岭估计在稀疏孔径望远镜主镜姿态控制中的应用

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。

Abstract

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.

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曹海峰, 张景旭, 杨飞, 安其昌. 岭估计在稀疏孔径望远镜主镜姿态控制中的应用[J]. 红外与激光工程, 2019, 48(3): 0318003. Cao Haifeng, Zhang Jingxu, Yang Fei, An Qichang. Application of ridge regression in pose control of telescope primary mirror with sparse aperture[J]. Infrared and Laser Engineering, 2019, 48(3): 0318003.

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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