高精度捷联惯导数值更新算法的设计与改进

论文总字数：26865字

摘 要

随着捷联惯导系统的不断发展，捷联惯导系统因其成本低、使用方便等优点逐渐取代平台惯导系统，越来越多的应用于各种低精度需求环境及复杂高精度需求环境中。但是传统的捷联惯导姿态更新算法在大角度机动环境下会产生较大的姿态漂移误差，严重影响导航精度。为了提高捷联惯导系统在各种复杂场合下的导航精度，针对姿态更新算法的设计与改进有十分重要的意义。

本文基于捷联惯导系统，首先介绍了惯性导航原理和传统姿态更新算法等基础知识。然后介绍了各种传统的姿态更新算法，并分析其原理性误差，比较了各种算法的计算量、使用限制和适用场合等。在分析这些算法优缺点的基础上，找到了根据四元数微分方程的毕卡级数解直接推导姿态更新的数值算法。该算法在计算过程中对不可交换误差做出了精确补偿。通过该算法的仿真实验，并与传统多子样优化算法同环境下仿真实验进行对比。可以确定该算法在高机动环境下尤其是大幅值圆锥运动和大角度机动环境情况中，有着极高的精度，明显优于传统算法。

关键词：捷联惯导，姿态更新算法，毕卡级数，四元数

Abstract

With the continuous development of strapdown inertial navigation system, strapdown inertial navigation system gradually replaces the platform inertial navigation system. Because of its low cost and convenient use, the system is more and more used in all kinds of environment. However, the traditional strapdown inertial navigation attitude updating algorithm will produce large attitude drift error in large angle maneuvering environment, which will seriously affect the navigation accuracy. In order to improve the navigation accuracy of strapdown inertial navigation system in various complex situations, the design and improvement of attitude updating algorithm is of great significance.

Based on strapdown inertial navigation system, firstly, this paper introduces the principle of inertial navigation and the traditional attitude updating algorithm. Then, various traditional attitude updating algorithms are introduced, and their principle errors are analyzed. The computational complexity, usage limitations and applicable situations of these algorithms are compared. Based on the analysis of the advantages and disadvantages of these algorithms, a numerical algorithm is found to directly deduce the attitude update according to the Picard series solution of the quaternion differential equation. The algorithm accurately compensates the non-interchangeable error in the calculation process. The simulation experiment of the algorithm is carried out and compared with the traditional multi-sample optimization algorithm in the same environment.The method has very high accuracy in high maneuvering environment, especially in large amplitude conical motion and large angle maneuvering environment, and is obviously superior to the traditional algorithm.

KEY WORDS: strapdown inertial navigation, attitude updating algorithm, Picard series, quaternion

目 录

摘 要 Ⅰ

Abstract Ⅱ

第一章 绪论 1

1.1课题背景 1

1.2课程研究意义 1

1.3国内外研究发展 2

第二章 捷联惯导系统简介 4

2.1捷联惯导系统的基本原理 4

2.2两种惯导系统对比 4

2.2.1软硬件要求 4

2.2.2系统精度 5

2.3常用坐标系 5

第三章 传统姿态更新算法 7

3.1 欧拉角法 7

3.1.1欧拉角的基本概念 7

3.1.2欧拉角微分方程式 7

3.1.3欧拉角法分析 8

3.2 方向余弦法 8

3.2.1方向余弦阵 8

3.2.2方向余弦矩阵微分方程 8

3.2.3方向余弦法分析 9

3.3 四元数法 10

3.3.1四元数基本概念 10

3.3.2四元数微分方程式 10

3.3.3四元数法分析 12

3.4 等效旋转矢量法 12

3.4.1旋转矢量基本概念 12

3.4.2旋转矢量微分方程 12

3.4.3旋转矢量法分析 14

第四章 捷联惯导数值更新算法优化设计 15

4.1四元数微分方程的毕卡求解法 15

4.1.1定时采样增量法 15

4.1.2定量采样增量法 17

4.2姿态更新算法设计 18

4.2.1由角增量构造角速度 18

4.2.2姿态四元数微分方程求解 19

4.3姿态更新算法的优化 21

第五章 仿真与分析 23

5.1圆锥运动仿真 23

5.2模拟真实环境仿真 27

5.2.1晃动基座无误差大角度下算法对比 28

5.2.2晃动基座无误差小角度下算法对比 29

5.2.3晃动基座有误差大角度下算法对比 31

5.2.4晃动基座有误差小角度下算法对比 32

5.2.5静基座无误差下算法对比 33

5.2.6不同采样间隔下算法对比 35

第六章 结论 38

参考文献 39

致 谢 41

1. 绪论

1.1课题背景

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