Cubature Kalman filters for nonlinear continuous-time fractional-order systems with uncorrelated and correlated noises

This paper presents cubature Kalman filters for nonlinear continuous-time fractional-order systems involving the uncorrelated and correlated process and measurement noises. A continuous-time fractional-order system is discretized by the Grumwald-Letnikov difference to gain a difference equation. By using the third-degree spherical-radial rule, the nonlinear functions in the state equation and output equation are performed by the cubature points. Based on these cubature points, the Kalman filters for the uncorrelated and correlated noises are given to achieve the effective state estimation. Besides, the estimation for unknown parameters in the investigated nonlinear fractional-order system is also discussed. Finally, three illustrative examples are provided to verify the proposed cubature Kalman filters in this paper.