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

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.