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To address noise inherent in electronic data acquisition systems and realworld sources, Araki et al. [Physica D: Nonlinear Phenomena, 417 (2021) 132819]demonstrated a grid based nonlinear technique to remove noise from a chaoticsignal, leveraging a clean high-fidelity signal from the same dynamical systemand ensemble averaging in multidimensional phase space. This method achieveddenoising of a time-series data with 100% added noise but suffered in regionsof low data density. To improve this grid-based method, here an unstructuredmesh based on triangulations and Voronoi diagrams is used to accomplish thesame task. The unstructured mesh more uniformly distributes data samples overmesh cells to improve the accuracy of the reconstructed signal. By empiricallybalancing bias and variance errors in selecting the number of unstructuredcells as a function of the number of available samples, the method achievesasymptotic statistical convergence with known test data and reduces syntheticnoise on experimental signals from Hall Effect Thrusters (HETs) with greatersuccess than the original grid-based strategy.

An Unstructured Mesh Approach to Nonlinear Noise Reduction for Coupled Systems