Simultaneous and sequential state and parameter estimation using receding-horizon nonlinear Kalman filter

Abstract

Online estimation of internal states and parameters is often required for process monitoring, fault diagnosis and real time optimization. The conventional approach to tracking drifting parameters is to model their variations as a random walk process and estimate them simultaneously with the states. However, tuning of the random walk model is not a trivial exercise. Recently, moving window based simultaneous state and parameter estimation schemes have been proposed under the assumption that the parameters change slowly and remain constant within the window. These formulations make use of the conventional recursive Bayesian estimators or moving horizon estimator (MHE) for state estimation. While simultaneous smoothing of states along with filtering gives an edge to MHE over the conventional recursive estimators, MHE is computation intensive scheme. Recently, developed Receding-horizon Nonlinear Kalman (RNK) filter combines advantages of MHE (simultaneous smoothing) and recursive estimators (less computation time). In this work, we extend the RNK formulation to carry out simultaneous state and parameter estimation schemes under the assumption that parameters change at a slow rate and remain constant within the RNK window. Two maximum likelihood (ML) based parameter estimation schemes are developed by constructing partial likelihood and complete likelihood functions. Both formulations are further extended under the Bayesian framework to derive their maximum a-posteriori (MAP) versions by incorporating prior information of the parameters. The only tuning parameter in the proposed parameter estimation schemes is the window size, which is relatively easy to select. The efficacies of the proposed formulations are evaluated using simulation studies on two reactor systems and experimental data obtained from the benchmark quadruple tank system. Simulation studies reveal that the complete likelihood based estimation schemes have an edge over the partial likelihood based estimation schemes. Also, the proposed estimation schemes generate reasonably accurate state and parameter estimates with a significant reduction in the average computation time.