基于选权迭代法的抗差整体最小二乘及其应用

Robust total least-squares based on selecting weight iteration method and its application

在测量数据处理中,观测向量与系数矩阵同时存在偶然误差时,整体最小二乘法能够得到更高精度的参数解,但整体最小二乘法无抗差能力,观测向量中的粗差将对参数求解产生较大影响。为解决上述问题,采用拉格朗日极值法推导了基于选权迭代法的抗差整体最小二乘计算公式,通过三维坐标转换参数求解实例对3种选权迭代法进行分析。结果表明,IGG法在抗差整体最小二乘解法中抗差效果最好。

In the measurement data processing,total least squares method can get more accurate parameter solution when observation vector and the coefficient matrix all exist random errors.But total least squares method doesn't have the ability to resist the gross errors,which will have great impact on parameters.To solve the above problem,it minimizs the target function of classical Lagrange approach and deduces the robust total least-squares estimation calculation formula based on selecting weight iteration.Then the three selecting weight iteration methods are applied to three-dimensional coordinate transformation.The results show that IGG method works best in the robust total least-squares method.