Euler-q algorithm for attitude determination from vector observations
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A new cost function for optimal attitude definition and the Euler-q algorithm based on this cost function are presented. The optimality criterion is derived from the Euler axis rotational property and allows a fast and reliable computation of the optimal eigenaxis. The mathematical procedure leads to the eigenanalysis of 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 defined, and an accuracy comparison test is performed between a previously accepted criterion of optimal attitude and the proposed one. Results show that the earlier definition of optimality is slightly more precise than Euler-q, which, in turn, demonstrates a clear gain in computational speed. Daniele Mortari is an Assistant Professor in the Aerospace Engineering School of the University of Rome "La Sapienza," Rome, Italy. He received a degree in nuclear engineering, attended the Aerospace Engineering School, and was trained at the NASA Goddard Space Flight Center for the attitude and orbit control systems. He joined the San Marco Project and cooperated in the activities for the San Marco 5 spacecraft. As a researcher he developed several new algorithms for attitude determination, attitude dynamics and control, misalignment determination, stars pattern recognition, matrix eigenanalysis, and data processing. He is the author of more than 35 papers. He is a member of the American Astronautical Society and of AIAA.
JOURNAL OF GUIDANCE CONTROL AND DYNAMICS
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