Fractional extended Kalman filtering for non-linear fractional system with Lévy noises

In this study, the extended Kalman filtering problem is discussed for fractional-order non-linear discrete system with Levy noises. Two different approximating methods are proposed, respectively, one is to obtain the approximated system measurement noise firstly, then calculates the iterative state vector and measurement vector, the other one is to approximate state vector and measurement vector directly, which seems to be more efficient. Based on the proposed approximating methods, two novel fractional extended Kalman filter designing strategies are developed for fractional-order non-linear discrete system with Levy noises, some detailed comparisons and discussions are presented to show that the obtained results are more general. Finally, some simulation results with necessary comparisons and discussions are given to illustrate the validity and correctness of the proposed methods.