Direct Method for Time-Varying Nonlinear Filtering Problems
Direct Method for Time-Varying Nonlinear Filtering Problems
复制标题
DOI：
10.1109/taes.2017.2651650
复制
发表时间：
2017-01
影响因子：
4.4
通讯作者：
Xiuqiong Chen;Xue Luo;S. Yau
中科院分区：
文献类型：
--
作者：
Xiuqiong Chen;Xue Luo;S. Yau
本文讨论如何通过 Duncan-Mortensen-Zakai (DMZ) 方程求解一类连续非线性时变系统的滤波问题。本文通过在每个时间间隔内进行指数变换，将原始DMZ方程转化为Kolmogorov前向方程（KFE），然后在某些假设下，KFE可以转化为时变薛定谔方程，并可显式求解。本文的新颖之处在于如何将KFE转化为薛定谔方程。作为直接应用，将“非线性滤波和时变薛定谔方程”论文的结果推广到时变 Yau 系统。
This paper discusses how to solve a filtering problem for a class of continuous nonlinear time-varying systems via the Duncan–Mortensen–Zakai (DMZ) equation. In this paper, the original DMZ equation is changed into the Kolmogorov forward equation (KFE) by exponential transformations in each time interval, and then, under some assumptions, the KFE can be transformed into a time-varying Schrödinger equation, which can be solved explicitly. The novelty of this paper lies in how to transform the KFE into the Schrödinger equation. As a direct application, the results of the paper “Nonlinear filtering and time varying Schrodinger equation” are extended for time-varying Yau systems.