Polar decomposition for attitude determination from vector observations

Bar-Itzhack, Itzhack Y.

This work treats the problem of weighted least squares fitting of a 3D Euclidean-coordinate transformation matrix to a set of unit vectors measured in the reference and transformed coordinates. A closed-form analytic solution to the problem is re-derived. The fact that the solution is the closest orthogonal matrix to some matrix defined on the measured vectors and their weights is clearly demonstrated. Several known algorithms for computing the analytic closed form solution are considered. An algorithm is discussed which is based on the polar decomposition of matrices into the closest unitary matrix to the decomposed matrix and a Hermitian matrix. A somewhat longer improved algorithm is suggested too. A comparison of several algorithms is carried out using simulated data as well as real data from the Upper Atmosphere Research Satellite. The comparison is based on accuracy and time consumption. It is concluded that the algorithms based on polar decomposition yield a simple although somewhat less accurate solution. The precision of the latter algorithms increase with the number of the measured vectors and with the accuracy of their measurement.

Document ID

19930015522

Acquisition Source

Legacy CDMS

Document Type

Conference Paper

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Date Acquired

September 6, 2013

Publication Date

February 1, 1993

Publication Information

Publication: Flight Mechanics(Estimation Theory Symposium, 1992

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Accession Number

93N24711

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Public

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