Unscented Kalman filter for continuous-time nonlinear fractional-order systems with process and measurement noises

This study proposes the design of unscented Kalman filter for a continuous-time nonlinear fractional-order system involving the process noise and the measurement noise. The nonlinear fractional-order system is discretized to get the difference equation. According to the unscented transformation, the design method of unscented Kalman filter for a continuous-time nonlinear fractional-order system is provided. Compared with the extended Kalman filter, the proposed method can obtain a more accurate estimation effect. For fractional-order systems containing non-differentiable nonlinear functions, the method proposed in this paper is still effective. The unknown parameters are also discussed by the augmented vector method to achieve the state estimation and parameter identification. Finally, two examples are offered to verify the effectiveness of the proposed unscented Kalman filter for nonlinear fractional-order systems.