Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Xiaopei Jiao

Tuesday, February 21, 2023 9:30 PM - 10:00 PM

Online

Ever since Brockett, Clark and Mitter introduced the estimation algebra method, it becomes a powerful tool to classify the finite dimensional filtering system. In this paper, we investigate estimation algebra on state dimension $n$ and linear rank $n-1$, especially case of $n=4$. Mitter conjecture is always a key question on classification of estimation algebra. Weaker form of Mitter conjecture states observation functions in finite dimensional filters are affine functions. In this paper, we will focus on weaker form of Mitter conjecture. In the first part, it will be shown that a sufficient condition of weaker Mitter conjecture is partially constant structure of $Omega$. In the second part, partially constant structure of $Omega$ will be proven true and weaker Mitter conjecture hold for $n=4$ case.

Jiao Xiaopei graduated with a bachelor's degree from the Zhi Yuan College of Shanghai Jiao Tong University (Physics Department) in 2017 and obtained his PhD from the Department of Mathematical Sciences at Tsinghua University in 2022, under the guidance of Professor Stephen Shing-Toung Yau (IEEE Fellow, former tenured professor at the University of Illinois at Chicago). He has conducted postdoctoral research at the Beijing Institute of Mathematica Science and Application and at the University of Twente in the Netherlands (under the guidance of Professor Johannes Schmidt-Hieber, Fellow of the Institute of Mathematical Statistics). His current research interests include control theory, numerical partial differential equations, and bioinformatics.