Efficient Implementation of Continuous-Discrete Extended Kalman Filters for State and Parameter Estimation of Nonlinear Dynamic Systems

The extended Kalman filter (EKF), one of the most popular state estimators for nonlinear uncertain dynamic systems, is considered here in its continuous-discrete (CD) form. The CD version enhances the EKF's accuracy but requires robust and computationally efficient numerical integration methods. The purpose of this article is to present several new efficient integration methods suited to the implementation of the CD-EKF and to compare them to classical implementations such as the Dormand–Prince 4/5 and Euler methods. They are first applied on two proposed nonlinear parameter estimation testbenches and to the stiff Curtiss and Hirschfelder model for state and parameter estimation. Then, they are applied to the estimation of the iron losses of a high-speed permanent-magnet synchronous motor. The results show that for highly nonlinear dynamic systems or for a low to medium sampling frequency, the implicit implementation of the EKF provides a better accuracy and convergence safety. For less nonlinear functions and a higher sampling frequency, classical explicit methods obviously give similar results in a lower computation time.