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.


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    Title :

    Iterative Optimal Orthogonalization of the Strapdown Matrix


    Contributors:


    Publication date :

    1975-01-01


    Size :

    1549628 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Strapdown Matrix Orthogonalization: The Dual Iterative Algorithm

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