一种分数阶卡尔曼滤波器

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 Fractional Order Kalman Filter〓

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.