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针对量测噪声模型为非高斯Lévy噪声,研究离散线性随机分数阶系统的卡尔曼滤波设计问题.通过剔除极大值的方法得到近似高斯白噪声的Lévy噪声,基于最小二乘原理,提出一种考虑非高斯Lévy量测噪声下的改进分数阶卡尔曼滤波算法.与传统的分数阶卡尔曼滤波相比,改进的分数阶卡尔曼滤波对非高斯Lévy噪声具有更好的滤波效果.最后,通过模拟仿真验证了所提出算法的正确性和有效性.
Aiming at the problem that the measured noise model is non-Gaussian Lévy noise, the Kalman filter design problem of discrete linear stochastic fractional system is studied. The Lévy noise of approximate Gaussian white noise is obtained by removing the maximum value. Based on the least square principle, Considering the improved fractional Kalman filter algorithm under non-Gaussian Lévy measurement noise, the improved fractional Kalman filter has better filtering effect on non-Gaussian Lévy noise than the traditional fractional Kalman filter.Finally, Simulation results verify the correctness and validity of the proposed algorithm.