Study on initial value problem for fractional-order cubature Kalman filters of nonlinear continuous-time fractional-order systems

To realize the state estimation of nonlinear continuous-time fractional-order systems, two types of fractional-order cubature Kalman filters are designed to solve problem on the initial value influence. For the first type of cubature Kalman filter (CKF), the initial value of the estimated system is also regarded as the augmented state, and the augmented state equation is constructed to obtain the CKF based on Grünwald–Letnikov difference. For the second type of CKF, the fractional-order hybrid extended-cubature Kalman filter is proposed to weaken the influence of initial value by the first-order Taylor expansion and the third-order spherical-radial rule. These two methods can reduce the influence of initial value on the state estimation effectively. Finally, the effectiveness of the proposed CKFs is verified by two simulation examples.