基于IMU体对角线旋转的双轴旋转方案

doi:10.12305/j.issn.1001-506X.2023.08.29

摘要/Abstract

摘要：

旋转调制技术可以有效降低惯导系统的导航误差，但目前常规旋转惯导系统的机械结构无法更进一步提升误差调制效果。基于惯性测量单元(inertial measurement unit，IMU)体对角线安装结构，提出了一种改进的双轴旋转方案。方案选取IMU 3个正交惯性器件的体对角线为水平旋转轴，与该轴正交的旋转轴为垂向旋转轴。通过改变水平和垂向旋转轴的旋转速度、方向和次序实现双轴旋转。由于旋转轴与惯性器件均不同向，在旋转的任意时刻，3个方向的惯性器件误差均得到了调制。首先，建立了基于体对角线旋转方案的数学模型，在此基础上推导了坐标变换关系与误差方程，得到了误差传播特性，验证了改进方案的优势。最后，进行了系统综合误差的仿真校验。在相同误差条件下，系统位置误差由传统方案的0.418 9海里/120小时减小到0.120 7海里/120小时，验证了改进方案抑制误差的有效性。

关键词: 旋转惯性导航系统, 旋转方案, 误差补偿, 双轴旋转

Abstract:

Rotational modulation technology can effectively reduce the navigation error of inertial navigation system, but the mechanical structure of conventional rotation inertial navigation system cannot further improve the error modulation effect. Based on the diagonal mounting structure of the inertial measurement unit(IMU), an improved biaxial rotation scheme is proposed. In the proposed scheme, the body diagonal of three orthogonal inertial devices of IMU is selected as the horizontal rotation axis, and the axis orthogonal to this axis is the vertical rotation axis. Double axis rotation is realized by changing the rotation speed, direction and order of horizontal and vertical rotation axes. Because the rotation axis and the inertial device are in different directions, the inertial device errors in the three directions are modulated at any time of rotation. Firstly, the mathematical model based on volume diagonal rotation scheme is established. On this basis, the coordinate transformation relationship and error equation are deduced, the error propagation characteristics are obtained, and the advantages of this scheme are verified. Finally, the simulation verification of system synthesis error is carried out. Under the same error condition, the system position error is reduced from 0.418 9 nautical miles / 120 hours of the traditional scheme to 0.120 7 nautical miles / 120 hours, which verifies the effectiveness of the scheme on error suppression.

Key words: rotational inertial navigation system, rotation scheme, error compensation, biaxial rotation

中图分类号:

U666.1

查峰, 位秋硕, 何泓洋, 李豹. 基于IMU体对角线旋转的双轴旋转方案[J]. 系统工程与电子技术, 2023, 45(8): 2546-2554.

Feng ZHA, Qiushuo WEI, Hongyang HE, Bao LI. Biaxial rotation scheme based on diagonal rotation of IMU body[J]. Systems Engineering and Electronics, 2023, 45(8): 2546-2554.

图/表 18

表1

图1

图2

表2

传统16位置旋转方案由刻度系数和安装误差引起的姿态误差"

旋转秩序	Φ_δK	Φ_δA
1	$\left[\begin{array}{lll}0 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & 2 k_2 & 0\end{array}\right]^{\mathrm{T}}$
2	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & 4 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
3	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 6 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
4	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 8 k_2 & 0\end{array}\right]^{\mathrm{T}}$
5	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 6 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
6	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & 4 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
7	$\left[\begin{array}{lll}0 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & 2 k_2 & 0\end{array}\right]^{\mathrm{T}}$
8	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$
9	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & -2 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
10	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & -4 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
11	$\left[\begin{array}{lll}0 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & -6 k_2 & 0\end{array}\right]^{\mathrm{T}}$
12	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & -8 k_2 & 0\end{array}\right]^{\mathrm{T}}$
13	$\left[\begin{array}{lll}0 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & -6 k_2 & 0\end{array}\right]^{\mathrm{T}}$
14	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}-2 k_2 & -4 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
15	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & -2 k_2 & 2 k_2\end{array}\right]^{\mathrm{T}}$
16	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$

表2

表3

改进方案由刻度系数和安装误差引起的姿态误差"

旋转秩序	Φ_δK	Φ_δA
1	$\left[\begin{array}{lll}0 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & \frac{4 \sqrt{2} k_2}{3} & \frac{5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
2	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{-2 {\rm{ \mathsf{ π} }} k_2}{3} & \frac{8 \sqrt{2} k_2}{3} & \frac{5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
3	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{-2 {\rm{ \mathsf{ π} }} k_2}{3} & 4 \sqrt{2} k_2 & 0\end{array}\right]^{\mathrm{T}}$
4	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & \frac{14 \sqrt{2} k_2}{3} & 0\end{array}\right]^{\mathrm{T}}$
5	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{2 {\rm{ \mathsf{ π} }} k_2}{3} & 4 \sqrt{2} k_2 & 0\end{array}\right]^{\mathrm{T}}$
6	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{2 {\rm{ \mathsf{ π} }} k_2}{3} & \frac{8 \sqrt{2} k_2}{3} & \frac{-5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
7	$\left[\begin{array}{lll}0 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}0 & \frac{4 \sqrt{2} k_2}{3} & \frac{-5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
8	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$
9	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{-2 {\rm{ \mathsf{ π} }} k_2}{3} & \frac{-4 \sqrt{2} k_2}{3} & 0\end{array}\right]^{\mathrm{T}}$
10	$\left[\begin{array}{lll}{\rm{ \mathsf{ π} }} k_1 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{-2 {\rm{ \mathsf{ π} }} k_2}{3} & \frac{-8 \sqrt{2} k_2}{3} & \frac{5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
11	$\left[\begin{array}{lll}0 & 0 & {\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}0 & -4 \sqrt{2} k_2 & \frac{5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
12	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}0 & \frac{-14 \sqrt{2} k_2}{3} & 0\end{array}\right]^{\mathrm{T}}$
13	$\left[\begin{array}{lll}0 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}0 & -4 \sqrt{2} k_2 & \frac{-5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
14	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & -{\rm{ \mathsf{ π} }} k_1\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{2 {\rm{ \mathsf{ π} }} k_2}{3} & \frac{-8 \sqrt{2} k_2}{3} & \frac{-5 {\rm{ \mathsf{ π} }} k_2}{3}\end{array}\right]^{\mathrm{T}}$
15	$\left[\begin{array}{lll}-{\rm{ \mathsf{ π} }} k_1 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccc}\frac{2 {\rm{ \mathsf{ π} }} k_2}{3} & \frac{-4 \sqrt{2} k_2}{3} & 0\end{array}\right]^{\mathrm{T}}$
16	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$

