Direct Methods

In this chapter, we will focus on the explicit solution of DMZ equation for some specific nonlinear systems. First, we focus on continuous time-invariant finite-dimensional filtering systems. It shows that Yau filtering system can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a Kolmogorov equation. Second, we will extend the direct method to time-invariant Yau filtering system with nonlinear observations. Third, we mainly consider time-invariant Yau systems with a class of nonlinear observation and give explicit solution under the Yau-Yau algorithm framework. Finally, we extend the previous results to time-varying Yau systems.