Geometry-Based Reconstruction Method for Profile Analysis of Measurement Data

Abstract

In the field of practical engineering, the moving least-squares (MLS) and moving total least-squares (MTLS) methods are widely used to approximate the measurement data. However, the fitting accuracy and robustness are affected inevitably by random errors and outliers, which results in distorted estimation. To solve this problem, we present an improved MTLS (IMTLS) method, in which a newly constructed parameter is introduced to characterize the geometric feature of abnormal points in each influence domain. The total least-squares (TLS) method is used to generate the fitting points at first. The corresponding variance of each node is then calculated, and the connection between abnormal degree and random errors is established to trim the nodes with a certain abnormal degree. The remaining nodes are used to find the local coefficients. This proposed algorithm can avoid the negative effects of outliers without human intervention and overelimination. The final results of the measurement experiments and numerical simulations demonstrate that the improved algorithm has better robustness and accuracy than the MLS and MTLS method.