抗差最小二乘估计在惯组外场标定中的应用
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摘要
惯组在外场进行标定时常常会受到环境的振动干扰,从而会对惯组的标定精度造成极大的影响。为解决这一问题,在分析了粗差对惯组标定精度影响的前提下,建立了一种改进的辨识惯组误差系数的数学模型,使其能够分辨出那些受到振动干扰影响的惯组误差系数。最后利用抗差最小二乘估计对惯组误差系数进行处理,通过等价权函数的连续降权和连续减弱影响处理,抵制了异常数据对惯组标定精度的影响。仿真结果表明,抗差最小二乘估计具有很强的抗差能力,能有效减弱异常干扰对参数估计的影响,提高惯组外场标定的精度和数据的可靠性。
Inertial measurement unit(IMU) is often interrupted by the ground vibration when it is calibrated in outfield.The vibration disturbance will lower the calibration accuracy of IMU greatly.To solve this problem,based on the analysis of the gross error influence on the IMU calibration result,a new mathematic model to calibrate error parameters of IMU is established.The new model could distinguish those abnormal error parameters.Finally,error parameter data is processed by using robust estimation of least-squares.By descending weights and weakening effects of abnormal data continuously via equivalent weight function,the influence of abnormal data on IMU calibration accuracy is minimized.Simulation result verifies that robust estimation of least-squares is more robust than least-squares estimation.It can degrade the influence of vibration disturbance effectively and improve the IMU outfield calibration accuracy and the data reliability.
Inertial measurement unit(IMU) is often interrupted by the ground vibration when it is calibrated in outfield.The vibration disturbance will lower the calibration accuracy of IMU greatly.To solve this problem,based on the analysis of the gross error influence on the IMU calibration result,a new mathematic model to calibrate error parameters of IMU is established.The new model could distinguish those abnormal error parameters.Finally,error parameter data is processed by using robust estimation of least-squares.By descending weights and weakening effects of abnormal data continuously via equivalent weight function,the influence of abnormal data on IMU calibration accuracy is minimized.Simulation result verifies that robust estimation of least-squares is more robust than least-squares estimation.It can degrade the influence of vibration disturbance effectively and improve the IMU outfield calibration accuracy and the data reliability.
引文
[1]蒋庆仙,王成宾,吴富梅,等.抗差估计在光纤陀螺信号处理中的应用[J].中国惯性技术学报,2009,17(1):71-75.JIANG Qing-xian,WANG Cheng-bin,WU Fu-mei,etal.Application of Robust Estimation to FOG Signal[J].Journal of Chinese Inertial Technology,2009,17(1):71-75.
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[5]谢波,秦永元,万彦辉.激光陀螺捷联惯导系统多位置标定方法[J].中国惯性技术学报,2011,19(2):157-162.XIE Bo,QIN Yong-yuan,WAN Yan-hui.MultipositionCalibration Method of Laser Gyro SINS[J].Journal ofChinese Inertial Technology,2011,19(2):157-162.
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[7]杨杰.捷联惯组外场标定动态数据处理与非线性辨识[D].西安:第二炮兵工程大学,2011.YANG Jie.Dynamic Data Processing and Nonlinear I-dentification to SIMU Outside Calibration[D].Xi’an:The Second Artillery Engineering University,2011.
[8]杨元喜.抗差估计理论及其应用[M].北京:八一出版社,1993.YANG Yuan-xi.The Theory and Application of RobustEstimation[M].Beijing:Bayi Press,1993.
[9]杨元喜,周江文,欧吉坤,等.抗差最小二乘法[M].武汉:华中理工大学出版社,1997.YANG Yuan-xi,Zhou Jiang-wen,OU Ji-kun,et al.Ro-bust Estimation of Least-Squares[M].Wuhan:Hua-zhong University of Science and Technology Press,1997.
[10]蒋庆仙,王成宾,马小辉,等.利用中位数进行光纤陀螺信号应用抗差估计[J].武汉大学学报,2011,36(6):656-659.JIANG Qing-xian,WANG Cheng-bin,MA Xiao-hui,etal.Robust Estimation for FOG Signal Based on MedianMethod[J].Geomatics and Information Science of Wu-han University,2011,36(6):656-659.
