基于C#编程实现高斯牛顿法求解激光跟踪干涉仪基站空间坐标

为了实现利用C#语言编程求解激光跟踪干涉仪基站空间坐标,对基站空间坐标的标定原理进行了研究,指出本质上基站空间坐标求解问题可转化为非线性最小二乘问题,为此分析了高斯牛顿法求解原理。进一步采用C#与MATLAB混合编程、仅依靠C#语言编程两种方式实现高斯牛顿法求解。对两种编程的关键技术进行了介绍,指出了混合编程存在的不足之处。通过坐标测量机及激光跟踪干涉仪组成实验系统,在3个不同的基站站位下开展了标定实验,实验结果表明C#编程计算结果与C#调用MATLAB的计算结果相比,差值在10-7数量级,并且效率更高,验证了C#实现高斯牛顿法求解激光跟踪干涉仪基站空间坐标的准确性,为后续激光跟踪干涉仪数据采集及处理软件的开发打下了基础。

Calculation of Base Station Coordinate for Tracking Interferometer with Gauss-Newton Algorithm Realized by C#

In order to solve the base station coordinates for tracking interferometer with C# programming language, the calibration principle of the spatial coordinates of base station is studied. It is pointed out that the problem for calculation of base station coordinates will be turned into nonlinear least square problem in essence, so the Gauss-Newton algorithm is applied for solving this problem and its principle is analyzed. Furthermore, Gauss-Newton algorithm are realized by two programming methods: C# and MATLAB mixed programming, only by C# programming. The key technologies for these two programming methods are described in detail, the shortcomings of mixed programming are pointed out as well. The experimental system is established by the combination of a coordinate measuring machine and a laser tracking interferometer, and calibration experiments are carried out at three different base stations respectively. The experimental results show the difference between the result of C# programming and the result of C# calling MATLAB function is an amount of 10^-7 orders of magnitude, and its more efficient, which verifies the calculation accuracy of base station coordinates for tracking interferometer with Gauss-Newton algorithm implemented by C#, and this lays a foundation for the subsequent development of the data acquisition and processing software of the laser tracking interferometer.