A geometrical approach for the angular velocity determination using a star sensor

In this paper, a geometrical investigation of the star sensor image is performed under dynamic conditions where the angular velocity effects are non-negligible. It is shown that, when the spacecraft is rotating, the streaks left by the stars’ signal onto the star sensor detector belong to portions of conic sections which features depend on the angles between the instantaneous rotation axis, the sensor line of sight and the stars’ direction. The geometrical properties discussed in the first part of the paper can be used to develop new numerical methods for the evaluation of the angular velocity. Hence, the chord method is proposed and discussed. This approach needs at least two stars in two successive images and, despite its simplicity, is quite effective to get a preliminary estimation of the spacecraft angular velocity in terms of direction and magnitude. Using the stars’ centroids from two successive images, the chord method evaluates the angular velocity direction as the intersection of the normals to the streaks. The proposed method is firstly presented by means of simple examples using some reference geometries, and then it is applied to real scenarios by using a high fidelity star sensor simulator. The pre-processing and processing of simulated images are discussed, presenting the geometrical techniques used to cluster the streaks and compute the centroids. Results are presented and discussed, validating the reported theoretical speculations.