摘要
在GPS静态测量工作中,由于大量重复基线和复杂数据的存在,平差计算的系数矩阵很可能存在一定数量的非满秩矩阵,或矩阵行列之间具有较强的线性关系,这样的系数矩阵会给平差计算带来模型上的误差,该类误差无法通过传统的最小二乘手段加以消除。总体最小二乘算法不仅将数据本身采集所带来的误差考虑在内,也会兼之考虑算法模型中带来的问题,针对上述问题,在传统总体最小二乘算法的基础上,引入距离权作为中间参数,以一种更接近实际模型并通过稳定的迭代来计算较高精度的估计值。借助实际算例引入距离权的总体最小二乘算法能够较好地解决系数矩阵奇异性GPS网平差问题,解算精度有较为明显的提高。
In GPS static surveying,due to the existence of a large number of repetitive baselines and complex data,the coefficient matrix of adjustment calculation may have a certain number of non-full rank matrices,or there is a strong linear relationship between the rows and columns of the matrix.Such coefficient matrix will bring model errors to adjustment calculation,which can not be eliminated by traditional least square method.Total least squares algorithm not only takes into account the errors caused by data acquisition itself,but also considers the problems brought by the algorithm model.In this paper,based on the traditional total least squares algorithm,distance weight is introduced as an intermediate parameter,which is close to the actual model,and a stable iteration is used to calculate the higher precision estimates.The total least squares algorithm with distance weight is introduced to solve the problem of coefficient matrix singularity adjustment of GPS network with practical examples,and the accuracy of the solution is improved obviously.
作者
徐晶鑫
董潇
XU Jing-xin;DONG Xiao(China Railway Shanghai Design Institute Group CO.,LTD,Shanghai 200070,China)
出处
《现代测绘》
2019年第5期51-53,共3页
Modern Surveying and Mapping
关键词
总体最小二乘
GPS网平差
奇异矩阵
total least squares
GPS network adjustmen
singular matrix
