, is independent of attitude, it depends only on the relative camera position. In other words, the same pair of landmarks will subtend the same directed angle at the onboard camera centre, irrespective of satellite's attitude, provided the camera position relative to the landmarks is unchanged. Therefore, the inter-landmark angular separation can be utilised for landmark identi cation provided the instantaneous position of the landmarks as well as the satellite is known. The proposed method of landmark-based attitude determination requires a catalogue where absolute position coordinates of the landmarks in a planet fixed frames are stored a priori. An auxiliary catalogue containing the inter-landmark angular separations between all combinations of landmarks for a given camera position is then constructed, the camera position is assumed to be known. The viewing directions to landmarks are found from the coordinates of landmarks imaged by the calibrated camera having known intrinsic parameters. The angular separations between pairs of look vectors towards the landmarks are computed next. The landmarks are identified by angular separation match with those stored in the auxiliary catalogue and the matched landmark look vector directions in the reference frame are retrieved from the main catalogue. If more than one such vector direction in the known reference frame and the observed camera fixed frame are available, the attitude matrix that transforms the reference frame to the camera fixed frame is determined by the two sets of vectors. Finally, the body attitude of the satellite relative to a reference can be recovered using the known camera mounting matrix. In the thesis, a novel method of attitude determination is also presented, which stems from a geometric interpretation of Euler principal axis corresponding to the attitude determined from vector observations. The advantage of the proposed landmark based method is that the absolute three-axis attitude of the camera, and hence the body, on which the camera is mounted, can be found with respect to a known reference frame. Also unlike the cases where rotation is extracted from homography, the landmarks need not be coplanar. The proposed method can not only serve as a back-up option in case of failure of conventional sensors, but also provide independent attitude updates that can be fused with other sensor measurements to aid autonomous navigation. This also opens up a possibility to use the images taken by the imaging payload itself, instead of employing a dedicated imaging sensor. The outcome of the proposed research can be especially useful in finding attitude of satellites where the payload instruments remain useful even after a decade of on-orbit operation but some of the attitude sensors have lost their functionalities due to ageing.