摘要
提出了一种基于多项式迭代的求解等效旋转矢量微分方程(Bortz方程)的新算法,以角速度多项式作为输入,利用泰勒级数将Bortz方程中的余切函数展开成多项式形式,将不可交换误差补偿中的叉乘和求模运算变换为多项式的卷积运算,通过迭代求取等效旋转矢量的多项式精确解,有效地解决了捷联惯导系统在大角度机动环境下的姿态精确确定问题。此外,还对新算法的数值运算量和迭代收敛精度进行了分析。最后,进行了半锥角90°、频率1 Hz、时长1 s的大幅值圆锥运动姿态更新仿真实验,与传统圆锥优化算法的5''姿态误差相比,新算法的误差仅为10^(-7)'',具有明显的精度优势。
A new numerical solution for the equivalent rotation vector differential equation(Bortz equation) based on polynomial iteration is proposed. In this algorithm, the angular velocity polynomial is taken as input, and the Taylor series is used for expanding the cotangent function into polynomial form in the Bortz equation. The cross-multiplication and the modulo operation in the non-commutative error compensation are transformed into polynomial convolution operation. Then an exact polynomial solution for the equivalent rotation vector can be iteratively obtained. By this algorithm, it is easy to reach high accuracy for strapdown attitude updating even under severe angular maneuver. Moreover, the calculation burden and iteration convergence precision of the new algorithm are also analyzed. Finally, a 1 s duration test is carried out under large coning motion with 90° apex angle and 1 Hz frequency. In comparison to the error of 5’’ by the traditional algorithm, the error by the new algorithm is only 10-7’’, showing that the new algorithm can significantly improve the accuracy.
作者
严恭敏
李思锦
秦永元
YAN Gongmin;LI Sijin;QIN Yongyuan(School of Automation, Northwestern Polytechnical University, Xi’an 710072, China)
出处
《中国惯性技术学报》
EI
CSCD
北大核心
2018年第6期708-712,共5页
Journal of Chinese Inertial Technology
基金
装备预研基金(6142506030105)
航空科学基金(20165853041)
关键词
捷联姿态更新算法
等效旋转矢量
迭代
圆锥运动
strapdown attitude algorithm
equivalent rotation vector
iteration
coning motion
