Reconstruction of Contaminated Measurement Dataset Using Domain-Based Chebyshev Basis Function

Outliers are usually unavoidable in measurement processes due to various factors and often compromise the robustness of data reconstruction. To address this issue, a novel moving domain Chebyshev basis function (MDCBF) method is developed. This method introduces the concept of the influence domain to build the moving models and eliminate the local abnormal points using Student’s t-regression and Jarvis–Patrick (JP) clustering. First, related points are incorporated into the local domains through the influence domain, transforming the entire model into multiple local models. Within each influence domain, iterative Student’s t-regression is employed to generate a series of preliminary estimation models. The absolute residual of each point can be calculated relative to the estimation model. JP clustering is then employed to remove the points associated with the clusters exhibiting larger absolute residuals, while the preserved points are used in the next regression iteration. Finally, a weighted Chebyshev basis function is employed to determine the local estimated value from the preserved points. By moving the influence domain across the dataset, global reconstruction can be achieved. Additionally, an enhanced MDCBF strategy is proposed to address the extreme case of continuous outliers. In both simulation and experimental datasets, the MDCBF method demonstrates superior robustness and enhanced reconstruction accuracy under varying levels of contamination.