含有分数阶有色关联噪声的分数阶系统的卡尔曼滤波器设计  

Design of Kalman filter for fractional-order systems with correlated fractional-order colored noises

作　　者：高哲 黄晓敏[1] 陈小姣 GAO Zhe;HUANG Xiao-min;CHEN Xiao-jiao(School of Mathematics,Liaoning University,Shenyang 110036,China;College of Light Industry,Liaoning University,Shenyang 110036,China)

机构地区：[1]辽宁大学数学院,沈阳110036 [2]辽宁大学轻型产业学院,沈阳110036

出　　处：《控制与决策》2021年第7期1672-1678,共7页Control and Decision

基　　金：辽宁省“兴辽英才计划”基金项目(XLYC1807229);辽宁省自然科学基金项目(20180520009);中国博士后科学基金项目(2019M651206);辽宁大学校级科学研究基金项目(LDGY2019020)。

摘　　要：提出基于Tustin生成函数的分数阶卡尔曼滤波器设计方法,以解决含有相互关联的分数阶有色过程噪声和分数阶有色测量噪声的连续时间线性分数阶系统的状态估计问题.通过Tustin生成函数方法,对连续时间线性分数阶系统进行离散化,将分数阶系统的微分方程转化为差分方程.利用增广向量法,将分数阶状态方程和分数阶有色噪声作为新的增广状态向量,从而将分数阶有色噪声转化为高斯白噪声.然后,提出一种基于Tustin生成函数的分数阶卡尔曼滤波算法,有效地实现对含有相互关联的分数阶有色过程噪声和分数阶有色测量噪声的连续时间线性分数阶系统的状态估计.与基于Gr¨unwald-Letnikov差分的离散化方法相比,所提出的基于Tustin生成函数的卡尔曼滤波算法得到的状态估计精度更高,状态估计效果更好.最后,通过仿真结果验证所提出算法的有效性.The design method of fractional-order Kalman filter based on Tustin generating function is proposed to solve the problem on the state estimation for continuous-time linear fractional-order systems with correlated fractionalorder colored process noise and fractional-order colored measurement noise.By Tustin generating function method,the continuous-time linear fractional-order system is discretized,the differential equation of fractional-order system is transformed into a difference equation.Using the augmented vector method,the fractional-order state equation and the fractional-order colored noises are constructed as a new augmented state vector,and the fractional-order colored noises are transformed into white Gaussian noises.Then,a fractional-order Kalman filter algorithm based on Tustin generating function is presented to achieve effectively the state estimation of the continuous-time linear fractional-order system involving correlated fractional-order colored process noise and fractional-order colored measurement noise.Compared with Gr¨unwald-Letnikov difference,the state estimation obtained by Kalman filter algorithm using Tustin generating function is more accurate and the effect is more satisfactory.Finally,the effectiveness of the proposed algorithms is validated by the simulation result.

关 键 词：线性分数阶系统 分数阶卡尔曼滤波器 状态估计 关联噪声 有色噪声 Tustin生成函数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]