High-order accurate continuous-discrete extended Kalman filter for chemical engineering

This paper elaborates a new version of extended Kalman filtering (EKF) for state estimation in chemical nonlinear continuous-discrete stochastic systems. Such a state estimation always compounds real measurements of some system׳s variables (depending on the utilized technology) with computation of remaining (not measurable) parameters by means of appropriate filtering algorithms. Here, we consider the continuous-discrete EKF and show that its quality is raised by using the adaptive sixth-order nested implicit Runge–Kutta (NIRK) method of Gauss type with automatic local and global error controls. Through case studies the new filtering technology is compared to another EKF implementation based on an adaptive ODE solver but with the sole local error control. Our numerical results exhibit that the designed state estimation algorithm not only outperforms the earlier published adaptive EKF method, but also resolves the so-called “EKF failure” case reported recently.