An Extended Moving Horizon Estimation embedded with an Abridged Gaussian Sum Extended Kalman Filer to handle non-Gaussian noises

Abstract

Most industrial processes involve changes in the operating conditions that may lead to non-Gaussian process uncertainties and measurement noises. Recently, an Abridged Gaussian Sum Extended Kalman Filter (AGS-EKF) and Extended Moving Horizon Estimation (EMHE) frameworks were proposed to capture non-Gaussian random uncertainties and noises often present in the chemical systems. Gaussian mixture models (GMM) are used in both estimation schemes to efficiently approximate the non-Gaussian distributions. Previous studies on EMHE considered a sufficiently long estimation horizon to minimize the arrival cost effect. The present work aims to further improve the performance of EMHE by introducing a suitable arrival cost estimator to shorten the estimation horizon. As the focus of this study is on systems involving non-Gaussian noises, AGS-EKF as a non-Gaussian state estimator is selected to estimate the arrival cost. The performance of the proposed estimation framework was tested using the open-loop unstable Williams-Otto reactor considering non-Gaussian uncertainties and noises. The results revealed that the proposed estimation framework improves the estimation in the presence of non-Gaussian noises when compared to the standard framework (MHE combined with EKF) thus making it a suitable estimation method for systems involving non-Gaussian noises.