QUATERNION COMPUTATION FROM A GEOMETRIC POINT-OF-VIEW

Global algorithms that solve for the quaternion generally have a four- fold multiplicity in order to avoid singularities. A geometrically-mot ivated construction is presented that automatically generates the four -fold multiplicity of algorithms once a single (possibly singular) alg orithm is known. As examples of the application of this procedure, lea st-squares attitude determination and the computation of the quaternio n from the direction-cosine matrix are examined. In the latter applica tion, the method proposed here leads to Shepperd's algorithm for extra cting the quaternion from the rotation matrix.