抗差加权总体最小二乘算法及其在矿区高程拟合中的应用

Robust weighted total least squares algorithm and its application in mine elevation transformation

文中针对矿区高程异常参数求解中，传统最小二乘系数矩阵易受观测值误差影响、总体最小二乘难以抵抗粗差等缺陷，提出一种抗差加权总体最小二乘算法。采用模拟和矿区实测数据对算法进行验证，结果表明：该算法既能削弱系数矩阵受观测值误差影响，也能较好抵抗观测粗差，极大提高了解算结果的精度与可靠性。

The traditional least squares coefficient matrix is easy to be influenced by the observational error in the process of solving the mine elevation transformation, total least squares algorithm can hardly avoid gross error,so ro- bust weighted total least squares was proposed. This algorithm was based on the weighted total least squares iterative algorithm, calculating the residual and standardizing it, using the median algorithm and IGGIII model construction as the weighting factor, adjusting the weight of observation and coefficient matrix, realizing robust estimation total least squares algorithm. The simulation and measurement results were presented that the RWTLS algorithm could not only reduce the affection for observation error of coefficient matrix, but also avoid observation gross error, and improve the accuracy and reliability. It can be applied to mine elevation transformation.