表3

图3

图4

表4

图5

表5

图6

图7

图8

图9

图10

图11

图12

图13

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旋转秩序	C_p^b	ω^b	ω^p
1	$\left[\begin{array}{ccc}\cos (\omega t) & -\sin (\omega t) & 0 \\\sin (\omega t) & \cos (\omega t) & 0 \\0 & 0 & 1\end{array}\right]$	$\left[\begin{array}{l}0 \\0 \\\omega\end{array}\right]$	$\left[\begin{array}{l}0 \\0 \\\omega\end{array}\right]$
2	$\left[\begin{array}{ccc}-1 & 0 & 0 \\0 & -\cos (\omega t) & -\sin (\omega t) \\0 & -\sin (\omega t) & \cos (\omega t)\end{array}\right]$	$\left[\begin{array}{l}\omega \\0 \\0\end{array}\right]$	$\left[\begin{array}{c}-\omega \\0 \\0\end{array}\right]$
3	$\left[\begin{array}{ccc}-\cos (\omega t) & \sin (\omega t) & 0 \\\sin (\omega t) & \cos (\omega t) & 0 \\0 & 0 & -1\end{array}\right]$	$\left[\begin{array}{c}0 \\0 \\-\omega\end{array}\right]$	$\left[\begin{array}{l}0 \\0 \\\omega\end{array}\right]$
4	$\left[\begin{array}{ccc}1 & 0 & 0 \\0 & -\cos (\omega t) & -\sin (\omega t) \\0 & \sin (\omega t) & -\cos (\omega t)\end{array}\right]$	$\left[\begin{array}{c}-\omega \\0 \\0\end{array}\right]$	$\left[\begin{array}{c}-\omega \\0 \\0\end{array}\right]$

旋转秩序	文献[6]方案	本文方案
1	(－2k₂)gt_r	0
2	(πk₁－4k₂)gt_r	$\left({\rm{ \mathsf{ π} }} k_1-\frac{2 k_2}{3}\right) g t_r$
3	(2πk₁－4k₂)gt_r	$\left(2 {\rm{ \mathsf{ π} }} k_1-\frac{4 k_2}{3}\right) g t_r$
4	(2πk₁－4k₂)gt_r	$\left(2 {\rm{ \mathsf{ π} }} k_1-\frac{4 k_2}{3}\right) g t_r$
5	(πk₁－4k₂)gt_r	$\left({\rm{ \mathsf{ π} }} k_1-\frac{2 k_2}{3}\right) g t_r$
6	(－6k₂)gt_r	0
7	(－8k₂)gt_r	0
8	(－8k₂)gt_r	0
9	(πk₁－8k₂)gt_r	$\left({\rm{ \mathsf{ π} }} k_1-\frac{2 k_2}{3}\right) g t_r$
10	(2πk₁－10k₂)gt_r	$\left(2 {\rm{ \mathsf{ π} }} k_1-\frac{4 k_2}{3}\right) g t_r$
11	(2πk₁－12k₂)gt_r	$\left(2 {\rm{ \mathsf{ π} }} k_1-\frac{4 k_2}{3}\right) g t_r$
12	(2πk₁－12k₂)gt_r	$\left(2 {\rm{ \mathsf{ π} }} k_1-\frac{4 k_2}{3}\right) g t_r$
13	(2πk₁－14k₂)gt_r	$\left(2 {\rm{ \mathsf{ π} }} k_1-\frac{4 k_2}{3}\right) g t_r$
14	(πk₁－16k₂)gt_r	$\left({\rm{ \mathsf{ π} }} k_1-\frac{2 k_2}{3}\right) g t_r$
15	(－16k₂)gt_r	0
16	(－16k₂)gt_r	0
平均	(πk₁－9k₂)gt_r	$\left({\rm{ \mathsf{ π} }} k_1-\frac{2 k_2}{3}\right) g t_r$

参数名称	参数数值
纬度/(°)	30.58
经度/(°)	114.23
横滚角/(°)	$3 \sin \left(\frac{2 {\rm{ \mathsf{ π} }} t}{7}\right)$
俯仰角/(°)	$5 \sin \left(\frac{{\rm{ \mathsf{ π} }} t}{6}\right)$
航向角	$0.5 \sin \left(\frac{{\rm{ \mathsf{ π} }} t}{4}\right)$
转台转速/(°/s)	6
转动时间、停止时间/s	30
陀螺仪零偏/(°/h)	0.001
陀螺仪随机游走系数/(°/$\sqrt{h}$)	0.000 3
陀螺仪刻度系数误差/ppm	5
陀螺仪安装误差/(″)	5
加速度计零偏/μg	10
加速度计随机噪声/μg	1
加速度计刻度系数误差/ppm	10
加速度计安装误差/(″)	10

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