State Estimation of Continuous-Time Linear Fractional-Order Systems Disturbed by Correlated Colored Noises via Tustin Generating Function

This paper proposes Kalman filters to investigate the state estimation of continuous-time linear fractional-order systems disturbed by correlated colored noises. A difference equation is obtained by discretizing the fractional-order differential equation via Tustin generating function. Besides, an augmented vector is determined by the state vector and the colored noise vector to deal with the problems on the colored process noise or the colored measurement noise with fractional-orders. In fact, a more accurate state estimation can be achieved using the discretization method via Tustin generation function for the investigated fractional-order systems, compared with Grünwald-Letnikov difference. Finally, two illustrative examples are provided to validate the effectiveness of the proposed algorithms in this paper.