An extended Kalman filter formulation for systematic transfer of information from batch to batch

Abstract

In this paper, a modified extended Kalman filter (EKF) formulation is developed that allows for a systematic batch-to-batch transfer of the parameter estimates and covariance information. A simple and tunable stochastic description for the batch-to-batch behavior of the model parameters and initial conditions is proposed. Then, a method for incorporating such a model into a general ODE model describing the batch process is presented. An extended Kalman filter formulated based on this augmented model is capable of systematically transferring the parameter estimates and the covariance information at the end of a batch run to initialize the filter for the next batch. This provides an advantage over traditional EKF formulations, which can suffer due to insufficient measurements imposed by the finite batch duration. A simple tuning parameter is introduced in the stochastic parameter model that weighs the relative importance of the variance components for the batchwise-correlated and independent portions. This would allow the filter performance to be tuned to the particular situation at hand. An application to a simple chemical reactor and a nylon 6,6 autoclave is discussed to demonstrate the usage and the benefits of the proposed formulation.