稳健估计的一种改进迭代算法

当观测值不含粗差、观测误差服从零均值分布时，最小二乘算法是最优无偏估计。若观测值包含粗差，由于最小二乘不具备抗差性，往往采用以M估计为代表的稳健估计方法，选权迭代算法是应用最为广泛的稳健估计方法之一。目前，选权迭代算法的每一步都需要对模型的稳健正交矩阵求逆，其运算复杂度是矩阵维数的三次方，在未知参数或粗差个数较多的情况下，计算量大、计算时间长。本文基于矩阵逆的运算法则，对现有选权迭代算法进行了改进，改进的选权迭代算法在迭代计算过程中仅需计算更新权阵后的解的改正项，不需要对正交矩阵求逆，显著提高了算法的效率。

On an Improved Iterative Reweighted Least Squares Algorithm in Robust Estimation

In geodesy,classical least squares (LS) estimation methods rely heavily on assumptions which are often not met in practice.In particular,it is often assumed that the data errors are zero mean distributed,at least appproximately.Unfortunately,when there are outliers in the data,the classical LS estimators frequently have meaningless performance.In this case,robust estimation such as M-type estimation is usually applied,which is numerically implemented by a so called iterative reweighted least squares algorithm.In the current reweighting process,however,the equivalent normal matrix is required to be inverted in every iteration,which needs an expensive computation demand,especially when the number of the unknown parameters is large.Therefore,in this contribution,the numerical process of the iterative reweighted least squares algorithm is essentially improved,which is mainly represented by avoiding the inversion of the equivalent normal matrix.The numerical example shows that the improved version is performed much superior to the previous one.