激光陀螺捷联惯性组合的标定方法研究
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摘要
由于激光陀螺具有精度高、可靠性好、成本低等优点,激光陀螺捷联惯导系统近年来已经成为惯性技术领域的一个重要研究方向。惯性测量组合是捷联惯导系统的核心部件,由加速度计和陀螺仪组成,用于敏感载体的加速度和姿态,因此惯性测量组合的精度将在很大程度上影响系统的导航精度。本文以激光陀螺捷联惯性组合为研究对象,主要分析了系统的误差模型、标定方法及测试设备误差对标定精度的影响。
根据惯性器件的误差来源和工作环境,并考虑安装引起的误差,本文分析了加速度计、激光陀螺及惯性测量系统的误差模型,并根据导航过程中器件误差的传播特性推导了捷联惯导系统的误差方程。在此基础上,完成了加速度计和陀螺仪的测试,为误差补偿提供基准。
研究了激光捷联惯性组合的分立标定方法,在双轴转台上完成了转台的对准及惯性组合的标定实验,设计并实现了加速度计组合的正十二面体20点实验,对实验结果进行分析和比较。通过坐标系变换和谐波分析的方法,分析了转台误差对加速度误差模型各项系数的影响程度,并通过仿真验证,从而为确定转台的精度指标提供了一定的依据。
捷联惯导系统的系统级标定根据标定场所不同分为实验室标定和外场标定。在实验室静基座条件下可以利用速度误差进行系统级标定。本文建立了误差参数标定模型,分析了器件误差可辨识性,完成了标定位置的编排。从理论上分析了外场标定时系统状态的可观测性及收敛速度。
Since laser gyro has the features of high precision, good reliability and low cost etc, laser gyro strapdown inertial navigation system has become an important development trend in recent years. Inertial measurement unit (IMU) which is the core of inertial navigation system (INS) is made up of laser gyros and accelerometers, sensitive to attitude and acceleration of carrier respectively. So the precision of IMU will affect the system navigation precision to a great extent. In this paper, research on error models, calibration methods and errors of the testing equipment on laser gyro strapdown inertial measurement unit are engaged.
Firstly, based on the error sources and working environment of inertial instruments, the installing errors, the error model of the accelerometer, the laser gyro and the IMU are analyzed. The error equation of strapdown inertial navigation system is established according to the error propagation characteristics of inertial instrument when in navigation state. Accelerometers and laser gyros are calibrated for later error compensation.
Then, methods of separate calibration of IMU are studied. Tests of turntable alignment, IMU calibration and dodecahedron 20 points plan are conducted on two-axis turntable, and all test results are compared and analyzed. Through methods of coordinate system transformation and harmonic analysis, the influence of turntable errors on accelerometers calibration precision is analyzed and verified by simulation. This can help to determine turntable precision specification more or less.
Finally, according to calibration field, systematic calibration of IMU could be divided into the laboratory calibration and the outer field calibration. We can carry out systematic calibration through velocity errors under stationary based laboratory condition. In this paper the calibration mathematical model is established, identifiability of instruments errors is analyzed, one arrangement of calibration position is also designed. The observability and convergence rate of system states are analyzed in terms of theory.
根据惯性器件的误差来源和工作环境,并考虑安装引起的误差,本文分析了加速度计、激光陀螺及惯性测量系统的误差模型,并根据导航过程中器件误差的传播特性推导了捷联惯导系统的误差方程。在此基础上,完成了加速度计和陀螺仪的测试,为误差补偿提供基准。
研究了激光捷联惯性组合的分立标定方法,在双轴转台上完成了转台的对准及惯性组合的标定实验,设计并实现了加速度计组合的正十二面体20点实验,对实验结果进行分析和比较。通过坐标系变换和谐波分析的方法,分析了转台误差对加速度误差模型各项系数的影响程度,并通过仿真验证,从而为确定转台的精度指标提供了一定的依据。
捷联惯导系统的系统级标定根据标定场所不同分为实验室标定和外场标定。在实验室静基座条件下可以利用速度误差进行系统级标定。本文建立了误差参数标定模型,分析了器件误差可辨识性,完成了标定位置的编排。从理论上分析了外场标定时系统状态的可观测性及收敛速度。
Since laser gyro has the features of high precision, good reliability and low cost etc, laser gyro strapdown inertial navigation system has become an important development trend in recent years. Inertial measurement unit (IMU) which is the core of inertial navigation system (INS) is made up of laser gyros and accelerometers, sensitive to attitude and acceleration of carrier respectively. So the precision of IMU will affect the system navigation precision to a great extent. In this paper, research on error models, calibration methods and errors of the testing equipment on laser gyro strapdown inertial measurement unit are engaged.
