NDLI: Quaternion averaging

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Quaternion averaging

Content Provider	NASA Technical Reports Server (NTRS)
Author	Oshman, Yaakov Markley Sr., F. Landis Cheng, Yang Crassidis, John L.
Copyright Year	2007
Description	Many 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.
File Size	517177
Page Count	10
File Format	PDF
Alternate Webpage(s)	http://archive.org/details/NASA_NTRS_Archive_20070017872
Archival Resource Key	ark:/13960/t1pg6nh99
Language	English
Publisher Date	2007-01-01
Access Restriction	Open
Subject Keyword	Mathematical And Computer Sciences (general) Normal Density Functions Attitude Inclination Algorithms Quaternions Average Scalars Maximum Likelihood Estimates Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science
Content Type	Text
Resource Type	Article

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