Robust moving total least squares: A technique for the reconstruction of measurement data in the presence of multiple outliers. (15th March 2022) - Gu, Tianqi; Lin, Hongxin; Tang, Dawei; Lin, Shuwen; Luo, Tianzhi
Highlights: A robust moving total least squares algorithm called RMTLS method is proposed which introduces a two-step pre-process to automatically suppress outliers without setting threshold. The outliers as well as random errors of all variables are considered by RMTLS method. The RMTLS method has great robustness to multiple outliers and achieves high reconstruction accuracy. Simulations and experiments confirm the validity of the RMTLS method. Abstract: This article is concerned with the reconstruction of contaminated measurement data based on the moving total least squares (MTLS) method, which is extensively applied to many engineering and scientific fields. Traditional MTLS method is lack of robustness and sensitive to the outliers in measurement data. Based on the framework of MTLS method, we proposed a robust MTLS method called RMTLS method by introducing a two-step pre-process to detect and remove the anomalous nodes in the support domain. The first step is an iterative regression procedure that combines with k-medoids clustering to automatically reduce the weight of anomalous node for a regression-based reference (curve or surface). Based on the distances between reference and discrete points, the second step adopts a density function defined by a sorted distance sequence to select the normal points without setting a threshold artificially. After the two-step pre-process, weighted total least square is performed on the selected point set to obtain the estimation value. By disposing of the anomalous nodes in each independent support domain, multiple outliers can be suppressed within the whole domain. Furthermore, the suppression of multiple continual outliers is possible by adopting asymmetric support domain and introducing previous estimation points. The proposed method shows great robustness and accuracy in reconstructing the simulation and experiment data.