An Unscented Kalman Filter For Continuous-Time Nonlinear Fractional-Order Systems With Correlated Noises

This study proposes an unscented Kalman filter for the state estimation of continuous-time nonlinear fractional-order systems with correlated process and measurement noises. The discretization of the nonlinear fractional-order system is performed by using the Grunwald-Letnikov difference, and the description corresponding to the difference equation is obtained. The unscented Kalman filter is used to realise the state estimation of the nonlinear fractional-order system by using the unscented transformation to improve the accuracy of the state estimation. For the non-differential nonlinear functions in continuous-time fractional-order systems. the proposed method is still valid. Finally, two simulation examples are given to illustrate the effectiveness of the unscented Kalman filter proposed in this paper.