Profile analysis with reconstruction robustness for measurement data subject to outliers

In the surface profile analysis, there are often a few observations that contain outliers. Due to the existence of outliers, the application of non-robust reconstruction algorithms for measurement data will become a huge problem because these methods are often sensitive to outliers and the approximation effectiveness will be greatly aggravated. In view of this, this paper presents a novel angle-based moving total least squares reconstruction method, to the best of our knowledge, that applies two-step pre-treatment to handle outliers. The first step is an abnormal point detection process that characterizes the geometric features of discrete points in the support domain through a new angle-based parameter constructed by total least square. Then, the point with the largest anomaly degree is removed, and a relevant weight function is defined to adjust the weights of the remaining points. After pre-treatment, the final estimates are calculated by weighted total least squares (WTLS) based on the compact weight function. The detection and removal of outliers are automatic, and there is no need to set a threshold value artificially, which effectively avoids the adverse impacts of human operation. Numerical simulations and experiments verify the applicability of the proposed algorithm as well as its accuracy and robustness.