Abstract
The moving least squares (MLS) and moving total least squares (MTLS) are two of the most popular methods used for reconstructing measurement data, on account of their good local approximation accuracy. However, their reconstruction accuracy and robustness will be greatly reduced when there are outliers in measurement data. This article proposes an improved MTLS method (IMTLS), which introduces an improved random sample consensus (RANSAC) algorithm and a correction parameter in the support domain, to deal with the outliers and random errors. Based on the nodes within the support domain, firstly the improved RANSAC is used to generate a model for establishing the group of pre-interpolation and calculating the residual of each node. Subsequently, the abnormal degree of the node with the largest residual is evaluated by the correction parameter associated with the node residual and random errors. The node with certain abnormal degree will be eliminated and the remaining nodes are used to obtain the approximation coefficients. The correction parameter can be used for data reconstruction without insufficient or excessive elimination. The results of numerical simulation and measurement experiment show that the reconstruction accuracy and robustness of the IMTLS method is superior to the MLS and MTLS method.
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