权值对整体最小二乘解算结果的影响分析

Impact Analysis of the Weight Value on the Total Least Squares Solutions

阐述了可以兼顾系数矩阵中随机误差的平差方法——整体最小二乘(TLS),详细讨论了TLS与经典最小二乘(LS)的区别与联系。以三维坐标转换实验为例,分别采用等权LS、等权TLS以及加权TLS进行参数估计,实验结果表明:采用加权TLS的参数解算结果精度最高;在等权的情况下, LS与TLS的参数解算结果精度相当。

This paper expounds the Total Least Squares （TLS） adjustment method which can take into account the randomerrors in the coefficient matrix, and discusses the distinctions and connections between TLS and the classical Least Squares（LS） in detail. Taking the three-dimensional coordinate transformation experiment as an example, parameter estimations are car-ried out respectively by equal weight LS, equal weight TLS and weighted TLS. The experiment results show that the weight-ed TLS has the highest accuracy of parameter solution, and the parameter solution results of LS and TLS havea consistentprecise in condition of equal weight.