Optimal orthonormalization of strapdown guidance systems
Abstract
The requirement for orthonormalization of the Direction Cosine Matrix (DCM) in strapdown guidance systems is explained. The orthonormalization problem is formulated in mathematical terms and a closed form solution is given in two equivalent forms. Three iterative processes to compute this matrix are introduced in order to alleviate the problem of computing square roots of matrices needed for the closed form solution. Using polar decomposition of matrices the convergence rate and range of the iterative processes are investigated. Finally, the computational effort required for the implementation of the iterative processes is examined theoretically and empirically. It is concluded that the 'Dual Process' is superior and should be used whenever the DCM is computed directly.
 Publication:

In: Position Location and Navigation Symposium
 Pub Date:
 1976
 Bibcode:
 1976posn.symp..122B
 Keywords:

 Convergence;
 Iterative Solution;
 Orthogonality;
 Run Time (Computers);
 Strapdown Inertial Guidance;
 Algorithms;
 Differential Equations;
 Matrices (Mathematics);
 Matrix Theory;
 Optimization;
 Space Communications, Spacecraft Communications, Command and Tracking