系统工程与电子技术 ›› 2023, Vol. 45 ›› Issue (8): 2521-2532.doi: 10.12305/j.issn.1001-506X.2023.08.27
张睿, 奔粤阳, 刘利强, 王坤, 侯靓, 邱天
收稿日期:
2022-06-21
出版日期:
2023-07-25
发布日期:
2023-08-03
通讯作者:
奔粤阳
作者简介:
张睿(1998—), 男, 硕士研究生, 主要研究方向为惯性导航系统标定技术基金资助:
Rui ZHANG, Yueyang BEN, Liqiang LIU, Kun WANG, Liang HOU, Tian QIU
Received:
2022-06-21
Online:
2023-07-25
Published:
2023-08-03
Contact:
Yueyang BEN
摘要:
捷联惯导系统的现场标定使用系统级标定方法, 由于可观测度较小的状态量不能用卡尔曼滤波辨识估计误差参数, 因此提出一种基于状态量正交基的可观测度计算方法, 并根据此方法设计出一种提高全状态量可观测度的转位方案。在转动过程中测量每个时刻静基座惯性导航的速度误差, 使用卡尔曼滤波器辨识出全状态量误差参数。经实验验证, 对比未设置转位方案的现场标定结果, 所提现场标定方法不仅能提高全状态量可观测度, 而且对系统级标定的结果也有提高, 具有较好的工程实用性。
中图分类号:
张睿, 奔粤阳, 刘利强, 王坤, 侯靓, 邱天. 捷联惯导系统全状态量现场标定方法[J]. 系统工程与电子技术, 2023, 45(8): 2521-2532.
Rui ZHANG, Yueyang BEN, Liqiang LIU, Kun WANG, Liang HOU, Tian QIU. Field calibration method of full state variables for strapdown inertial navigation system[J]. Systems Engineering and Electronics, 2023, 45(8): 2521-2532.
表1
绕x轴转动3次各状态量的可观测度"
状态量 | 转动一次 | 转动两次 | 转动三次 |
εx/(°/h) | 1.671 | 284.711 | 1.650×103 |
εy/(°/h) | 0.091 | 13.639 | 304.403 |
εz/(°/h) | 0.063 | 179.117 | 1.734×103 |
Δx/μg | 1.140×10-5 | 0.006 | 0.529 |
Δy/μg | 0.006 | 0.177 | 0.310 |
Δz/μg | 0.008 | 0.032 | 0.539 |
Kgx/ppm | 0.597 | 8.934 | 17.838 |
Egyx/(″) | 0.002 | 1.250 | 14.276 |
Egzx/(″) | 0.002 | 2.152 | 28.397 |
Egxy/(″) | 1.094×10-4 | 82.451 | 156.938 |
Kgy/ppm | 1.027×10-6 | 0.963 | 1.147 |
Egzy/(″) | 2.758×10-7 | 24.635 | 146.249 |
Egxz/(″) | 4.573×10-4 | 0.019 | 92.586 |
Egyz/(″) | 2.825×10-7 | 5.487×10-4 | 111.916 |
Kgz/ppm | 1.024×10-6 | 0.011 | 60.843 |
Kax/ppm | 5.648×10-8 | 1.691×10-5 | 3.804 |
Eayx/(″) | 2.441×10-6 | 0.027 | 3.002 |
Eazx/(″) | 3.232×10-6 | 1.072×10-4 | 3.146 |
Eaxy/(″) | 0.002 | 0.356 | 5.071 |
Kay/ppm | 0.111 | 2.440 | 3.987 |
Eazy/(″) | 2.455×10-7 | 1.562 | 5.519 |
Eaxz/(″) | 0.001 | 0.359 | 5.125 |
Eayz/(″) | 2.455×10-7 | 1.378 | 3.037 |
Kaz/ppm | 0.085 | 2.510 | 3.636 |
Ka2x/(μg/g2) | 1.605×10-11 | 4.146×10-6 | 35.487 |
Ka2y/(μg/g2) | 1.654 | 17.826 | 34.681 |
