A Robust Moving Total Least-Squares Fitting Method for Measurement Data

Abstract

The moving least-squares (MLS) and moving total least-squares (MTLS) methods have been widely used for fitting measurement data. They can be used to achieve good approximation properties. However, these two methods are susceptible to outliers due to the way of determining local approximate coefficients, which leads to distorted estimation. To reduce the influence of outliers and random errors of all variables without adding small weights or setting the threshold subjectively, we present a robust MTLS (RMTLS) method, in which an improved least trimmed squares (ILTS) method is used for obtaining the local approximants of the influence domain. The ILTS method divides the nodes in the influence domain into a certain number of subsamples, achieves the local approximants by the total least-squares (TLS) method with compact support weight function, and trims the node with the largest orthogonal residual from each subsample, respectively. The remaining nodes from the subsamples are used to determine the local coefficients. The measurement experiment and numerical simulations are provided to demonstrate the robustness and accuracy of the presented method in comparison with the MLS and MTLS methods.