Firstly, based on the error sources and working environment of inertial instruments, the installing errors, the error model of the accelerometer, the laser gyro and the IMU are analyzed. The error equation of strapdown inertial navigation system is established according to the error propagation characteristics of inertial instrument when in navigation state. Accelerometers and laser gyros are calibrated for later error compensation.
Then, methods of separate calibration of IMU are studied. Tests of turntable alignment, IMU calibration and dodecahedron 20 points plan are conducted on two-axis turntable, and all test results are compared and analyzed. Through methods of coordinate system transformation and harmonic analysis, the influence of turntable errors on accelerometers calibration precision is analyzed and verified by simulation. This can help to determine turntable precision specification more or less.
Finally, according to calibration field, systematic calibration of IMU could be divided into the laboratory calibration and the outer field calibration. We can carry out systematic calibration through velocity errors under stationary based laboratory condition. In this paper the calibration mathematical model is established, identifiability of instruments errors is analyzed, one arrangement of calibration position is also designed. The observability and convergence rate of system states are analyzed in terms of theory.
引文
1.张开东.激光陀螺捷联惯导系统连续自动标定技术研究.国防科技大学工学硕士论文. 2002:1~4
2.杨晓霞,黄一.外场标定条件下捷联惯导系统误差状态可观测性分析.中国惯性技术学报. 2008, 16(6):657~664
3. IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-axis, Nongyroscopic Accelerometers. IEEE Std 1293~1998
4.李海强,詹丽娟,卿立.捷联惯性测量装置在整弹上的标定方法研究.战术导弹控制技术. 2006, 2:32~37
5.黄显林.惯导加速度表误差模型优化辨识及实验计划优化设计.哈尔滨工业大学博士论文. 1991:159~193
6.余凯,郑辛,纪志农,刘保中.捷联惯性测量组合的不指北标定方法研究.战术导弹控制技术. 2005, 3:60~63。
7. J. G. Lee, C. G. Park, H. W. Park. Multiposition Alignment of Strapdown Inertial Navigation System. IEEE Transactions on Aerospace and Electronic Systems. 1993, 29(4):1323~1328
8. W. S. Widnall, P. A. Grundy, W. G. Murch. Inertial Navigation System Tests having Improved Observability of Error Sources. Aircraft. 1976,13(1):12~21.
9.王宇.机抖激光陀螺捷联惯导系统的初步探索.国防科技大学工学博士论文, 2005:41~45
10. M. S. Grewal, V. D. Henderson, R. S. Miyasako. Applcation of Kalman Filtering to the Calibration and Alignment of Inertial Navigation Systems. IEEE Transactions on Automatic Control. 1991, 36(1):4~13
11.马越,王跃钢.过载振动复合环境下惯性器件误差建模方法研究.电光与控制. 2005, 12(3):60~62
12.王岩.机抖激光陀螺捷联惯导系统的标定方法研究.国防科技大学工学硕士论文. 2004:6~15
13.杨晓霞,黄一.利用ESO和TD进行的激光捷联惯组误差参数外场标定方法.中国惯性技术学报. 2010, 18(1):1~9
14.严恭敏,秦永元.捷联惯组中陀螺组合标定方法研究.弹箭与制导学报. 2005, 25(4):872~875
15.林玉荣,邓正隆.激光陀螺捷联惯导系统中惯性器件误差的系统级标定.哈尔滨工业大学学报. 2001, 33(1):112~115
16. M. J. Yu, H. W. Park, C. B. Jeon. Equivalent Nonlinear Error Models of Strapdown Inertial Navigation System. American Institute of Aeronautics and Astronautics. 1997:581~587
17.邢海峰.精密离心机误差对加速度计标定误差的影响研究.哈尔滨工业大学硕士学位论文. 2009:53~60
18.傅振宪.惯导平台漂移误差建模与参数辨识研究.哈尔滨工业大学博士论文. 2002:110~142
19. S. H. Wei, L. X. Xiao. Research on ballistic missile laser SIMU error propagation mechanism. Journal of Systems Engineering and Electronics. 2008, 19(2):356~362.
