A systematic tuning approach for the use of extended Kalman filters in batch processes

State estimation methods, like the extended Kalman filter (EKF) are used for obtaining reliable estimates of the states from the available measurements in the presence of model uncertainties and unmeasured disturbances. The main open issue in applying EKF is the need to quantify the accuracy of the model in terms of the process noise covariance matrix, Q. The present paper proposes two methods that utilize the parametric model uncertainties to calculate the Q matrix of an EKF. The first approach is based on a Taylor series expansion of the nonlinear equations around the nominal parameter values. The second approach accounts for the nonlinear dependence of the system on the fitted parameters by use of Monte Carlo simulations that are easily be performed online. The value of the process noise covariance matrix (Q) obtained is not limited to a diagonal and constant matrix and is dependent on the current state of the dynamic system. The paper also discusses the application of these techniques to an example process