A NEW MATHEMATICAL FORMULATION FOR STRAPDOWN INERTIAL NAVIGATION PDF

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. Title: A New Mathematical Formulation for Strapdown Inertial Navigation. Authors : Bortz, John. Publication: IEEE Transactions on Aerospace and Electronic. Aug 9, A New Mathematical Formulation for Strapdown Inertial Navigation JOHN E. BORTZ, Member, IEEE The Analytic Sciences Corporation.

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Post on Aug views. The timederivative of this vector is the sum of the inertially measurableangular velocity vector and of the inertially nonmeasurablenoncommutativity rate vector. It is precisely this noncommutativity rate vector that causes thecomputational problems when numerically integrating the direc-tion cosine matrix.

The orientation vector formulation allows thenoncommutativity 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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A New Mathematical Formulation for Strapdown Inertial Navigation – [PDF Document]

This integration is carried out numer-ically using the incremental outputs from the systemgyros. The major problem in this method is inertiial wellknown phenomenon of noncommutativity of finite rota-tions. The two bavigation ways of combatting errorsdue to this effect are 1 to update the direction cosinematrix at or near the gyro rebalance frequency using asimple update algorithm or 2 to update the directioncosine matrix after many rebalance cycles using a moresophisticated algorithm.

Even the most efficient algorithmplaces a moderate to heavy burden on the navigationsystem computer.

A New Mathematical Formulation for Strapdown Inertial Navigation

If the update process is slowed down toease the computational load, system bandwidth and ac-curacy are sacrificed. I The mathematical theory presented here was actually intro-duced by J. Unfortunately, at the timethere was no sustaining external interest in this work and theresults never became widely known. Laning’s complete and eleganttreatment of finite angles and rotations was presented in ratherabstract terms.

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A New Mathematical Formulation for Strapdown Inertial Navigation

The development given here is original with theauthor and highly motivated in a physical sense. In order to differentiate 10two derivativesare obtained first.

The geometry of rotation. Symbolic hybrid system diagram.

The basic principle involved is to generate a set ofsignals aX, Uy, and oz representing the components of thenoncommutativity rate vector a. It is mathsmatical in [2] thatunder certain reasonable conditions and system designchoices,IJI.