含分数阶有色关联噪声的分数阶系统的卡尔曼滤波器
作者:
作者单位:

辽宁大学

作者简介:

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中图分类号:

TP273

基金项目:

中国博士后科学基金


Kalman filter for fractional-order systems with correlated fractional-order colored noises
Author:
Affiliation:

Liaoning University

Fund Project:

China Postdoctoral Science Foundation

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    摘要:

    本文提出了基于 Tustin 生成函数的分数阶卡尔曼滤波器设计方法, 解决了含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, 提出了一种基于Tustin 生成函数的分数阶卡尔曼滤波算法, 有效地实现了对含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$\ddot{u}$nwald-Letnikov 差分的离散化方法相比, 本文提出的基于 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, 通过仿真结果验证提出算法的有效性.

    Abstract:

    In this paper, 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 fractional-order 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 noise are constructed as a new augmented state vector, and the fractional-order colored noises are dealt with as Gaussian white 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$\ddot{u}$nwald-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.

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历史
  • 收稿日期:2019-10-09
  • 最后修改日期:2020-12-14
  • 录用日期:2020-03-17
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