岭估计在稀疏孔径望远镜主镜姿态控制中的应用
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摘要
研究了稀疏孔径镜面硬点与边缘传感器布局对稀疏孔径相对位姿控制精度的影响。利用离散孔径镜面几何特性,建立了一个由7个圆形子孔径组成的主镜模型,并推导了子孔径间相对位姿控制矩阵。鉴于控制矩阵条件数大这一特点,采用广义最小二乘法求解,引入岭估计并给出了控制矩阵误差函数上确界,分析了128种边缘传感器与硬点布局以及几何距离对控制矩阵条件数的影响。仿真结果表明:硬点和边缘传感器的几何布局与系数矩阵存在内在联系;离散孔径相对位姿控制系数矩阵存在严重的复共线现象,法矩阵出现严重病态;硬点布局与改善系数矩阵病态性弱相关;在硬点布局一定时,增大相邻两边缘传感器间距,控制矩阵条件数明显减小。针对控制矩阵病态问题,采用岭估计通过选择合适的岭参数病态特征得到了有效抑制,该方法更能有效利用冗余的边缘传感器结构,实现数据融合并保证测量系统的稳定可靠。
The influence of the position of the sparse aperture mirror hard spot and the layout of the edge sensor on the precision of the relative pose control was studied. Using the geometry characteristic of sparse aperture, a primary mirror model composed of seven circular apertures was established and the control matrix of relative pose among apertures was derived. The generalized least squares method was used to solve this problem, considering the large condition number of control matrix, ridge regression was introduced and the intrinsic bound on the error function of the control matrix was also given. The possible 128 location strategies between edge sensors and hard spots and the effect of geometric distance on the condition number of control matrix were analyzed. The results show that the layout of the hard points and edge sensors is intrinsically linked to the coefficient matrix, the sparse aperture is serious Multi-Collinearity with respect to the coefficient matrix of pose control, and the normal matrix appears seriously ill-conditioned. The condition number of normal matrix are reduced significantly when the distances between the adjacent two edge sensors while the layout is fixed. For the ill-conditioned problem of the normal matrix, the ridge regression is used to effectively suppress the ill-conditioned characteristic by choosing appropriate ridge parameters. Using this method, the redundant edge sensor structure can be effectively used to realize data fusion and ensure the stability and reliability of the measurement system.
The influence of the position of the sparse aperture mirror hard spot and the layout of the edge sensor on the precision of the relative pose control was studied. Using the geometry characteristic of sparse aperture, a primary mirror model composed of seven circular apertures was established and the control matrix of relative pose among apertures was derived. The generalized least squares method was used to solve this problem, considering the large condition number of control matrix, ridge regression was introduced and the intrinsic bound on the error function of the control matrix was also given. The possible 128 location strategies between edge sensors and hard spots and the effect of geometric distance on the condition number of control matrix were analyzed. The results show that the layout of the hard points and edge sensors is intrinsically linked to the coefficient matrix, the sparse aperture is serious Multi-Collinearity with respect to the coefficient matrix of pose control, and the normal matrix appears seriously ill-conditioned. The condition number of normal matrix are reduced significantly when the distances between the adjacent two edge sensors while the layout is fixed. For the ill-conditioned problem of the normal matrix, the ridge regression is used to effectively suppress the ill-conditioned characteristic by choosing appropriate ridge parameters. Using this method, the redundant edge sensor structure can be effectively used to realize data fusion and ensure the stability and reliability of the measurement system.
引文
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[17]Ma Chaozhong,Du Yuanlu,Gui Qingming.Generalized robust ridge estimation in Gauss-Markov model[J].Henan Science,2012,30(7):823-824.(in Chinese)马朝忠,杜院录,归庆明.Guass-Markov模型的广义抗差岭估计[J].河南科学,2012,30(7):823-824.
[18]Zou W Y.Generalized figure-control algorithm for large segmented telescope mirrors[J].J Opt Soc Am A,2001,18(3):639-643.
[19]Lu Tieding.Research on the total least squares and it applications in surveying data processing[D].Wuhan University of Wuhan,2010.(in Chinese)鲁铁定.总体最小二乘平差理论及其在测绘数据处理中的应用[D].武汉:武汉大学,2010.
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[21]Huang Hailan,Niu Ben.Study on the determination of ridge parameters[J].Science of Surveying and Mapping,2011,36(4):31-32.(in Chinese)黄海兰,牛犇.岭参数确定的研究[J].测绘科学,2011,36(4):31-32.
[2]Fan Lei,Yang Hongbo,Zhang Jingxu,et al.Hardpoint defining structure for large aperture primary mirror[J]Infrared and Laser Engineering,2012,41(12):3367-3371(in Chinese)范磊,杨洪波,张景旭,等.大口径反射镜轴向硬点定位[J].红外与激光工程,2012,41(12):3368-3371.
