An unscented particle filter (UPF) is proposed for a nonlinear fractional-order system (NFOS) with an unknown order (UO) and unknown parameters. The Grünwald–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 fractional-order 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.

中文翻译：

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具有未知分数阶和未知参数的非线性分数阶系统的自适应无味粒子滤波器

提出了一种用于具有未知阶数 (UO) 和未知参数的非线性分数阶系统 (NFOS) 的无迹粒子滤波器 (UPF)。利用 Grünwald-Letnikov 差分对连续时间 NFOS 进行离散化，得到相应的差分方程。对于每个采样的粒子，应用无味变换，然后使用重采样算法对粒子进行优化。此外，通过增广向量法建立了状态、UO和未知参数的增广方程。所提出的分数阶 UPF 在估计状态方面比分数阶无迹卡尔曼滤波器和分数阶粒子滤波器更准确。此外，自适应分数阶UPF有效地估计了UO和未知参数。最后，通过两个数值例子和一个实际例子验证了所提算法的有效性。