Yau-Yau Algorithm

In this chapter, we will present a numerical algorithm to solve general nonlinear filtering problems based on the DMZ equations introduced in Chap. 5 . This algorithm, which is called the Yau-Yau algorithm, is named after Shing-Tung Yau and Stephen S.-T. Yau, who proposed this algorithm in the beginning of this century. Generally speaking, the idea of this algorithm is to separate the task of solving nonlinear filtering problems into two phases, and the procedure of solving partial differential equations (PDEs), which is computationally expensive, can be dealt with off-line. We will start with the formulation of the Yau-Yau algorithm and present a rigorous convergence analysis. Later on, its applications in time-variant filtering systems will be discussed and some suitable numerical methods of solving PDEs will also be summarized.