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Quaternion AveragingMany applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.
Document ID
Document Type
Preprint (Draft being sent to journal)
Markley, F. Landis
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Cheng, Yang
(State Univ. of New York Amherst, NY, United States)
Crassidis, John L.
(State Univ. of New York Amherst, NY, United States)
Oshman, Yaakov
(Technion - Israel Inst. of Tech. Haifa, Israel)
Date Acquired
August 23, 2013
Publication Date
January 1, 2007
Subject Category
Mathematical And Computer Sciences (General)
Distribution Limits
Public Use Permitted.
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