一种新的捷联惯性导航系统姿态四元数方程求解方法

doi:10.3969/j.issn.1000-1093.2018.03.013

兵工学报 ›› 2018, Vol. 39 ›› Issue (3): 511-518.doi: 10.3969/j.issn.1000-1093.2018.03.013

一种新的捷联惯性导航系统姿态四元数方程求解方法

周召发，胡文，张志利，徐梓皓，陈河

（火箭军工程大学兵器发射理论与技术国家重点学科实验室，陕西西安 710025）

收稿日期:2017-07-17 修回日期:2017-07-17 上线日期:2018-05-07
作者简介:周召发(1973—), 男, 教授，博士生导师。E-mail: bite1apple@163.com
基金资助:
国家自然科学基金项目（41174162）

A New Calculation Method of Quaternion Differential Equation for Attitude of Strapdown Inertial Navigation System

ZHOU Zhao-fa, HU Wen, ZHANG Zhi-li, XU Zi-hao, CHEN He

(State Key Discipline Laboratory of Armament Launch Theory and Technology, Rocket Force University of Engineering， Xi'an 710025, Shaanxi, China)

Received:2017-07-17 Revised:2017-07-17 Online:2018-05-07

摘要/Abstract

摘要： 为了解决传统四元数算法计算精度不高的问题，借鉴三子样旋转矢量法的求解过程，提出了一种新的四元数微分方程求解方法——三子样四元数法。三子样四元数法结合四元数微分方程求解旋转四元数的高阶导数，用抛物线拟合载体的角速度并给出角增量形式的计算公式，再根据旋转四元数泰勒展开式建立求解模型。仿真结果表明，当三子样四元数法取到9阶时，整体结果优于三子样旋转矢量法。

关键词: 捷联惯性导航系统, 三子样四元数法, 旋转矢量法, 泰勒级数

Abstract: A new calculation method of quaternion differential equation, which is called three-subsample quaternion algorithm, is presented to solve the problem of low calculation accuracy of traditional quaternion algorithm by using the calculation process of three-subsample rotation vector algorithm for reference. In the calculation process, the higher derivative of rotation quaternion is calculated on the basis of quaternion differential equation, the angular velocity of carrier is fitted by the parabola, the expression is given for angular increment, and then a model for calculating quaternion differential equation is established by means of the Taylor expansion of rotation quaternion. The simulated result indicates that the three-subsample quaternion algorithm is better than three-subsample rotation vector algorithm. Key

Key words: strapdowninertialnavigationsystem, three-subsamplequaternionalgorithm, rotationvectoralgorithm, Taylorseries

中图分类号:

TJ765.1

周召发，胡文，张志利，徐梓皓，陈河. 一种新的捷联惯性导航系统姿态四元数方程求解方法[J]. 兵工学报, 2018, 39(3): 511-518.

ZHOU Zhao-fa, HU Wen, ZHANG Zhi-li, XU Zi-hao, CHEN He. A New Calculation Method of Quaternion Differential Equation for Attitude of Strapdown Inertial Navigation System[J]. Acta Armamentarii, 2018, 39(3): 511-518.

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第3期2018 年3月兵工学报ACTA
ARMAMENTARIIVol.39No.3Mar.2018

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一种新的捷联惯性导航系统姿态四元数方程求解方法

A New Calculation Method of Quaternion Differential Equation for Attitude of Strapdown Inertial Navigation System

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