Practical implementation of extended Kalman filtering in chemical systems with sparse measurements

• Published in: Russian journal of numerical analysis and mathematical modelling Vol. 33; no. 1; pp. 41 - 53
• Main Authors: Kulikov, Gennady Yu, Kulikova, Maria V.
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.02.2018; Walter de Gruyter GmbH
• Subjects: 93E11; Algorithms; Automatic control; Chemical engineering; continuous-discrete stochastic system; Differential equations; Dynamical systems; Extended Kalman filter; MDE solver with error control; Nonlinear dynamics; Ordinary differential equations; reaction state estimation; Software sensor; sparse measurements; State estimation
• ISSN: 0927-6467; 1569-3988; 1569-3988
• DOI: 10.1515/rnam-2018-0004

Chemical systems are often characterized by a number of peculiar properties that create serious challenges to state estimator algorithms. They may include hard nonlinear dynamics, states subject to some constraints arising from a physical nature of the process (for example, all chemical concentrations must be nonnegative), and so on. The classical Extended Kalman Filter (EKF), which is considered to be the most popular state estimator in practice, is shown to be ineffective in chemical systems with infrequent measurements. In this paper, we discuss a recently designed version of the EKF method, which is grounded in a high-order Ordinary Differential Equation (ODE) solver with automatic global error control. The implemented global error control boosts the quality of state estimation in chemical engineering and allows this newly built version of the EKF to be an accurate and efficient state estimator in chemical systems with both short and long waiting times (i.e., with frequent and infrequent measurements). So chemical systems with variable sampling periods are algorithmically admitted and can be treated as well.