Ka2z/(μg/g2) | 0.962 | 17.426 | 30.055 |
表2
3种转动次序误差参数的可观测度"
状态量 | xyz | xzy | yxz |
εx/(°/h) | 1.650×103 | 1.412×103 | 293.278 |
εy/(°/h) | 304.403 | 1.361×103 | 1.649×103 |
εz/(°/h) | 1.734×103 | 1.997×103 | 1.724×103 |
Δx/μg | 0.529 | 0.501 | 0.312 |
Δy/μg | 0.310 | 0.484 | 0.590 |
Δz/μg | 0.539 | 0.504 | 0.595 |
Kgx/ppm | 17.838 | 19.379 | 1.377 |
Egyx/(″) | 14.276 | 14.142 | 160.514 |
Egzx/(″) | 28.397 | 29.801 | 163.561 |
Egxy/(″) | 156.938 | 105.465 | 15.174 |
Kgy/ppm | 1.147 | 98.902 | 17.920 |
Egzy/(″) | 146.249 | 99.910 | 30.960 |
Egxz/(″) | 92.586 | 55.976 | 114.867 |
Egyz/(″) | 111.916 | 69.792 | 99.790 |
Kgz/ppm | 60.843 | 57.637 | 61.039 |
Kax/ppm | 3.804 | 4.416 | 3.996 |
Eayx/(″) | 3.002 | 4.944 | 5.594 |
Eazx/(″) | 3.146 | 5.157 | 6.035 |
Eaxy/(″) | 5.071 | 4.772 | 3.014 |
Kay/ppm | 3.987 | 4.647 | 3.867 |
Eazy/(″) | 5.519 | 5.379 | 3.152 |
Eaxz/(″) | 5.125 | 4.727 | 3.066 |
Eayz/(″) | 3.037 | 4.544 | 5.586 |
Kaz/ppm | 3.636 | 4.667 | 3.584 |
Ka2x/(μg/g2) | 35.487 | 63.204 | 35.225 |
Ka2y/(μg/g2) | 34.681 | 54.684 | 35.151 |
Ka2z/(μg/g2) | 30.055 | 55.214 | 29.967 |
表3
其余3种转动次序误差参数的可观测度"
状态量 | yzx | zxy | zyx |
εx/(°/h) | 1.503×103 | 1.617×103 | 1.209×103 |
εy/(°/h) | 1.433×103 | 852.538 | 3.894×103 |
εz/(°/h) | 2.101×103 | 926.849 | 680.545 |
Δx/μg | 0.468 | 0.047 | 0.500 |
Δy/μg | 0.466 | 0.483 | 0.039 |
Δz/μg | 0.427 | 0.441 | 0.421 |
Kgx/ppm | 112.513 | 16.739 | 1.146 |
Egyx/(″) | 111.234 | 10.034 | 195.471 |
Egzx/(″) | 98.915 | 13.540 | 83.377 |
Egxy/(″) | 14.389 | 194.768 | 25.275 |
Kgy/ppm | 23.022 | 1.676 | 16.571 |
Egzy/(″) | 29.980 | 118.956 | 29.710 |
Egxz/(″) | 87.479 | 41.815 | 22.316 |
Egyz/(″) | 69.542 | 25.359 | 36.595 |
Kgz/ppm | 45.749 | 0.054 | 0.041 |
Kax/ppm | 4.735 | 8.443×10-5 | 3.658 |
Eayx/(″) | 4.963 | 0.030 | 1.129 |
Eazx/(″) | 6.114 | 0.018 | 4.468 |
Eaxy/(″) | 4.971 | 1.023 | 0.058 |
Kay/ppm | 4.820 | 3.690 | 4.910×10-5 |
Eazy/(″) | 5.687 | 4.380 | 0.043 |
Eaxz/(″) | 5.330 | 1.021 | 4.859 |
Eayz/(″) | 4.961 | 4.795 | 2.391 |
