Averaging quaternions

被引:269
作者
Markley, F. Landis [1 ]
Oshman, Yaakov
机构
[1] NASA, Goddard Space Flight Ctr, Guidance Navigat & Control Syst Engn Branch, Greenbelt, MD 20771 USA
[2] SUNY Buffalo, Dept Mech & Aerosp Engn, Buffalo, NY 14260 USA
[3] Technion Israel Inst Technol, Dept Aerosp Engn, IL-32000 Haifa, Israel
关键词
D O I
10.2514/1.28949
中图分类号
V [航空、航天];
学科分类号
08 ; 0825 ;
摘要
Researchers have derived an algorithm that determines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Another methor method has been derived to maximize likelihood estimation and develop sufficient conditionfor the uniqueness of the average quaternion and thec equivalence of the minimization problem. The solution to the problem involved performing an eigenvalue or eigenvector decomposition of a matrix that is composed of the given average quaternions and weights. It was found that the optimal average quaternion can be determined by the computationally efficient QUEST algorithm, for both the scalar- and matrix-weighted cases. The average quaternion was found to be a maximum likelihood estimate in the matrix-weighted case, when the matrix was derived by the inverse of the covariance of the small attitude vector errors.
引用
收藏
页码:1193 / 1197
页数:5
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