A New Mathematical Formulation for Strapdown Inertial Navigation

1 January 1971

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Aerospace and Electronic Systems

Vol. AES-7 (1) , 61-66
https://doi.org/10.1109/taes.1971.310252

Abstract

A differential equation is developed for the orientation vector relating the body frame to a chosen reference frame. The time derivative of this vector is the sum of the inertially measurable angular velocity vector and of the inertially nonmeasurable noncommutativity rate vector. It is precisely this noncommutativity rate vector that causes the computational problems when numerically integrating the direction cosine matrix. The orientation vector formulation allows the noncommutativity contribution to be isolated and, therefore, treated separately and advantageously. An orientation vector mechanization is presented for a strap down inertial system. Further, an example is given of the applica tion of this formulation to a typical rigid body rotation problem.

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