Kaz/ppm | 245.849 | 3.466 | 3.455 |
Ka2x/(μg/g2) | 36.784 | 1.086×10-5 | 31.206 |
Ka2y/(μg/g2) | 43.079 | 30.851 | 3.621×10-5 |
Ka2z/(μg/g2) | 41.161 | 27.884 | 27.278 |
表5
标定真实值设定"
状态量 | 真实值 |
εx/(°/h) | 0.25 |
εy/(°/h) | 0.25 |
εz/(°/h) | 0.25 |
Δx/μg | 25 |
Δy/μg | 25 |
Δz/μg | 25 |
Kgx/ppm | 20 |
Egyx/(″) | -30 |
Egzx/(″) | -50 |
Egxy/(″) | -10 |
Kgy/ppm | 20 |
Egzy/(″) | -60 |
Egxz/(″) | -20 |
Egyz/(″) | -40 |
Kgz/ppm | 20 |
Kax/ppm | 20 |
Eayx/(″) | -10 |
Eazx/(″) | -20 |
Eaxy/(″) | 0 |
Kay/ppm | 20 |
Eazy/(″) | -30 |
Eaxz/(″) | 0 |
Eayz/(″) | 0 |
Kaz/ppm | 20 |
Ka2x/(μg/g2) | 25 |
Ka2y/(μg/g2) | 25 |
Ka2z/(μg/g2) | 25 |
表7
传统转位方案的可观测度计算结果"
状态量 | 可观测度 |
εx/(°/h) | 6.021×105 |
εy/(°/h) | 4.354×105 |
εz/(°/h) | 1.056×105 |
Δx/μg | 495.414 |
Δy/μg | 270.582 |
Δz/μg | 228.641 |
Kgx/ppm | 1.767×104 |
Egyx/(″) | 4.546×104 |
Egzx/(″) | 3.247×104 |
Egxy/(″) | 1.518×104 |
Kgy/ppm | 5.724×103 |
Egzy/(″) | 9.801×103 |
Egxz/(″) | 7.864×104 |
Egyz/(″) | 9.436×104 |
Kgz/ppm | 1.314×103 |
Kax/ppm | 2.980×103 |
Eayx/(″) | 1.334×103 |
Eazx/(″) | 1.473×103 |
Eaxy/(″) | 369.099 |
Kay/ppm | 2.882×103 |
Eazy/(″) | 1.423×103 |
Eaxz/(″) | 1.417×103 |
Eayz/(″) | 2.121×103 |
Kaz/ppm | 4.195×103 |
Ka2x/(μg/g2) | 1.858×104 |
Ka2y/(μg/g2) | 1.770×104 |
Ka2z/(μg/g2) | 2.288×104 |
表8
转位可观测度计算结果"
状态量 | 可观测度 |
εx/(°/h) | 5.559×105 |
εy/(°/h) | 9.992×105 |
εz/(°/h) | 1.015×106 |
Δx/μg | 1.186×103 |
Δy/μg | 452.664 |
Δz/μg | 717.058 |
Kgx/ppm | 1.297×105 |
Egyx/(″) | 9.366×104 |
Egzx/(″) | 1.029×105 |
Egxy/(″) | 5.535×104 |
Kgy/ppm | 8.352×104 |
Egzy/(″) | 7.521×104 |
Egxz/(″) | 5.551×104 |
Egyz/(″) | 5.398×104 |
Kgz/ppm | 7.991×104 |
Kax/ppm | 4.977×103 |
Eayx/(″) | 1.387×103 |
Eazx/(″) | 2.478×103 |
Eaxy/(″) | 2.794×103 |
Kay/ppm | 4.697×103 |
Eazy/(″) | 1.885×103 |
Eaxz/(″) | 2.592×103 |
Eayz/(″) | 1.642×103 |
Kaz/ppm | 4.596×103 |
Ka2x/(μg/g2) | 2.455×104 |
Ka2y/(μg/g2) | 3.500×104 |
Ka2z/(μg/g2) | 3.314×104 |
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