Gaussian Mixture Model-Based Ensemble Kalman Filtering for State and Parameter Estimation for a PMMA Process

Polymer processes often contain state variables whose distributions are multimodal; in addition, the models for these processes are often complex and nonlinear with uncertain parameters. This presents a challenge for Kalman-based state estimators such as the ensemble Kalman filter. We develop an estimator based on a Gaussian mixture model (GMM) coupled with the ensemble Kalman filter (EnKF) specifically for estimation with multimodal state distributions. The expectation maximization algorithm is used for clustering in the Gaussian mixture model. The performance of the GMM-based EnKF is compared to that of the EnKF and the particle filter (PF) through simulations of a polymethyl methacrylate process, and it is seen that it clearly outperforms the other estimators both in state and parameter estimation. While the PF is also able to handle nonlinearity and multimodality, its lack of robustness to model-plant mismatch affects its performance significantly.