A Tutorial on Yau-Yau Nonlinear Filtering Algorithm: from Model-Driven to Data-Driven

Filtering is a subject of providing sequential estimations of a given stochastic dynamical system based on noisy observations. At the beginning of this century, a two-stage algorithm framework was proposed and analyzed for general nonlinear filtering problems, which is now referred to as the Yau-Yau algorithm. The two-stage structure of this framework theoretically guarantees the potential of solving nonlinear filtering problems in a real-time manner, which is crucial for practical applications. With the introduction of spectral method and neural networks, numerous model-driven and data-driven implementations of Yau-Yau algorithms have been proposed in the last decade. In this paper, we will present a thorough review of the development of nonlinear filters under the Yau-Yau algorithm framework, from model-driven approaches to data-driven approaches, which serves as a guidance for practitioners. Current status and promising future directions in the research of Yau-Yau nonlinear filtering algorithm framework are also summarized and discussed in this paper.