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

摘要/Abstract

摘要：

针对传统的传递对准模型在大失准角下的强非线性问题以及由残余杆臂误差导致的传递对准精度下降问题, 提出了一种改进的惯性系传递对准算法。首先, 对子惯导姿态矩阵进行链式分解, 得到常值姿态矩阵; 然后, 利用罗德里格斯参数等价替代该常值姿态矩阵, 建立关于罗德里格斯参数和残余杆臂误差的具有弱非线性量测的传递对准模型; 最后, 利用非线性滤波对状态进行估计。基于摇摆运动的仿真实验表明, 在存在大安装误差角以及残余杆臂误差情况下, 算法相比于现有方法, 对准速度更快, 对准精度更高, 在5~10 s内即可完成传递对准。车载试验结果也间接说明算法具有更高的传递对准性能。

关键词: 惯性导航系统, 传递对准, 非线性卡尔曼滤波, 安装误差角, 失准角

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

中图分类号:

U666.1

徐庚, 何永旭, 张勇刚. 基于罗德里格斯参数的惯性系传递对准算法[J]. 系统工程与电子技术, 2022, 44(9): 2903-2913.

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

图/表 24

表1

图1

表2

表3

图2

图3

图4

图5

表4

图6

图7

图8

图9

表5

图10

图11

图12

图13

图14

图15

图16

图17

图18

图19

参考文献 34

1	WU Y Y , WU M P , HU X P , et al. Optimization-based alignment for inertial navigation systems: theory and algorithm[J]. Aerospace Science and Technology, 2011, 15 (1): 1- 17. doi: 10.1016/j.ast.2010.05.004
2	KANG T Z , FANG J C , WANG W . Quaternion-optimization-based in-flight alignment approach for airborne POS[J]. IEEE Trans.on Instrumentation and Measurement, 2012, 61 (11): 2916- 2923. doi: 10.1109/TIM.2012.2202989
3	GROVES P D. Transfer alignment using an integrated INS/GPS as the reference[C]//Proc. of the 55th Annual Meeting of the Institute of Navigation, 1999: 731-737.
4	GROVES P D, HADDOCK J. An all-purpose rapid transfer alignment algorithm set[C]//Proc. of the National Technical Meeting of the Institute of Navigation, 2001: 160-171.
5	GROVES P D, WILSON G G, MATHER C J. Robust rapid transfer alignment with an INS/GPS reference[C]//Proc. of the National Technical Meeting of The Institute of Navigation, 2002: 301-311.
6	GRAHAM W R, RABOURN C, SHORTELLE K J. Rapid alignment prototype (RAP) flight test demonstration[C]//Proc. of the National Technical Meeting of the Institute of Naviga-tion, 1998.
7	GRAHAM W R, SHORTELLE K J, RABOURN C. F-16 flight tests of a rapid transfer alignment procedure[C]//Proc. of the IEEE Position Location and Navigation Symposium, 1996.
8	WANG T D , CHENG J H , GUAN D X . Modified compensation algorithm of lever-arm effect and flexural deformation for polar shipborne transfer alignment based on improved adaptive Kalman filter[J]. Measurement Science and Technology, 2017, 28 (9): 095101. doi: 10.1088/1361-6501/aa781a
9	HUANG Y L , ZHANG Z , DU S Y , et al. A high-accuracy GPS-aided coarse alignment method for MEMS-based SINS[J]. IEEE Trans.on Instrumentation and Measurement, 2020, 69 (10): 7914- 7932. doi: 10.1109/TIM.2020.2983578
10	GROVES P D . Optimising the transfer alignment of weapon INS[J]. Journal of Navigation, 2003, 56 (2): 323- 335. doi: 10.1017/S0373463303002261
11	LU J Z , XIE L L , LI B G . Applied quaternion optimization method in transfer alignment for airborne AHRS under large misalignment angle[J]. IEEE Trans.on Instrumentation and Measurement, 2016, 65 (2): 346- 354. doi: 10.1109/TIM.2015.2502838
12	LU J Z , YE L L , DONG J . Applied singular value decomposition method in transfer alignment and bias calibration[J]. IET Radar, Sonar & Navigation, 2020, 14 (5): 700- 706.
13	崔潇, 秦永元, 严恭敏, 等. 任意失准角无奇异快速传递对准[J]. 宇航学报, 2018, 39 (10): 1127- 1133. doi: 10.3873/j.issn.1000-1328.2018.10.008
	CUI X , QIN Y Y , YAN G M , et al. Nonsingular rapid transfer alignment for SINS at random misalignment angles[J]. Journal of Astronautics, 2018, 39 (10): 1127- 1133. doi: 10.3873/j.issn.1000-1328.2018.10.008
14	BAZIW J , LEONDES C T . In-flight alignment and calibration of inertial measurement units, Part Ⅰ: general formulation[J]. IEEE Trans.on Aerospace and Electronic Systems, 1972, 8 (4): 439- 449.
15	BAZIW J , LEONDES C T . In-flight alignment and calibration of inertial measurement units, Part Ⅱ: experimental results[J]. IEEE Trans.on Aerospace and Electronic Systems, 1972, 8 (4): 450- 465.
16	KAIN J, CLOUTIER J. Rapid transfer alignment for tactical weapon applications[C]//Proc. of the AIAA Guidance, Navigation and Control Conference, 1989: 3581.
