Abstract
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.
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