Direct Method for Time-Varying Nonlinear Filtering Problems

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 Schrodinger equation, which can be solved explicitly. The novelty of this paper lies in how to transform the KFE into the Schrodinger equation. As a direct application, the results of the paper “Nonlinear filtering and time varying Schrodinger equation” are extended for time-varying Yau systems.