基于罗德里格斯参数的惯性系传递对准算法

doi:10.12305/j.issn.1001-506X.2022.09.25

Abstract

Abstract:

Aiming at the strong nonlinear problem for the conventional transfer alignment model with large misalignment angle and the problem of the degraded alignment accuracy induced by the residual lever arm error, an improved inertial-frame-based transfer alignment (ITA) method is proposed for inertial navigation system (INS). Firstly, a constant attitude matrix is obtained based on the chain rule for the attitude matrix of slave INS. Then, the constant attitude matrix is equivalently replaced by the Rodriguez parameter, and a novel transfer alignment model with weakly nonlinear measurement equation is established based on the Rodriguez parameter and the residual lever arm error. Finally, the nonlinear Kalman filters are implemented for the estimation. Simulation results under the sway motion illustrate that when the installation error angles are large and the residual lever arm error exists, the ITA method has the faster alignment speed and the better alignment accuracy than existing transfer alignment methods, and the transfer alignment can be completed in 5~10s. The field test results also illustrate that the ITA method has significantly better alignment performance.

Key words: inertial navigation system (INS), transfer alignment, nonlinear Kalman filter, installation error angle, misalignment angle

CLC Number:

U666.1

Geng XU, Yongxu HE, Yonggang ZHANG. Inertial-frame-based transfer alignment using Rodriguez parameters[J]. Systems Engineering and Electronics, 2022, 44(9): 2903-2913.

Figures/Tables 24

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符号	说明
i	惯性坐标系
n	导航坐标系(东-北-天)
e	地球坐标系(地心地固坐标系)
m	主惯导体坐标系(右-前-上)
s	子惯导体坐标系(右-前-上)
φ, γ,Ψ	纵摇角、横摇角、航向角
C_x^y	x系到y系的方向余弦矩阵
ω_xy^z	y系相对x系的角速度在z系上的投影
I_a, 0_a×b	a×a单位阵, a×b零矩阵(向量)
diag(·)	把向量转换为对角矩阵
(·)^－1	矩阵求逆运算
(·)^T	矩阵(向量)转置运算
(α×)	向量α的反对称阵

参数	设定值
摇摆幅值/(°)	φ_m=5, γ_m=4, Ψ_m=3
摇摆周期/s	T_φ=7, T_γ=8, T_Ψ=9
初始角度/(°)	φ_I=0, γ_I=0, Ψ_I=45
离散时间/s	T_s=0.01

传感器	启动零偏	角度/速度随机游走
陀螺仪	100°/h	1°/$\sqrt{\mathrm{h}}$
加速度计	5 mg	100 μg/$\sqrt{\mathrm{Hz}}$

传感器	相关时间/s	过程方差
陀螺仪	50	(10°/h)²
加速度计	50	(1 mg)²

传递对准算法	统计方法	μ_x^m	μ_y^m	μ_z^m
UKF-TA	均值	-3.507 0	-1.340 9	0.127 8
UKF-TA	RMS	3.554 7	1.347 7	0.137 3
SVD-TA	均值	3.531 8	-9.124 3	1.933 7
SVD-TA	RMS	3.532 0	9.130 8	1.957 8
MKF-TA	均值	1.566 6	-3.078 3	0.241 0
MKF-TA	RMS	1.590 2	3.079 9	0.675 8
EKF-ITA	均值	0.005 1	-0.052 1	-0.055 9
EKF-ITA	RMS	0.031 1	0.056 5	0.062 9
UKF-ITA	均值	0.013 6	-0.050 9	-0.057 5
UKF-ITA	RMS	0.034 1	0.054 3	0.064 7

传感器	零偏稳定性	角度/速度随机游走
陀螺仪	1°/h	0.1°/$\sqrt{\mathrm{h}}$
加速度计	1 mg	100 μg/$\sqrt{\mathrm{Hz}}$

Inertial-frame-based transfer alignment using Rodriguez parameters

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