Extended Kalman Filters for Continuous-time Nonlinear Fractional-order Systems Involving Correlated and Uncorrelated Process and Measurement Noises

In order to improve the estimation accuracy of the state information and save the computing time for fractional-order systems containing correlated and uncorrelated process and measurement noises, this paper investigates fractional-order extended Kalman filters for continuous-time nonlinear fractional-order systems using the method of fractional-order average derivative. Compared with Grünwald-Letnikov difference, the estimation accuracy is improved via the fractional-order average derivative method. Meanwhile, the computing time in the state estimation is saved. To deal with the correlated and uncorrelated process and measurement noises, two kinds of extended Kalman filters for nonlinear fractional-order systems are given. Finally, the effectiveness of the proposed fractional-order extended Kalman filters based on fractional-order average derivative is validated by two examples.