A New Process Noise Covariance Matrix Tuning Algorithm for Kalman Based State Estimators

A suitable design of state estimators requires a representative model for capturing the plant behavior and knowledge about the noise statistics, which are generally not known in practical applications. While the measurement noise covariance can be directly derived from the measurement device reproducibility, the choice of the process noise covariance is much less straightforward. Further, processes such as continuous process with grade transitions and batch or semi-batch process are characterized by time-varying structural uncertainties which are, in many cases, partially and indirectly reflected in the uncertainty of the model parameters. It has been shown that the robust performance of state estimators significantly enhances with a time-varying and non-diagonal process noise covariance matrix, which explicitly takes parameter uncertainty into account. For this case, the parameter uncertainty is quantified through the parameter covariance matrix. This paper presents a direct and a sensitivity method for the parameter covariance matrix computation. In the direct method, the parameter covariance matrix is found during the parameter estimation step of the SELEST algorithm, while in the sensitivity method, the parameter covariance matrix is obtained through a time-varying sensitivity matrix. The results have shown the efficacy of these methods in improving the performance of an extended Kalman filter (EKF) for a semi-batch reactor process.