Extended Kalman filters for nonlinear fractional-order systems perturbed by colored noises. (July 2020) - Yang, Chao; Gao, Zhe; Liu, Fanghui; Ma, Ruicheng
Abstract: The fractional-order extended Kalman filter (FEKF) algorithm for a nonlinear fractional-order system perturbed by the colored noise is presented. Firstly, the first-order Taylor expansion is employed to linearize the nonlinear functions in the estimated system. Then, Grünwald–Letnikov difference (GLD) and the concept of fractional-order average derivative (FOAD) are employed to discretize nonlinear fractional-order systems perturbed by colored fractional-order process or measurement noise. An augmented system determined by the state and colored noises is presented to treat colored noises. Hence, the FEKFs using GLD and FOAD are carried out, respectively. By comparing two kinds of Kalman filters, FEKFs using FODA can gain the better effect of filtering for colored process or measurement noise to raise the estimation precision. Finally, we discuss three examples to show the validity of investigated FEKFs. Highlights: The nonlinear fractional-order systems perturbed by colored noises are investigated. By fractional-order average derivative and G–L difference, nonlinear fractional-order systems are discretized. Construct an augmented system regarding the state and colored noises. Propose the fractional-order extended Kalman filters.