Adaptive Fractional-order Unscented Kalman Filters for Nonlinear Fractional-order Systems

In this paper, the Grüwald-Letnikov method is used to discretize a continuous-time nonlinear fractional-order system with unknown parameters and fractional-order, and an adaptive fractional-order unscented Kalman filter is proposed. Taking the unknown fractional-order and parameters as the augmented states, the augmented state equation is established to solve the problem on the unknown fractional-order and parameters. In order to improve the accuracy of state estimation, an adaptive fractional-order unscented Kalman filter is designed to deal with the nonlinear functions by using the unscented transformation. Meanwhile, the problem on state estimation for the estimated system with a non-differentiable nonlinear functions is also solved. Finally, the effectiveness of the proposed algorithm is verified by two simulation examples.