Accurate state estimation of stiff continuous-time stochastic models in chemical and other engineering

This paper presents two square-root accurate continuous-discrete extended Kalman filters designed for estimating stiff continuous-time stochastic models. These methods are grounded in the nested implicit Runge-Kutta formulas of orders 4 and 6. The implemented automatic local and global error control mechanisms raise the accuracy of state estimation and make the novel techniques more effective than the traditional extended Kalman filter (EKF) based on the Euler-Maruyama discretization and other existing nonlinear Kalman-like algorithms. The designed state estimators are examined numerically on the stochastic Oregonator model, which is a famous stiff example in chemical engineering. The superiority of our sixth-order method is confirmed in this experiment. In addition, we reveal such a counterintuitive result that the traditional EKF may outperform the contemporary advanced cubature and unscented Kalman filters both in the accuracy and in the efficiency of state estimation when applied to stiff continuous-time stochastic models in chemical and other engineering.