COMPUTATIONAL ERRORS IN THE GENERATION OF THE DIRECTION COSINE MATRIX IN A STRAPDOWN SYSTEM

Avery A. Morgan

Peer Reviewed

Abstract: Abstract THE MAJOR ERRORS arising in the computation of the body to navigation transformation matrix in a strapdown system employing three orthogonal pulse rebalanced gyros are examined. Particular emphasis is given to the propagation of truncation error. A closed form solution to the error propagation arising from a rotation about a constant (but arbitrary) axis is derived. This solution is applied to three computational algorithms. These are the first order, the second order, and the incremental sequential first order algorithms. The later algorithm is presently programmed on the Honeywell SIGN-I strapdown guidance computer. To predict the SIGN-I error propagation, an expression for the propagation of the non-zero expected value of roundoff error is also derived. Errors reduced from SIGN-I tests are shown to compare closely with the predicted error model.
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 14, Number 1
Pages: 95 - 104
Cite this article: Morgan, Avery A., "COMPUTATIONAL ERRORS IN THE GENERATION OF THE DIRECTION COSINE MATRIX IN A STRAPDOWN SYSTEM", NAVIGATION, Journal of The Institute of Navigation, Vol. 14, No. 1, Spring 1967, pp. 95-104.
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