A robust moving horizon estimation under unknown distributions of process or measurement noises

Industrial processes are often subject to unexpected process uncertainties or measurement noises such that their distributions may become non-Gaussian and unforeseeable. A Moving Horizon Estimation (MHE) framework that can explicitly accommodate unknown non-Gaussian distributions is absent. This study presents a novel robust MHE (RMHE) scheme that approximates the unknown non-Gaussian distributions of uncertainties or noises using an optimal Gaussian mixture model that is adapted online. The proposed RMHE considers additional constraints and decision variables than in the standard MHE framework, which are needed to approximate the distributions of the uncertainties (or noises) to Gaussian mixture models online. Therefore, RMHE increases the robustness of the estimation with respect to the unexpected noises or uncertainties occurring in the process. RMHE is an efficient scheme as it does not increase significantly the computational costs required by the standard MHE. Case studies involving multiple scenarios are presented to illustrate the benefits of RMHE. (C) 2021 Elsevier Ltd. All rights reserved.