20.徐兵华,杨孟兴.激光陀螺捷联惯性导航系统的误差系数标定研究.导弹与航天运载技术. 2008, 4:22~25。
21.姜复兴,王卫阳,吴广玉.辨识捷联陀螺仪动态误差模型速率实验计划的优化设计.哈尔滨工业大学学报. 1994, 26(5):63~67。
22.任春华.激光陀螺捷联惯导系统若干关键技术及应用研究.重庆大学博士学位论文. 2007:4~16
23. M. E. Pittelkau. Kalman Filtering for Spacecraft System Alignment Calibration. Journal of Guidance Control and Dynamics. 2001, 24(6):1187~1195
24.罗宇锋,范耀祖,富立.正交设计及D最优设计在陀螺测试中的应用.压电与声光. 2008, 30(4):393~397
25. P. G. Savage. Strapdown Inertial Navigation Integration Algorithm Design Part 1: Attitude Algorithms. Journal of Guidance Control and Dynamics. 1998, 21(1):19~28
26.郭喜庆,武克用.基于环形激光陀螺调制输出的寻北系统.光电工程. 2001, 28(2):11~13
27. M. Goldshtein, Y. Oshman, T. Efrati. Seeker Gyro Calibration via Model-Based Fusion of Visual and Inertial Data. International Conference on Information Fusion. 2007. 7
28. FU Zhenxian, DENG Zhenglong. Continuous Calibration of Inertial Platform Drifting Error Parameters. Journal of Harbin Institute of Technology. 2000, 7(3):24~26
29.陈北鸥,孙文胜,张桂宏,陈东海,蒋顺成.捷联组合(设备无定向)六位置测试标定.导弹与航天运载技术. 2001, 3:23~27
30. IEEE standard specification format guide and test procedure for Single-Axis Laser Gyro[S]. IEEE, Std. 647-1995
31.杨晓霞,黄一.激光捷联惯导系统的一种系统级标定方法.中国惯性技术学报. 2008, 16(1):1~7
32. Camberlein. L, Mazzananti. F. Calibration Technology for Laser Gyro Srtapdown Inertial Navigation Systems. Symposium Gyro Technology. Stuttgart. Gennnay. 1985
33. C. N. Lawrence. On the Appliation of Allan Variance Methods for Ring Gyro Performance Characterization. UCRL-ID-115685, October 15, 1993
34. A. Matthews, D. A. Bauer. The Hemispherical Resonator Gyro for Precision Pointing Applications. Space Guidance, Control, and Tracking II, Orlando, FL, USA, 17 April 1995: 128-139
35.白雪峰,赵剡.单轴速率三轴位置惯性测试转台误差及传递分析.航天控制. 2006, 24(2):26~29
36.姜复兴,吴广玉.单轴位置滚转法辨识加速度计静态模型的改进方法.测试技术与设备.中国惯性技术学报. 1994, 2(1):24~29
37.刘峰,徐丹,尚克军,徐策.基于导航误差的系统级标定方法中时间参数选取原则分析.中国惯性技术学报. 2009, 17(6):642~647
38.祁家毅,任顺清,王常虹.用三轴转台辨识陀螺仪误差模型系数时的速率实验设计.宇航学报. 2006, 27(3):565~570
39. Yang Xiaoxia, Huang Yi.Capability of Extended State Observer for Estimating Uncertainties. Proceedings of the 2009 American Control Conference.St Louis, MO, USA , 2009:3700~3705.
