Numerical robustness of extended Kalman filtering based state estimation in ill‐conditioned continuous‐discrete nonlinear stochastic chemical systems

Abstract

SummaryThis paper presents a case study investigation of numerical robustness of extended Kalman filters used for estimation of stochastic chemical systems with ill‐conditioned measurements. Here, we consider both a batch reactor model and that of a continuously stirred tank reactor. Our purpose is to explore performance of extended Kalman filtering–based state estimators when the measurement model becomes increasingly ill conditioned. In this way, we determine numerically robust methods, which are suitable for accurate estimation of stochastic chemical systems in the presence of round‐off and other disturbances. We examine both conventional filters and their square‐root forms. All these algorithms are implemented by means of the conventional matrix inversion used in their measurement update steps and the Moore‐Penrose pseudoinversion as well. Furthermore, the square‐root filters under investigation are obtained in two ways, namely, by solving square‐root moment differential equations and by square rooting the filter itself. We show that only the square‐root filters grounded in the second approach (with use of stable orthogonal decompositions) are numerically robust and provide the excellent estimation accuracy within all our ill‐conditioned stochastic chemical system scenarios considered in this paper. In addition, the convectional filters and the square‐root variants based on solving moment equations are rather sensitive to round‐off and may be useful and accurate if the chemical system at hand is rather well conditioned.