17	XU G , HUANG Y L , GAO Z X , et al. A computationally efficient variational adaptive Kalman filter for transfer alignment[J]. IEEE Sensors Journal, 2020, 20 (22): 13682- 13693. doi: 10.1109/JSEN.2020.3004621
18	GONG X L , FAN W , FANG J C . An innovational transfer alignment method based on parameter identification UKF for airborne distributed POS[J]. Measurement, 2014, 58, 103- 114. doi: 10.1016/j.measurement.2014.08.034
19	ZOU S Y , LI J L , LU Z X . A nonlinear transfer alignment of distributed POS based on adaptive second-order divided difference filter[J]. IEEE Sensors Journal, 2018, 18 (23): 9612- 9618. doi: 10.1109/JSEN.2018.2869979
20	CHENG J H , WANG T D , GUAN D X , et al. Polar transfer alignment of shipborne SINS with a large misalignment angle[J]. Measurement Science and Technology, 2016, 27 (3): 035101. doi: 10.1088/0957-0233/27/3/035101
21	严恭敏, 秦永元, 卫育新, 等. 一种适用于SINS动基座初始对准的新算法[J]. 系统工程与电子技术, 2009, 31 (3): 634- 637. doi: 10.3321/j.issn:1001-506X.2009.03.036
	YAN G M , QIN Y Y , WEI Y X , et al. New initial alignment algorithm for SINS on moving base[J]. Systems Engineering and Electronics, 2009, 31 (3): 634- 637. doi: 10.3321/j.issn:1001-506X.2009.03.036
22	梅春波. 捷联惯性导航系统惯性系非线性初始对准技术研究[D]. 西安: 西北工业大学, 2016.
	MEI C B. Nonlinear initial alignment in inertial frame for SINS[D]. Xi'an: Northwestern Polytechnical University, 2016.
23	CUI X , MEI C B , QIN Y Y , et al. A unified model for transfer alignment at random misalignment angles based on second-order EKF[J]. Measurement Science and Technology, 2017, 28 (4): 045106. doi: 10.1088/1361-6501/aa5b75
24	MOCHALOV A V, PRIVALOV V E, KAZANTASEV A V. Use of the ring laser units for measurement of the moving object deformation[C]//Proc. of the 2nd International Conference on Lasers for Measurement and Information Transfer, 2002.
25	吕遐东, 刘佳铭, 姚腾钢. 船舶动态变形特性分析与测量方法研究[J]. 华中科技大学学报: 自然科学版, 2013, 41 (S1): 215- 218.
	LYU X D , LIU J M , YAO T G . Research on ship dynamic deformation characteristic analysis and measurement method[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2013, 41 (S1): 215- 218.
26	李四海, 王珏, 刘镇波, 等. 快速传递对准中机翼弹性变形估计方法比较[J]. 中国惯性技术学报, 2014, 22 (1): 38- 44.
	LI S H , WANG J , LIU Z B , et al. Comparison of wing distortion estimation methods in transfer alignment[J]. Journal of Chinese Inertial Technology, 2014, 22 (1): 38- 44.
27	WANG B , DENG Z H , LIU C , et al. Estimation of information sharing error by dynamic deformation between inertial navi-gation systems[J]. IEEE Trans.on Industrial Electronics, 2014, 61 (4): 2015- 2023. doi: 10.1109/TIE.2013.2271595
28	严恭敏, 李四海, 秦永元. 惯性仪器测试与数据分析[M]. 北京: 国防工业出版社, 2015: 136- 147.
	YAN G M , LI S H , QIN Y Y . Inertial instrument testing and data analysis[M]. Beijing: National Defense Industry Press, 2015: 136- 147.
29	DAMBECK J , BLUM C . Analytical assessment of the propagation of colored sensor noise in strapdown inertial navigation[J]. Sensors, 2020, 20 (23): 6914. doi: 10.3390/s20236914
30	FARRELL J A, SILVA F O, RAHMAN F, et al. IMU error modeling tutorial: INS state estimation with real-time sensor calibration[EB/OL]. [2021-11-06]. https://escholarship.org/uc/item/1vf7j52p.
31	CUI X , YAN G M , FU Q W . A unified nonsingular rapid transfer alignment solution for tactical weapon based on matrix Kalman filter[J]. IEEE Access, 2018, 6, 78700- 78709. doi: 10.1109/ACCESS.2018.2885144
32	WU Y X , PAN X F . Velocity/position integration formula part Ⅰ: application to in-flight coarse alignment[J]. IEEE Trans.on Aerospace and Electronic Systems, 2013, 49 (2): 1006- 1023. doi: 10.1109/TAES.2013.6494395
33	CHOUKROUN D , WEISS H , BAR-ITZHACK I Y , et al. Kalman filtering for matrix estimation[J]. IEEE Trans.on Aerospace and Electronic Systems, 2006, 42 (1): 147- 159. doi: 10.1109/TAES.2006.1603411
34	严恭敏, WANGJinling, 周馨怡. 基于实测轨迹的高精度捷联惯导模拟器[J]. 导航定位学报, 2015, 3 (4): 27- 31.
	YAN G M , WANG J L , ZHOU X Y . High-precision simulator for strapdown inertial navigation systems based on real dynamics[J]. Journal of Navigation and Positioning, 2015, 3 (4): 27- 31.

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/$\sqrt{\mathrm{Hz}}$