40. Goshen-Meskin. D, Bar-Itzhack. I. Y. Observability Analysis of Piece-wise Constant Systems. IEEE Transactions on Aerospace and Electronic System. 1992, 28(4):1056~1075
41.王卫阳.惯性器件和系统误差模型辨识理论及应用研究.哈尔滨工业大学博士学位论文. 1997:30~55
42. IEEE Recommended Practice for Precision Centrifuge Testing of Linear Accelerometers. IEEE Std 836~2001
43. Brown A, Ebner R, Mark J. A Calibration Technique for A Laser GyroStrapdown Inertial Navigation System Conference Proceedings-Symposium Gyro Technology. Stuttgart, 1982:12. 0~12. 20
44. W. Q. Wu, M. Jiang, Z. H. Tuo. Successive Rotating Technique for A Ring Laser Gyro North-finder. International Conference on Navigation, Guidance and Control, 2001: 143~145
45. C. N. Lawrenence, J. P. Darryll. Characterization of Ring Laser Gyro Performance Using the Allan Variance Method. Journal of Guidance, 1996, 20(1): 211~214
2.杨晓霞,黄一.外场标定条件下捷联惯导系统误差状态可观测性分析.中国惯性技术学报. 2008, 16(6):657~664
3. IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-axis, Nongyroscopic Accelerometers. IEEE Std 1293~1998
4.李海强,詹丽娟,卿立.捷联惯性测量装置在整弹上的标定方法研究.战术导弹控制技术. 2006, 2:32~37
5.黄显林.惯导加速度表误差模型优化辨识及实验计划优化设计.哈尔滨工业大学博士论文. 1991:159~193
6.余凯,郑辛,纪志农,刘保中.捷联惯性测量组合的不指北标定方法研究.战术导弹控制技术. 2005, 3:60~63。
7. J. G. Lee, C. G. Park, H. W. Park. Multiposition Alignment of Strapdown Inertial Navigation System. IEEE Transactions on Aerospace and Electronic Systems. 1993, 29(4):1323~1328
8. W. S. Widnall, P. A. Grundy, W. G. Murch. Inertial Navigation System Tests having Improved Observability of Error Sources. Aircraft. 1976,13(1):12~21.
9.王宇.机抖激光陀螺捷联惯导系统的初步探索.国防科技大学工学博士论文, 2005:41~45
10. M. S. Grewal, V. D. Henderson, R. S. Miyasako. Applcation of Kalman Filtering to the Calibration and Alignment of Inertial Navigation Systems. IEEE Transactions on Automatic Control. 1991, 36(1):4~13
11.马越,王跃钢.过载振动复合环境下惯性器件误差建模方法研究.电光与控制. 2005, 12(3):60~62
12.王岩.机抖激光陀螺捷联惯导系统的标定方法研究.国防科技大学工学硕士论文. 2004:6~15
13.杨晓霞,黄一.利用ESO和TD进行的激光捷联惯组误差参数外场标定方法.中国惯性技术学报. 2010, 18(1):1~9
14.严恭敏,秦永元.捷联惯组中陀螺组合标定方法研究.弹箭与制导学报. 2005, 25(4):872~875
15.林玉荣,邓正隆.激光陀螺捷联惯导系统中惯性器件误差的系统级标定.哈尔滨工业大学学报. 2001, 33(1):112~115
16. M. J. Yu, H. W. Park, C. B. Jeon. Equivalent Nonlinear Error Models of Strapdown Inertial Navigation System. American Institute of Aeronautics and Astronautics. 1997:581~587
17.邢海峰.精密离心机误差对加速度计标定误差的影响研究.哈尔滨工业大学硕士学位论文. 2009:53~60
18.傅振宪.惯导平台漂移误差建模与参数辨识研究.哈尔滨工业大学博士论文. 2002:110~142
19. S. H. Wei, L. X. Xiao. Research on ballistic missile laser SIMU error propagation mechanism. Journal of Systems Engineering and Electronics. 2008, 19(2):356~362.