[11]杨玲,沈云中,楼立志.基于中位参数初值的等价权抗差估计方法[J].测绘学报,2011,40(1):28-32.YANG Ling,SHEN Yun-zhong,LOU Li-zhi.EquivlentWeight Robust Estimation Method Based on Median Pa-rameter Estimates[J].Acta Geodaetica et CartographicaSinica,2011,40(1):28-32.
[12]杨元喜,吴富梅.临界值可变的抗差估计等价权权函数[J].测绘科学技术学报,2006,23(5):317-320.YANG Yuan-xi,WU Fu-mei.Modified EquivalentWeight Function with Variable Criterion for Robust Esti-mation[J].Journal of Geomatics Science and Technolo-gy,2006,23(5):317-320.
[2]LAMPRECHT H A,TROMP H,ABOTT M A.BaseMotion Compensation for a Fiber-Optic North-SeekingGyroscope[C]∥Symposium Gyro Technology.Stutt-gart,Germany:1996:10.0-10.18.
[3]PRIEL B.Method to Improve North Finder Accuracy[C]∥Symposium Gyro Technology.Stuttgart,Germa-ny:1989:3.0-3.11.
[4]杨晓霞,孟浩然,王帅.激光陀螺捷联惯导系统的外场动态标定方法[J].中国惯性技术学报,2011,19(4):393-398.YANG Xiao-xia,MENG Hao-ran,WANG Shuai.Cali-bration Method for Laser Gyro SINS under Outer FieldDynamic Conditions[J].Journal of Chinese InertialTechnology,2011,19(4):393-398.
[5]谢波,秦永元,万彦辉.激光陀螺捷联惯导系统多位置标定方法[J].中国惯性技术学报,2011,19(2):157-162.XIE Bo,QIN Yong-yuan,WAN Yan-hui.MultipositionCalibration Method of Laser Gyro SINS[J].Journal ofChinese Inertial Technology,2011,19(2):157-162.
[6]刘刚,杨杰,汪立新,等.惯组野外测试时振动干扰的检测与提取[J].噪声与振动控制,2011,4(2):80-83.LIU Gang,YANG Jie,WANG Li-xin,et al.Detectingand Extracting Vibration Disturbing in IMU Outside Cal-ibration[J].Noise and Vibration Control,2011,4(2):80-83.
[7]杨杰.捷联惯组外场标定动态数据处理与非线性辨识[D].西安:第二炮兵工程大学,2011.YANG Jie.Dynamic Data Processing and Nonlinear I-dentification to SIMU Outside Calibration[D].Xi’an:The Second Artillery Engineering University,2011.
[8]杨元喜.抗差估计理论及其应用[M].北京:八一出版社,1993.YANG Yuan-xi.The Theory and Application of RobustEstimation[M].Beijing:Bayi Press,1993.
[9]杨元喜,周江文,欧吉坤,等.抗差最小二乘法[M].武汉:华中理工大学出版社,1997.YANG Yuan-xi,Zhou Jiang-wen,OU Ji-kun,et al.Ro-bust Estimation of Least-Squares[M].Wuhan:Hua-zhong University of Science and Technology Press,1997.
[10]蒋庆仙,王成宾,马小辉,等.利用中位数进行光纤陀螺信号应用抗差估计[J].武汉大学学报,2011,36(6):656-659.JIANG Qing-xian,WANG Cheng-bin,MA Xiao-hui,etal.Robust Estimation for FOG Signal Based on MedianMethod[J].Geomatics and Information Science of Wu-han University,2011,36(6):656-659.
[11]杨玲,沈云中,楼立志.基于中位参数初值的等价权抗差估计方法[J].测绘学报,2011,40(1):28-32.YANG Ling,SHEN Yun-zhong,LOU Li-zhi.EquivlentWeight Robust Estimation Method Based on Median Pa-rameter Estimates[J].Acta Geodaetica et CartographicaSinica,2011,40(1):28-32.
[12]杨元喜,吴富梅.临界值可变的抗差估计等价权权函数[J].测绘科学技术学报,2006,23(5):317-320.YANG Yuan-xi,WU Fu-mei.Modified EquivalentWeight Function with Variable Criterion for Robust Esti-mation[J].Journal of Geomatics Science and Technolo-gy,2006,23(5):317-320.