Communications in Information and Systems

Volume 19 (2019)

Number 2

A survey of direct methods for Yau filtering systems

Pages: 167 – 191



Xiuqiong Chen (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Wenhui Dong (Department of Mathematical Sciences, Tsinghua University, Beijing, China)


Filtering problem has been studied since the early 1960s when the famous Kalman filter was proposed and there have been a variety of filtering algorithms springing up since then. One useful filtering method is the so called direct method for Yau filtering system which was proposed in 1990s. In the early works about the direct method, they all assume that the filtering system is time-invariant. However, this limitation excludes the situation where the filtering system also depends on the time, i.e., the filtering system is time-varying, which can be very common in real applications. Recently, Yau and his collaborators have extended the work to the time-varying case and make it more applicable for practical filtering problems. In this work, we shall briefly go through the direct method for both the time-invariant and the time-varying Yau filtering system.

Received 15 March 2019

Published 19 September 2019