In order to improve the estimation accuracy of the state information and save the computing time for fractional-order systems containing correlated and uncorrelated process and measurement noises, this paper investigates fractional-order extended Kalman filters for continuous-time nonlinear fractional-order systems using the method of fractional-order average derivative. Compared with Grünwald-Letnikov difference, the estimation accuracy is improved via the fractional-order average derivative method. Meanwhile, the computing time in the state estimation is saved. To deal with the correlated and uncorrelated process and measurement noises, two kinds of extended Kalman filters for nonlinear fractional-order systems are given. Finally, the effectiveness of the proposed fractional-order extended Kalman filters based on fractional-order average derivative is validated by two examples.

为了提高状态信息的估计精度并节省包含相关和不相关过程和测量噪声的分数阶系统的计算时间，本文研究了连续时间非线性分数阶系统的分数阶扩展卡尔曼滤波器。分数阶平均导数的方法。与Grünwald-Letnikov差分相比，通过分数阶平均导数方法可以提高估计精度。同时，节省了状态估计中的计算时间。为了处理相关和不相关的过程和测量噪声，给出了两种用于非线性分数阶系统的扩展卡尔曼滤波器。最后，