基于高阶多项式迭代的捷联姿态更新优化方法  

Optimized method for strapdown attitude algorithm based on high-order polynomial iteration

作　　者：刘锡祥[1,2] 赵苗苗 张玉鹏 郭小乐 王磊[3] LIU Xixiang;ZHAO Miaomiao;ZHANG Yupeng;GUO Xiaole;WANG Lei(Key Laboratory of Micro-inertial Instrument and Advanced Navigation Technology,Ministry of Education,Southeast University,Nanjing 210096,China;School of Instrument Science&Engineering,Southeast University,Nanjing 210096,China;College of Optical Science and Engineering,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]东南大学仪器科学与工程学院,南京210096 [2]微惯性仪表与先进导航技术教育部重点实验室,南京210096 [3]浙江大学光电科学与工程学院,杭州310027

出　　处：《中国惯性技术学报》2020年第6期729-734,741,共7页Journal of Chinese Inertial Technology

基　　金：国家自然科学基金(51979041,61973079);教育部装备预研联合基金(6141A02011906)。

摘　　要：文献《基于多项式迭代的等效旋转矢量微分方程精确数值算法》提出的算法(RVPI)有效避免了Bortz方程的原理性近似误差,而角速度多项式的拟合精度仍是制约其算法精度的关键因素。针对此问题,提出了角速度拟合多项式的一种改进方法。通过引入圆锥运动,利用角速度各阶导数之间的解析关系增加约束条件,使得角速度拟合多项式的阶数由原来的n-1增加到n或n+1。其后为旋转矢量提供精确的高阶多项式解,有效地实现姿态更新。分别以圆锥运动和多项式角运动作为输入进行仿真,并与传统优化圆锥算法、RVPI算法作对比。结果表明,在圆锥运动条件下,与传统算法相比,改进算法与RVPI具有类似的误差特征,但改进算法精度较RVPI有全面提升;在多项式角运动环境下,改进算法与RVPI精度相当。The algorithm(RVPI)in the literature"Accurate numerical solution for differential equation of equivalent rotation vector based on polynomial iteration"effectively avoided the principle error of the Bortz equation,however,the fitting accuracy of the angular velocity polynomial is still the key factor restricting the accuracy of the algorithm.In order to solve this problem,an improved method of angular velocity fitting polynomial is proposed.By introducing cone motion,the analytical relationship between the various derivatives of angular velocity is used to add constraint conditions,so that the order of the angular velocity fitting polynomial is increased from n-1 to n or n+1.Then it provides an accurate higher-order polynomial solution for the rotation vector,which accomplishing attitude updating effectively.Finally,under the cone motion and polynomial angular motion,the improved algorithm is compared with the traditional algorithm and RVPI algorithm.The results show that under the cone motion,the improved algorithm has similar accuracy characteristics as RVPI,compared to the traditional algorithm,but the accuracy of the improved algorithm is comprehensively improved compared to RVPI;under the polynomial angular motion,the improved algorithm has the same accuracy as RVPI.

关 键 词：旋转矢量 圆锥运动 高阶多项式 姿态更新 

分 类 号：U666.1[交通运输工程—船舶及航道工程]