If both the coefficient matrix and the observation vector are affected by noise, a total least-squares algorithm should be applied to obtain the solution. However, if they are also contaminated by outliers, the solution of the algorithm will seriously deviate from the true values. Therefore, the effect of outliers needs to be eliminated. For this purpose, the robust estimation is introduced into the total least-squares algorithm, developing a new robust weighted total least-squares algorithm. Simultaneously, considering the robustness of structure space, the standardized residuals are utilized to construct the weight function. Finally, the robustness and efficiency of this algorithm are verified by three experiments involving line-fitting and 2D affine transformation.

如果系数矩阵和观测向量都受到噪声的影响，则应采用全最小二乘算法来求解。但是，如果它们也受到异常值的污染，算法的解将严重偏离真实值。因此，需要消除异常值的影响。为此，在全最小二乘算法中引入了稳健估计，开发了一种新的稳健加权全最小二乘算法。同时，考虑到结构空间的鲁棒性，利用标准化残差构造权重函数。最后，通过线拟合和二维仿射变换的三个实验验证了该算法的鲁棒性和效率。