20.徐兵华,杨孟兴.激光陀螺捷联惯性导航系统的误差系数标定研究.导弹与航天运载技术. 2008, 4:22~25。
21.姜复兴,王卫阳,吴广玉.辨识捷联陀螺仪动态误差模型速率实验计划的优化设计.哈尔滨工业大学学报. 1994, 26(5):63~67。
22.任春华.激光陀螺捷联惯导系统若干关键技术及应用研究.重庆大学博士学位论文. 2007:4~16
23. M. E. Pittelkau. Kalman Filtering for Spacecraft System Alignment Calibration. Journal of Guidance Control and Dynamics. 2001, 24(6):1187~1195
24.罗宇锋,范耀祖,富立.正交设计及D最优设计在陀螺测试中的应用.压电与声光. 2008, 30(4):393~397
25. P. G. Savage. Strapdown Inertial Navigation Integration Algorithm Design Part 1: Attitude Algorithms. Journal of Guidance Control and Dynamics. 1998, 21(1):19~28
26.郭喜庆,武克用.基于环形激光陀螺调制输出的寻北系统.光电工程. 2001, 28(2):11~13
27. M. Goldshtein, Y. Oshman, T. Efrati. Seeker Gyro Calibration via Model-Based Fusion of Visual and Inertial Data. International Conference on Information Fusion. 2007. 7
28. FU Zhenxian, DENG Zhenglong. Continuous Calibration of Inertial Platform Drifting Error Parameters. Journal of Harbin Institute of Technology. 2000, 7(3):24~26
29.陈北鸥,孙文胜,张桂宏,陈东海,蒋顺成.捷联组合(设备无定向)六位置测试标定.导弹与航天运载技术. 2001, 3:23~27
30. IEEE standard specification format guide and test procedure for Single-Axis Laser Gyro[S]. IEEE, Std. 647-1995
31.杨晓霞,黄一.激光捷联惯导系统的一种系统级标定方法.中国惯性技术学报. 2008, 16(1):1~7
32. Camberlein. L, Mazzananti. F. Calibration Technology for Laser Gyro Srtapdown Inertial Navigation Systems. Symposium Gyro Technology. Stuttgart. Gennnay. 1985
33. C. N. Lawrence. On the Appliation of Allan Variance Methods for Ring Gyro Performance Characterization. UCRL-ID-115685, October 15, 1993
34. A. Matthews, D. A. Bauer. The Hemispherical Resonator Gyro for Precision Pointing Applications. Space Guidance, Control, and Tracking II, Orlando, FL, USA, 17 April 1995: 128-139
35.白雪峰,赵剡.单轴速率三轴位置惯性测试转台误差及传递分析.航天控制. 2006, 24(2):26~29
36.姜复兴,吴广玉.单轴位置滚转法辨识加速度计静态模型的改进方法.测试技术与设备.中国惯性技术学报. 1994, 2(1):24~29
37.刘峰,徐丹,尚克军,徐策.基于导航误差的系统级标定方法中时间参数选取原则分析.中国惯性技术学报. 2009, 17(6):642~647
38.祁家毅,任顺清,王常虹.用三轴转台辨识陀螺仪误差模型系数时的速率实验设计.宇航学报. 2006, 27(3):565~570
39. Yang Xiaoxia, Huang Yi.Capability of Extended State Observer for Estimating Uncertainties. Proceedings of the 2009 American Control Conference.St Louis, MO, USA , 2009:3700~3705.
40. Goshen-Meskin. D, Bar-Itzhack. I. Y. Observability Analysis of Piece-wise Constant Systems. IEEE Transactions on Aerospace and Electronic System. 1992, 28(4):1056~1075
41.王卫阳.惯性器件和系统误差模型辨识理论及应用研究.哈尔滨工业大学博士学位论文. 1997:30~55
42. IEEE Recommended Practice for Precision Centrifuge Testing of Linear Accelerometers. IEEE Std 836~2001
43. Brown A, Ebner R, Mark J. A Calibration Technique for A Laser GyroStrapdown Inertial Navigation System Conference Proceedings-Symposium Gyro Technology. Stuttgart, 1982:12. 0~12. 20
44. W. Q. Wu, M. Jiang, Z. H. Tuo. Successive Rotating Technique for A Ring Laser Gyro North-finder. International Conference on Navigation, Guidance and Control, 2001: 143~145
45. C. N. Lawrenence, J. P. Darryll. Characterization of Ring Laser Gyro Performance Using the Allan Variance Method. Journal of Guidance, 1996, 20(1): 211~214