EULER-q algorithm for attitude determination from vector observations
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This paper presents a new optimal attitude definition, which is based on the Euler axis rotational property, and the EULER-q optimal estimation algorithm derived from it. The mathematical procedure leads to the eigenanalysis of a symmetric 3x3 matrix whose eigenvector, associated to the smallest eigenvalue min, is the optimal Euler axis. minis evaluated in a closed form and, the associated eigenvector is computed as a cross vector. A discussion of the singular case is then included. The QUEST-2 algorithm, which provides the closed-form expressions of the eigenvalues and computes the optimal quaternion by using either a generalized cross product in a 4D-space or a 3x3 matrix inversion, is also included. After the rotational error has been analyzed and defined, an accuracy comparison test has been performed between the Wahba's optimal criterion and the proposed new one. Results show that Wahba's optimal definition is on average better, but with very small differences which decrease as the number of the observed directions increase. However, the clear gain in computational speed validates both EULER-q and QUEST-2 as particularly suitable for fast on-board attitude determination systems, such as those involving many observed vectors, e.g. when using wide field-of-view startrackers.
SPACEFLIGHT MECHANICS 1996, PTS 1 AND 2
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