Fractional-order Kalman filters for continuous-time fractional-order systems involving correlated and uncorrelated process and measurement noises

This paper presents fractional-order Kalman filters using the fractional-order average derivative method for linear fractional-order systems involving process and measurement noises. By using the fractional-order average derivative method, a difference equation model is obtained by discretizing the investigated continuous-time fractional-order system, and the accuracy of state estimation is improved. Meanwhile, compared with the Tustin generating function, the fractional-order average derivative method proposed in this paper can reduce computation load and save calculation time. Two kinds of fractional-order Kalman filters are given, for the correlated and uncorrelated cases, in terms of the process and measurement noises for linear fractional-order systems, respectively. Finally, simulation results are illustrated to verify the effectiveness of the proposed Kalman filters using the fractional-order average derivative method.