Beijing Institute of Mathematical Sciences and Applications

Shing Toung Yau

Xiao Pei Jiao

Tuesday, January 31, 2023 9:30 PM - 10:00 PM

Online

Ever since Brockett, Clark and Mitter introduced estimation algebra method, it becomes powerful tool to classify the finite dimensional filtering system. In this paper, we investigate finite dimensional estimation algebra with non-maximal rank. Structure of Omega will be focused on which is critical for known classification of estimation algebra. In this paper, we first consider general estimation algebra with non-maximal rank and determine the linear structure of submatrix of Omega by using rank condition and quality of Euler operator. In the second part, we proceed to consider case of linear rank n-1 and prove the linear structure of Omega. Finally, we give the structure of nonlinear filters which implies the drift term must be a quadratic function plus a gradient of smooth function.

Xiaopei Jiao received his bachelor's degree from the Zhiyuan College of Shanghai Jiao Tong University and his Ph.D. from the Department of Mathematical Sciences at Tsinghua University. He subsequently worked as a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and at the University of Twente in the Netherlands. His current research interests include finite-dimensional filtering theory, Yau-Yau filtering methods, physics-informed neural networks, and bioinformatics. His research focuses primarily on: (1) using geometric tools such as Lie algebras for solving partial differential equations and classifying nonlinear systems; (2) designing novel numerical algorithms based on physics-informed neural networks.