An adaptive unscented particle filter for a nonlinear fractional-order system with unknown fractional-order and unknown parameters

An unscented particle filter (UPF) is proposed for a nonlinear fractional -order system (NFOS) with an unknown order (UO) and unknown parameters. The Gr & uuml;nwald-Letnikov difference is used to discretize the continuous -time NFOS and the corresponding difference equation is acquired. For each sampled particle, a unscented transformation is applied, and the particles are afterwards optimized using a resampling algorithm. Furthermore, the augmented equations of the states, UO, and unknown parameters are established by an augmented vector method. The proposed fractional -order UPF is more accurate in estimating states than the fractional -order unscented Kalman filter and the fractional -order particle filter. Besides, the adaptive fractionalorder UPF effectively estimate the UO and unknown parameters. Finally, two numerical examples and a practical example are used to verify the effectiveness of the proposed algorithm.