Adaptive Extended Kalman Filters for Nonlinear Fractional-order Systems with Colored Noises

We study the state estimation problems of continuous-time nonlinear fractional-order systems involving unknown parameters with fractional-order colored process or measurement noises respectively. We discretize and linearize the state equations describing continuous-time nonlinear fractional-order systems by the Grünwald-Letnikov (G-L)difference method and the first-order Taylor expansion. By constructing the augmented vector determined by the state, the unknown parameter and fractional-order colored noises, we design an adaptive fractional-order extended Kalman filter algorithm to estimate the state and parameters of continuous-time nonlinear fractional-order systems with colored noises. Finally, the effectiveness of the proposed adaptive Kalman filter is verified by analyzing simulation examples.