A solution to spacecraft position and attitude determination from an imaged ellipsoid

When imaged through a camera, an illuminated ellipsoid gives rise, in general, to two ellipses on the image plane, namely the limb ellipse and the terminator ellipse. If the directum of illumination is known in the ellipsoid frame. then the full six degrees of freedom pose of the camera can be retrieved, apart from ambiguities which anse due to symmetry, by solving a quadnc-to-comc plus conic-to-conic correspondence problem. A solution to such task is proposed in this manuscript. By fittmg an ellipse to the imaged planetary limb arc, another ellipse to the terminator points, and exploiting analytical results available from projective geometry equations for computing the entire pose are formulated. The position is expressed as the least squares solution of an over-determined system of four equations m three unknowns, while the attitude is estimated tough a modified orthogonal Procrustes problem, whose solution involves the spectral decomposition of symmetric 3x3 matrices. Preliminar^ validation using synthetically generated images of illuminated ellipsoids suggests that the proposed algorithm can achieve position relative accuracy up to 10-3, and attitude error withm the milli-rad.