Systems Engineering and Electronics ›› 2023, Vol. 45 ›› Issue (8): 2521-2532.doi: 10.12305/j.issn.1001-506X.2023.08.27
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Field calibration method of full state variables for strapdown inertial navigation system
Rui ZHANG, Yueyang BEN, Liqiang LIU, Kun WANG, Liang HOU, Tian QIU
- College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China
-
Received:2022-06-21Online:2023-07-25Published:2023-08-03 -
Contact:Yueyang BEN
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Cite this article
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.
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Table 1
Observability degree of each state quantity rotated three times about the x axis"
| 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 |
Table 1
Table 2
Observability degree of three rotation order error parameters"
| 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 |
Table 2
Table 3
Observability degree of the other three rotation order error parameters"
| 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 |
Table 3
Fig.1
Design flowchart of transposition scheme"
Fig.1
Table 4
The new designed calibration transposition scheme"
| 转动次序 | 三轴指向 | 转动90° |
| 1 | 东北天 | +ox |
| 2 | 东地北 | +ox |
| 3 | 东南地 | +ox |
| 4 | 东天南 | －ox |
| 5 | 东南地 | －ox |
| 6 | 东地北 | －ox |
| 7 | 东北天 | +oy |
| 8 | 天北西 | +oz |
| 9 | 南天西 | +oz |
| 10 | 地南西 | +oz |
| 11 | 北地西 | －oz |
| 12 | 地南西 | －oz |
| 13 | 南天西 | －oz |
| 14 | 天北西 | +oy |
| 15 | 西北地 | +ox |
| 16 | 西天北 | +ox |
| 17 | 西南天 | +ox |
| 18 | 西地南 | －ox |
| 19 | 西南天 | －ox |
| 20 | 西天北 | －ox |
| 21 | 西北地 | －oy |
| 22 | 天北西 | －oy |
| 23 | 东北天 | 停止 |
Table 4
Table 5
Calibration true value setting"
| 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 |
Table 5
Table 6
Calibration transposition scheme"
| 转动次序 | 三轴指向 | 转动90° |
| 1 | 东北天 | +oy |
| 2 | 天北西 | +oy |
| 3 | 西北地 | +oy |
| 4 | 地北东 | －oy |
| 5 | 西北地 | －oy |
| 6 | 天北西 | －oy |
| 7 | 东北天 | +oz |
| 8 | 南东天 | +ox |
| 9 | 南地东 | +ox |
| 10 | 南西地 | +ox |
| 11 | 南天西 | －ox |
| 12 | 南西地 | －ox |
| 13 | 南地东 | －ox |
| 14 | 南东天 | +oz |
| 15 | 西南天 | +oz |
| 16 | 北西天 | －oz |
| 17 | 西南天 | －oz |
| 18 | 南东天 | －oz |
| 19 | 东北天 | 停止 |
Table 6
Table 7
Calculation results of observability degree of the traditional transposition scheme"
| 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 |
Table 7
Fig.2
Gyro drift calibration"
Fig.2
Fig.3
Accelerometer bias calibration"
Fig.3
Fig.4
Scale factor error calibration"
Fig.4
Fig.5
Installation error calibration"
Fig.5
Fig.6
Quadratic nonlinear error calibration"
Fig.6
Fig.7
Gyro drift covariance"
Fig.7
Fig.8
Accelerometer bias covariance"
Fig.8
Fig.9
Scale factor error covariance"
Fig.9
Fig.10
Installation error covariance"
Fig.10
Fig.11
Quadratic nonlinear error covariance"
Fig.11
Table 8
Calculation results of observability degree with transposition"
| 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 |
Table 8
Fig.12
Gyro drift calibration"
Fig.12
Fig.13
Accelerometer bias calibration"
Fig.13
Fig.14
Scale factor error calibration"
Fig.14
Fig.15
Installation error calibration"
Fig.15
Fig.16
Quadratic nonlinear error calibration"
Fig.16
Fig.17
Gyro drift covariance"
Fig.17
Fig.18
Accelerometer bias covariance"
Fig.18
Fig.19
Scale factor error covariance"
Fig.19
Fig.20
Installation error covariance"
Fig.20
Fig.21
Quadratic nonlinear error covariance"
Fig.21
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