Iterative Optimal Orthogonalization of the Strapdown Matrix

This paper treats the problem of finding an orthogonal matrix which is the closest, in the Forbenius norm, to a given nonorthogonal matrix. This nonorthogonal matrix is the result of a fast but rather inaccurate computation of the well-known direction cosine matrix (DCM) of a strapdown inertial navi...

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Bibliographic Details
Published in:IEEE transactions on aerospace and electronic systems 1975-01, Vol.AES-11 (1), p.30-37
Main Author: Bar-itzhack, Itzhack Y.
Format: Article
Language:English
Subjects:
Aerospace control
Aerospace simulation
Closed-form solution
Computational modeling
Euclidean distance
Inertial navigation
Iterative methods
Lagrangian functions
Pollution measurement
Symmetric matrices
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Summary:This paper treats the problem of finding an orthogonal matrix which is the closest, in the Forbenius norm, to a given nonorthogonal matrix. This nonorthogonal matrix is the result of a fast but rather inaccurate computation of the well-known direction cosine matrix (DCM) of a strapdown inertial navigation system. The known closed-form solution to this problem is rederived using the directional derivative method, and the conditions for minimum distance are derived and discussed. A new iterative technique for solving this problem is derived as a result of the application of the gradient projection technique and the directional derivative method. The practical computational problems involved in this technique are discussed. The new technique is demonstrated by three examples. Although particular attention is given to the 3 X 3 direction cosine matrix, the conclusions are nonetheless valid higher order matries.
ISSN:0018-9251
1557-9603
DOI:10.1109/TAES.1975.308025