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.

工业过程通常会受到意外过程不确定性或测量噪声的影响，因此它们的分布可能变得非高斯分布且不可预见。没有可以明确适应未知非高斯分布的移动地平线估计 (MHE) 框架。本研究提出了一种新颖的鲁棒 MHE (RMHE) 方案，该方案使用在线调整的最佳高斯混合模型来近似不确定性或噪声的未知非高斯分布。建议的 RMHE 考虑了比标准 MHE 框架中的额外约束和决策变量，这些是在线将不确定性（或噪声）分布近似到高斯混合模型所需要的。因此，相对于过程中出现的意外噪声或不确定性，RMHE 增加了估计的鲁棒性。RMHE 是一种有效的方案，因为它不会显着增加标准 MHE 所需的计算成本。提供了涉及多个场景的案例研究来说明 RMHE 的好处。