Journal of Astronautics ›› 2017, Vol. 38 ›› Issue (7): 723-727.doi: 10.3873/j.issn.1000-1328.2017.07.007

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A General Method to Obtain Noncommutativity Error Compensation Coefficients for Strapdown Attitude Algorithm

YAN Gong min, YANG Xiao kang, WENG Jun, QIN Yong yuan   

  1. School of Automation, Northwestern Polytechnical University, Xi’an 710072, China
  • Received:2017-03-14 Revised:2017-05-15 Online:2017-07-15 Published:2017-07-25


In a strapdown attitude updating algorithm, a general numerical method for obtaining the multi-sample noncommutativity error compensation coefficients is presented. Under the condition of the angular motion expressed as polynomial, the linear relationships between the angular velocity polynomial, angular increment polynomial and multi-sample angular increments are established in this paper. According to the vector cross product operation of the noncommutativity error polynomial in the equivalent rotation vector differential equation, the cross product is converted into the convolution operation of the polynomial coefficients. Then, the numerical methods to compute the noncommutativity error compensation coefficients of the arbitrary multiple samples are presented in deduction, which are easy to be implemented with computer programming. Finally, simulations are carried out to obtain the 2~6-sample compensation coefficients, in which the 2~4-sample coefficients are consistent with the existing literatures and the 5 or 6-sample coefficients are firstly proposed by the authors.

Key words: Strapdown attitude algorithm, Equivalent rotation vector, Noncommutativity error, Numerical solution

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