Journal of Astronautics ›› 2017, Vol. 38 ›› Issue (12): 1307-1313.doi: 10.3873/j.issn.1000-1328.2017.12.007

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An Accurate Numerical Solution for Strapdown Attitude Algorithm Based on Picard Iteration

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

  1. School of Automation, Northwestern Polytechnical University, Xi’an 710072, China
  • Received:2017-02-23 Revised:2017-09-21 Online:2017-12-15 Published:2017-12-25


For strapdown attitude updating algorithm, in order to reach a high accuracy under a high attitude maneuver, a new numerical attitude algorithm is proposed based on the Picard series solution for the attitude quaternion differential equation. In this new algorithm, the angular velocity polynomial fit is obtained for the gyro angular increment, and the product of the polynomial quaternion is converted into the convolution operation of the angular velocity polynomial coefficients, then the Picard series solution is well settled. There exists no approximation or hypothesis in this deduction, which means the new algorithm is analytically accurate. Finally, under the large amplitude cone motion and high maneuver environment, some comparison tests both using the traditional algorithm and the new presented algorithm are carried out, and the results show the significant accuracy improvement in the new algorithm.

Key words: Strapdown attitude algorithm, Picard series, Polynomial fit, Simulation test

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