EULER-Q ALGORITHM FOR ATTITUDE DETERMINATION FROM VECTOR OBSERVATIONS

A new cost function for optimal attitude definition and the Euler-q al gorithm based on this cost function are presented, Tile optimality cri terion is derived from the Euler axis rotational property and a!laws a fast and reliable computation of the optimal eigenaxls. The mathemati cal procedure leads to the eigenanalysis of a 3 x 3 symmetric matrix w hose eigenvector, associated with the smallest eigenvalue, is the opti mal Euler axis. This eigenvector is evaluated by a simple cross vector , and the singularity is avoided using the method of sequential rotati ons. The rotational error is then analyzed and defined, and an accurac y comparison test is performed between a previously accepted criterion of optimal attitude and the proposed one, Results show that the earli er definition of optimality is slightly more precise than Euler-q, whi ch, in turn, demonstrates a clear gain in computational speed.