Shankar Narasimhan S

Kalman filter and its variants have been used for state estimation of systems described by ordinary differential equation (ODE) models. While state and parameter estimation of ODE systems has been studied extensively, differential algebraic equation (DAE) systems have received much less attention. However, most realistic chemical engineering processes are modelled as DAE systems and hence state and parameter estimation of DAE systems is a significant problem. Becerra et al. (2001) proposed an extension of the extended kalman filter (EKF) for estimating the states of a system described by nonlinear differential-algebraic equations (DAE). One limitation of this approach is that it only utilizes measurements of the differential states, and is therefore not applicable to processes in which algebraic states are measured. In this paper, we address the state estimation of constrained nonlinear DAE systems. The novel aspects of this work are: (i) development of a modified EKF approach that can utilize measurements of both algebraic and differential states, (ii) development of a recursive approach for the inclusion of constraints, and (iii) development of approaches that utilize unscented sampling in state and parameter estimation of nonlinear DAE systems; this has not been attempted before. The utility of these estimators is demonstrated using electrochemical and reactive distillation processes. © 2010 Elsevier Ltd.

State estimation is an important problem in process operations. For linear dynamical systems, Kalman Filter (KF) results in optimal estimates. Chemical engineering problems are characterized by nonlinear models and constraints on the states. Nonlinearities in these models are handled effectively by the Extended Kalman Filter (EKF), whereas constraints pose more serious problems. Several constrained estimation problems where the EKF approach fails have been reported in the literature. To address this issue, receding horizon approaches such as the Moving Horizon Estimation (MHE) have been proposed. The MHE approach has been shown to provide the most reliable estimates in several example problems; albeit at a high computational price. Unlike the KF, the MHE formulation does not use an explicit predictor-corrector approach. In this paper, we study the following questions in nonlinear constrained state estimation: (i) can the EKF be extended to include a receding horizon in a simple intuitive fashion? (ii) are there any performance gains over an EKF due to a receding horizon? and, (iii) are there any computational gains over the standard MHE through such an extension? A Receding Nonlinear Kalman (RNK) Filter formulation is proposed to answer these questions. The RNK formulation follows a predictor-corrector approach and uses linearization of the state space model for covariance calculation much like the EKF approach. We demonstrate through examples that inclusion of a receding horizon improves performance over the standard EKF approach. We also discuss the computational properties of RNK in comparison with MHE. © 2011 Elsevier B.V.