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

Abstract

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

CLC Number:

U666.1

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.

Figures/Tables 18

Table 1

Fig.1

Fig.2

Table 2

Attitude error caused by scale factor and installation error in the traditional 16-position rotation scheme"

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	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$

Table 2

Table 3

Attitude error caused by scale factor and installation error in the improved scheme"

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	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]^{\mathrm{T}}$

Table 3

Fig.3

Fig.4

Table 4

Fig.5

Table 5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.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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Biaxial rotation scheme based on diagonal rotation of IMU body

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