测量数据的曲线曲面拟合算法

移动最小二乘法由于其良好的逼近性能而广泛用于曲线曲面拟合，但处理含有粗大误差的数据时，拟合结果极不稳定.为了减少粗大误差对拟合精度的影响，本文提出一种移动最小截平方法，该方法在支持域内引入最小截平方法代替最小二乘法，在所有节点当中选出剔除异常值的最优节点组合，确定局部拟合系数.该方法不需要人为地分配权重或设定阈值，可避免主观操作带来的影响.数值模拟和实验数据处理表明，移动最小截平方法能有效地处理测量数据中的粗大误差，拟合结果明显优于移动最小二乘法，具有良好的拟合精度和鲁棒性.

Curve and Surface Fitting Algorithm for Measurement Data

The moving least squares (MLS) method is widely used in curve and surface fitting due to its good approximation performance. However， the fitting accuracy is extremely unstable when processing data with gross error.In order to reduce the effect of gross error on the fitting accuracy， a moving least trimmed squares (MLTS)method was proposed. In this method， the least trimmed square (LTS) method was introduced in the influence domain to replace the least square (LS) method， and the optimal group of nodes without abnormal data was selected among all the nodes to determine the local fitting coefficient.Assigning weights or setting threshold values artificially is unnecessary， which avoids the influence of subjective operations. Numerical simulation and experimental data processing showed that the gross error of measurement data can be handled effectively， and the fitting results of the MLTS method are better than those of the MLS method， which has good fitting accuracy and robustness.