靶道空间三点法标定与误差分析

为了避免现有激光准直标定系统在激光光斑对准过程中的困难,简化标定系统组成,提高标定效率和标定精度,增强标定系统的场地适应性。利用空间内任意不共线的三点分别在标定坐标系和靶道坐标系下的坐标构造过渡坐标系,得到标定坐标系到靶道坐标系的转换关系。研究标定坐标系下标定点的位置偏差以及靶道坐标系下对应点的测量误差对最终待测点测量误差自协方差的影响,通过雅克比矩阵得到相应的误差模型,导出坐标测量误差均值和方差的表达式。依据向量范数和矩阵范数之间的关系以及Cauchy-Schwarz不等式研究测量误差均值与方差的增益系数的理论上限。通过实弹击发实验,考察三点标定方法的实践效果。研究结果表明:最终测量误差均值向量的模长等于被测点在标定坐标系下均值向量的模长;确定标定坐标系到靶道坐标系转换关系的任意不共线三点之间距离及其包围的面积越大,则测量误差的自协方差增益系数越小;将过渡坐标系原点靠近预计弹道线有利于减小测量误差的自协方差增益系数;取决于测量方法及其误差形式,随着标定坐标系原点远离靶道坐标系原点,与靶道坐标系中三点坐标测量误差相关的被测点测量误差自协方差增益有所不同;基于三点标定方法,使用常见的通用仪器、设备就可以完成标定过程,且经过三点法标定的靶道测量数据质量较高。

Three-point Method and Error Analysis of Ballistic Range Calibration

To avoid the difficulty from laser spot alignment of existing laser collimation system in calibration process, a system composition is simplified, the efficiency and accuracy of calibration are improved, and the adaptability of calibration system is enhanced. A transformation matrix between calibration system and ballistic range system is presented by using the coordinates of three non-collinear points in calibration system and ballistic range system. The mean value and the variance-covariance matrix of the final measuring error are studied by an error model founded by Jacobian matrix between the measuring and various error sources.The self-covariance of measuring error is studied based on the Cauchy-Schwarz inequality and the relationship between vector and matrix norms. An firing experiment of live ammunition is performed to verify the three-point calibration method of ballistic range. The research results show that the mean vector length of final measuring error about a point in ballistic range system is equal to the mean vector length of measuring error associated with same point in the calibration system; the larger the distance and the area surrounded by three non-collinear points which links the calibration system and ballistic range system together are, the smaller the self-covariance of the final measuring error is; the self-covariance decreases when the transition coordinate origin which is defined by the three non-collinear points is close to a projected trajectory line; based on the measurement method and the error of the three-point coordinates in ballistic system, the self-covariance of measuring error are changed when the calibration system origin moves away from the ballistic range system origin; and the calibration system based on the three-point method can be build-up by general instruments, and the quality of measured data is better.