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This paper compares two basic approaches to solving ordinary differentialequations, which form the basis for attitude computation in strapdown inertialnavigation systems, namely, the Taylor series expansion approach that was usedin its low-order form for deriving all mainstream algorithms and the functionaliterative integration approach developed recently. They are respectivelyapplied to solve the kinematic equations of major attitude parameters,including the quaternion, the Rodrigues vector and the rotation vector.Specifically, the mainstream algorithms, which have relied on the simplifiedrotation vector without exception, are considerably extended by the Taylorseries expansion approach using the exact rotation vector and recursivecalculation of high-order derivatives. The functional iterative integrationapproach is respectively implemented on both the normal polynomial and theChebyshev polynomial. Numerical results under the classical coning motion arereported to assess all derived attitude algorithms. It is revealed that in therelative frequency range when the coning to sampling frequency ratio is below0.05-0.1 (depending on the chosen polynomial truncation order), all algorithmshave the same order of accuracy if the same number of samples are used to fitthe angular velocity over the iteration interval; in the range of higherrelative frequency, the group of Quat/Rod/RotFIter algorithms (by thefunctional iterative integration approach combined with the Chebyshevpolynomial) perform the best in both accuracy and robustness, thanks to theexcellent numerical stability and powerful functional representation capabilityof the Chebyshev polynomial.

Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion