Iterative Orthogonalization of the Direction Cosine Matrix.

Abstract

When the Direction Cosine Matrix (DCM) is used in Strapdown Inertial Navigation or other aerospace systems to describe vehicular attitude, it is computed inaccurately due to the use of fast but imprecise algorithms, and the resulting matrix is often not orthogonal. By periodically restoring the orthogonality of the erroneous DCM, the errors can be reduced. A natural way of restoring the orthogonality is to replace the DCM with an orthogonal matrix which is closest in the Euclidean sense to the computed DCM. The expression for this matrix, which is of course a function of the computed DCM, is difficult to evaluate explicitly, so that iterative techniques have been suggested in this work and elsewhere. The use of iterative techniques raises the question of convergence criteria and properties which had not been thoroughly investigated. This work deals with the investigation of the convergence of five such iterative techniques.

Document Details

Document Type
Technical Report
Publication Date
Jul 04, 1976
Accession Number
ADA032033

Entities

People

  • I. Y. Bar-itzhack
  • Jarod Meyer

Organizations

  • Technion – Israel Institute of Technology

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Convergence
  • Inertial Navigation
  • Navigation
  • Orthogonality

Readers

  • Approximation Theory.
  • Inertial Navigation Systems.

Technology Areas

  • Space