受观察噪声影响的不可料非线性滤波方程及线性滤波稳定性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1244-1254.

受观察噪声影响的不可料非线性滤波方程及线性滤波稳定性

李继泽¹,邱吉秀¹,周永辉^2,^*()

¹贵州师范大学数学科学学院贵阳 550025
²贵州师范大学大数据与计算机科学学院贵阳 550025

收稿日期:2022-09-01 修回日期:2023-02-06 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 周永辉 E-mail:yonghuizhou@gznu.edu.cn
基金资助:
国家自然科学基金(11861025);贵州省科技计划项目(黔科中引地[2022]4055)

Anticipative Nonlinear Filtering Equations Affected by Observation Noises and Stability of Linear Filtering

Li Jize¹,Qiu Jixiu¹,Zhou Yonghui^2,^*()

¹School of Mathematics and Sciences, Guizhou Normal University, Guiyang 550025
²School of Big Data and Computer Sciences, Guizhou Normal University, Guiyang 550025

Received:2022-09-01 Revised:2023-02-06 Online:2023-08-26 Published:2023-07-03
Contact: Yonghui Zhou E-mail:yonghuizhou@gznu.edu.cn
Supported by:
Natural Science Foundation of China(11861025);QKZYD of Guizhou ([2022]4055)

摘要/Abstract

摘要：

针对一类不可料信号过程噪声与观察过程噪声相关的非线性系统, 借助信息域扩张方法, 将该系统转化为关于扩张信息域相适应的更高维系统, 然后导出高维适应系统的Zakai方程和Kushner-FKK方程及其在线性情况下的显式解. 作为应用, 得到一类不可料常系数线性系统滤波的渐近稳定性.

关键词: 不可料非线性系统, 非线性滤波, Zakai方程, Kushner-FKK方程, 线性滤波渐近稳定性

Abstract:

In this paper, the filtering problem of an anticipative nonlinear signal-observation system with correlated noises over time is studied. With the help of enlargement of filtration, we turn the anticipative system into a higher dimensional and adaptive one, then for the new one's filtering problem, and derive both Zakai's equation and Kushner-FKK's equation together with their explicit solutions in a linear case. As an application, we obtain asymptotic stability of a linear filtering with some constant coefficients, which is similar to that of the classical Kalman-Bucy filtering.

Key words: Anticipative nonlinear system, Non-linear filtering, Zakai's equation, Kushner-FKK's equation, Asymptotic stability of linear filtering

中图分类号:

李继泽,邱吉秀,周永辉. 受观察噪声影响的不可料非线性滤波方程及线性滤波稳定性[J]. 数学物理学报, 2023, 43(4): 1244-1254.

Li Jize,Qiu Jixiu,Zhou Yonghui. Anticipative Nonlinear Filtering Equations Affected by Observation Noises and Stability of Linear Filtering[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1244-1254.

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