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Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion

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Abstract—There are two basic approaches to strapdown attitude computation, namely, the traditional Taylor series expansion approach and the Picard iterative method. The latter was recently implemented in a recursive form basing on the Chebyshev polynomial approximation and resulted in the so-called functional iterative integration approach. Up to now a detailed comparison of these two approaches with arbitrary number of gyroscope samples has been lacking for the reason that the first one is based on the simplified rotation vector equation while the second one uses the exact form. In this paper, the mainstream algorithms are considerably extended by the Taylor series expansion approach using the exact differential equation and recursive calculation of high-order derivatives, and the functional iterative integration approach is re-implemented on the normal polynomial. This paper applies the two approaches to solve the strapdown attitude problem, using the attitude parameter of quaternion as a demonstration. Numerical results under the classical coning motion are reported to assess all derived attitude algorithms. It is revealed that in the low and middle relative conic frequency range all algorithms have the same order of accuracy, but in the range of high relative frequency the algorithm by the functional iterative integration approach performs the best in both accuracy and robustness if the Chebyshev polynomials and a larger number of gyroscope samples are to be used. The main conclusion applies to other attitude parameters as well.

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Notes

  1. Abbreviation “FIter” stands for Functional Iterative integration; ‘np’ stands for normal polynomial.

  2. The unoptimized 3-sample algorithm is used, as given in (7) therein, as the current paper reasonablly assumes no priori knowldege of the experienced attitude motion. The optimized version instead would not affect the main conclusion.

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Funding

The first author of the paper was supported in part by National Key R&D Program of China (2018YFB1305103) and National Natural Science Foundation of China (61673263).

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Authors and Affiliations

  1. Shanghai Jiao Tong University, 200240, Shanghai, China

    Yuanxin Wu

  2. Central Scientific and Research Institute “Elektropribor”, 197046, Saint Petersburg, Russia

    Yury A. Litmanovich

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  1. Yuanxin Wu
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  2. Yury A. Litmanovich
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Correspondence to Yuanxin Wu or Yury A. Litmanovich.

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Wu, Y., Litmanovich, Y.A. Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion. Gyroscopy Navig. 11, 263–276 (2020). https://doi.org/10.1134/S2075108720040124

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