State and Parameter Estimation for Dynamical Systems by Using Unscented Kalman Filter

Abstract

This paper considers the state and parameter estimation problems for nonlinear dynamical systems by using the Unscented Kalman filter (UKF). Since unlike the extended Kalman filter (EKF), the UKF does not require Jacobians of nonlinear transformations, we show that the UKF can be used together with the higher order Runge-Kutta approximation. We then derive a Runge-Kutta based UKF algorithm for nonlinear dynamical systems. Numerical studies show that the Runge-Kutta based UKF provides better numerical results compared with EKF and UKF algorithms coupled with the Euler approximation.