Yang Chao, Gao Zhe, Liu Fanghui, Ma Ruicheng
School of Mathematics, Liaoning University, Shenyang 110036, PR China.
School of Mathematics, Liaoning University, Shenyang 110036, PR China; College of Light Industry, Liaoning University, Shenyang 110036, PR China.
ISA Trans. 2020 Jul;102:68-80. doi: 10.1016/j.isatra.2019.07.010. Epub 2019 Jul 11.
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.
提出了一种用于受有色噪声干扰的非线性分数阶系统的分数阶扩展卡尔曼滤波器（FEKF）算法。首先，采用一阶泰勒展开对估计系统中的非线性函数进行线性化。然后，利用 Grünwald-Letnikov 差分（GLD）和分数阶平均导数（FOAD）的概念对受有色分数阶过程或测量噪声干扰的非线性分数阶系统进行离散化。提出了一个由状态和有色噪声确定的增广系统来处理有色噪声。因此，分别实现了使用 GLD 和 FOAD 的 FEKF。通过比较两种卡尔曼滤波器，使用 FODA 的 FEKF 对有色过程或测量噪声能获得更好的滤波效果，从而提高估计精度。最后，我们讨论了三个例子以说明所研究的 FEKF 的有效性。
