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

Abstract

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

CLC Number:

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

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