Extended moving horizon estimation for chemical processes under non‐Gaussian noises

Abstract

Studies on moving horizon estimation (MHE) for applications featuring process uncertainties and measurement noises that follow time-dependent non-Gaussian distributions are absent from the literature. An extended version of MHE (EMHE) is proposed here to improve the estimation for a general class of non-Gaussian process uncertainties and measurement noises at no significant additional computational costs. Gaussian mixture models are introduced to the proposed EMHE to approximate offline the non-Gaussian densities of these random variables. Moreover, the proposed EMHE-based estimation scheme can be updated online by re-approximating the corresponding Gaussian mixture models when the distributions of noises/uncertainties change due to sudden or seasonal changes in the operating conditions. These updates are not expected to increase the central processing unit times considerably. Illustrative case studies featuring open-loop operation and closed-loop control using nonlinear model predictive control have shown that the practical features offered by EMHE resulted in significant improvements in state estimation and online control.

Dynamic stationary subspace analysis based on Gaussian mixture models for ironmaking process monitoring

“…Therefore, Yu further developed a particle filter-based dynamic GMM (DGMM) by using a particle filter resampling method to dynamically update the parameters of the mixture model. [8] To improve the estimation of the general class of non-Gaussian processes without incurring high additional computational costs, Valipour and Ricardez-Sandoval proposed an extended version of moving horizon estimation (EMHE) [9] . Furthermore, Valipour and Ricardez-Sandoval proposed a constrained abridged Gaussian sum extended Kalman filter (constrained AGS-EKF), which uses a GMM to improve the estimation of the extended Kalman filter (EKF) [10] .…”

State estimation for a class of nonlinear non‐Gaussian cyber–physical systems under false data injection attacks

“…But a large number of particles will be required to guarantee the required estimation accuracy of the particle filter, which will result in high computational complexity and particle depletion. The Gaussian sum-based methods mainly include the Gaussian sum filter method, the Gaussian sum EKF method, and the Gaussian sum UKF method [18][19][20]. These methods are based on the result that a Gaussian sum can approximate any density to an arbitrary degree of accuracy.…”