Euler-q Algorithm for Attitude Determination from Vector Observations

A new cost function for optimal attitude dee nition and the Euler- q algorithm based on this cost function are presented. Theoptimality criterion isderived from theEuler axis rotational property and allowsa fast and reliable computation of the optimal eigenaxis. The mathematical procedure leads to the eigenanalysisof a 3 £ 3 symmetric matrix whose eigenvector, associated with the smallest eigenvalue, is the optimal Euler axis. This eigenvector is evaluated by a simple cross vector, and the singularity is avoided using the method of sequential rotations. The rotational error is then analyzed and dee ned, and an accuracy comparison test is performed between a previously accepted criterion of optimal attitude and the proposed one. Results show that the earlier dee nition of optimality is slightly more precise than Euler- q, which, in turn, demonstrates a clear gain in computational speed.