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  

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

作　　者：李继泽 邱吉秀 周永辉 Li Jize;Qiu Jixiu;Zhou Yonghui(School of Mathematics and Sciences,Guizhou Normal University,Guiyang 550025;School of Big Data and Computer Sciences,Guizhou Normal University,Guiyang 550025)

机构地区：[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

出　　处：《数学物理学报（A辑）》2023年第4期1244-1254,共11页Acta Mathematica Scientia

基　　金：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)。

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.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.

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 

分 类 号：O23[理学—运筹学与控制论]