EULER-2 and EULER-n algorithms for attitude determination from vector observations
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This paper presents two new mathematical approaches to the optimal spacecraft attitude determination based on vector observations: EULER-2 and EULER-n. They compute the optimal Euler axis and angle by a deterministic and an iterative method, respectively. EULER-2, whose application is restricted when only two unit-vector pairs are available (n = 2), is based on the attitude matrix rotation property and on a demonstrated co-planarity condition. This co-planarity condition allows also the extension of the existing TRIAD algorithm to the optimal solution, getting TRIAD-2. The EULER-n algorithm, which has no limitation on the unit-vector number n, uses a recursive equation which converges with only one or two iterations when using EULER-2 for evaluating the starting point. Some numerical tests on accuracy and computational speed are performed for EULER-2, TRIAD-2, and EULER-n. Plots show that all these three new optimal attitude estimation algorithms are particularly suitable for fast optimal attitude determination. © 1997 Elsevier Science Ltd.
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