分数阶Unscented卡尔曼滤波器研究

摘要

分数阶微积分在控制系统中的应用日益广泛,随着分数阶动态系统模型的引入,需要求解分数阶状态估计问题的方法.该文从分数阶非线性动态系统模型出发,以概率论为基础,导出分数阶的Unscented卡尔曼滤波器,得到其递推模型并应用于典型的非线性系统,UNGM(Univariate Nonstationary Growth Model)模型和再入飞行器跟踪模型.实验结果证明在合理设置分数阶Unscented卡尔曼滤波器阶次的情况下,能够取得优于Unscented卡尔曼滤波器的效果.%Fractional calculus is widely used in control system theory. Owing to introducing of fractional dynamic system model, searching solution method of fractional state estimation is an urgent issue. Starting from fractional nonlinear dynamic system model, fractional unscented Kalman filter is derived based on probability theory. The filter is applied to two- typical nonlinear systems, Univariate Nonstationary Growth Model (UNGM) model and Reentry Vehicle Tracking (RVT) model. Experiment results prove the performance of fractional unscented Kalman filter given in this paper is better than that of the unscented Kalman filter in the context of reasonable setting of the fractional order.