一种分数阶卡尔曼滤波器  

A Fractional-Order Kalman Filter

作　　者：刘禄[1] 潘峰[1] 薛定宇[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110819

出　　处：《东北大学学报（自然科学版）》2014年第8期1069-1072,1077,共5页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(61174145);中央高校基本科研业务费专项资金资助项目(N110404026;N110804005)

摘　　要：传统卡尔曼滤波器一般适用于整数阶系统,为了使卡尔曼滤波器的应用由整数阶系统扩展到分数阶系统,将分数阶系统与卡尔曼滤波算法相结合——将离散分数阶微积分定义的状态空间表达式融入传统卡尔曼滤波器的表达形式中,推导得到一种基于分数阶系统的卡尔曼滤波器算法.仿真实验将输出量与两个状态量分别作为研究对象,利用MATLAB设计了分数阶卡尔曼滤波器算法模块,通过对象的输入和受到噪声污染的输出最优估计出对象的状态,证明了本文提出的分数阶卡尔曼滤波器具有良好的滤波和状态估测力.A conventional Kalman filter is suitable for integer-order systems. In order to apply the Kalman filter to fractional-order systems, a state-space expression defined by discrete fractional- order calculus is introduced into the conventional Kalman filter, thus a fractional-order Kalman filter algorithm is proposed. A simulation experiment is carried out, with two state variables and one output signal as research objects. The fractional-order Kalman filter module is designed in MATLAB. The states of the system are estimated by the input variables and the output variable with noise, showing that the fractional-order Kalman filter algorithm proposed has satisfactory filtering and state-estimating capacity.

关 键 词：分数阶系统 卡尔曼滤波器 状态估计 仿真 MATLAB 

分 类 号：TP202[自动化与计算机技术—检测技术与自动化装置]