ORTHOGONALIZATION TECHNIQUES OF A DIRECTION COSINE MATRIX

Three orthogonalization techniques to correct errors in the computed direction cosine matrix are introduced. One of these techniques is a vectorial technique based on the fact that the three rows of a direction cosine matrix constitute an orthonormal set of vectors in a three-dimensional space. The other two iterative techniques are based on the fact that the inverse and transpose of an orthogonal matrix are equal. In computing a time-varying direction cosine matrix computational errors are accompanied by the loss of the orthogonality property of the matrix. When one of these three techniques is used to restore the orthogonality of the matrix, the computational errors are also corrected. These techniques were tested experimentally and the results, given in this paper, were compared with a method used by the Honeywell Corporation. Copyright © 1969 by The Institute of Electrical and Electronics Engineers, Inc.