[3]Lan Bin,Wu Xiaoxia,Yang Hongbo,et al.Application o generalized least squares method in the calibration of active optics mode[J].Infrared and Laser Engineering,2017,46(6):0617001.(in Chinese)兰斌,吴小霞,杨洪波,等.广义最小二乘法在主动光学模式定标中的应用[J].红外与激光工程,2017,46(6)0617001.
[4]Peng Yao,Zhang Jingxu,Yang Fei,et al.Hardpoint location technique of large mirror based on active optics[J].Laser&Infrared,2016,46(2):139-143.(in Chinese)彭尧,张景旭,杨飞,等.基于主动光学的大口径反射镜硬点定位技术[J].激光与红外,2016,46(2):139-143.
[5]Gajjar H,Menzies J,Buckley D,et al.SALT:Active contro of the primary mirror with inductive edge sensors[C]//SPIE2016,9906:990639.
[6]Wasmeier M,Hackl J,Leveque S.Inductive sensors based on embedded coil technology for nanometric inter-segmen position sensing of the E-ELT[C]//SPIE,2014,914591451R.
[7]Conan R,Bouchez A,Quiros-Pacheco F,et al.The GMTactive optics control strategies[C]//SPIE,2016,990999091T.
[8]Yang Dehua,Qi Yongjun,Zhu Zhendong,et al.Design and test of the active micro-motion mechanism for optical mirro segement[J].Optics and Precision Engineering,2005,13(2):191-197.(in Chinese)杨德华,戚永军,朱振东,等.光学拼接镜面微位移主动调节机构的设计和实测[J].光学精密工程,2005,13(2)191-197.
[9]Su Dingqiang,Cui Xiangqun.Active optics-key technology of the new generation telescopes[J].Progress in Astronomy1999,17(1):1-14.(in Chinese)苏定强,崔向群.主动光学-新一代大望远镜的关键技术[J].天文学进展,1999,17(1):1-14.
[10]Lin Xudong,Chen Tao,Wang Jianli,et al.Active optic figure control of segmented mirror[J].Optics and Precision Engineering,2009,17(1):98-102.(in Chinese)林旭东,陈涛,王建立,等.拼接镜的主动光学面形控制[J].光学精密工程,2009,17(1):98-102.
[11]Cui X Q,Su D Q,Li G P,et al.Experiment system o LAMOST active optics[C]//SPIE,2004,5489:974-984.
[12]Guo Wenyue,Yu Anzhu,Liu Haiyan,et al.Regularized total least squares used in remote sensing image positioning of optical line array[J].Optics and Precision Engineering,2017,25(1):236-242.(in Chinese)郭文月,余岸竹,刘海砚,等.正则化总体最小二乘用于光学线阵遥感影像定位[J].光学精密工程,2017,25(1):236-242.
[13]Li Lijuan,Zhao Yanhui,Lin Xuezhu.Application of WTLSin coordinate transformation of laser tracker[J].Optics and Precision Engineering,2015,23(9):2570-2577.(in Chinese)李丽娟,赵延辉,林雪竹.加权整体最小二乘在激光跟踪仪转站中的应用[J].光学精密工程,2015,23(9):2570-2577.
[14]Mu Zhiya,Ai Hua,Fan Xiaohe,et al.Inference fringe image registration using total least square method[J].Chinese Optics,2016,9(6):625-632.(in Chinese)穆治亚,艾华,樊孝贺,等.采用整体最小二乘法的条纹图配准方法[J].中国光学,2016,9(6):625-632.(in Chinese)
[15]Hoerl A E,Kennard R W.Ridge regression:biased estimation for nonorthogonal problems[J].Technometrics,2000,42(1):80-86.
[16]Dai Jianhua,Wang Shiqing.The conditions of ridge estimation superior to the least squares estimation[J].Mathematical Statistics and Applied Probability,1994,9(2)53-57.(in Chinese)戴俭华,王石青.岭估计优于最小二乘估计的条件[J].数理统计与应用概率,1994,9(2):53-57.
[17]Ma Chaozhong,Du Yuanlu,Gui Qingming.Generalized robust ridge estimation in Gauss-Markov model[J].Henan Science,2012,30(7):823-824.(in Chinese)马朝忠,杜院录,归庆明.Guass-Markov模型的广义抗差岭估计[J].河南科学,2012,30(7):823-824.
[18]Zou W Y.Generalized figure-control algorithm for large segmented telescope mirrors[J].J Opt Soc Am A,2001,18(3):639-643.
[19]Lu Tieding.Research on the total least squares and it applications in surveying data processing[D].Wuhan University of Wuhan,2010.(in Chinese)鲁铁定.总体最小二乘平差理论及其在测绘数据处理中的应用[D].武汉:武汉大学,2010.
[20]Tikhonov A N,Goncharsky A V,Stepanov V V,et al Numerical Methods for the Solution of III-Posed Problems[M].Berlin:Springer,1995.
[21]Huang Hailan,Niu Ben.Study on the determination of ridge parameters[J].Science of Surveying and Mapping,2011,36(4):31-32.(in Chinese)黄海兰,牛犇.岭参数确定的研究[J].测绘科学,2011,36(4):31-32.