Attitude determination from triaxial ellipsoid of unknown orientation

Abstract

Presented is the derivation for the rotation matrix describing the principal axis of a celestial body of unknown attitude relative to a spacecraft of known attitude. Through the use of the lit limb of an ellipsoidal body and the body’s principal axis, a modified orthogonal Procrustes problem can be solved for attitude determination. Due to the natural symmetry of triaxial ellipsoids, the solution method presents a twofold equivocacy in the attitude of the observed body. In addition, it presents a different method for mapping the quadric surface of an ellipsoidal body to the projection on an image plane. Then, through matrix factorization, the position relative to the celestial body can be derived. The method presented offers an exact solution and avoids the error associated with ellipse fitting an image.