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BIMSA Digital Economy Lab Seminar
Finite dimensional filter: from classification to numerical approximation
Finite dimensional filter: from classification to numerical approximation
Speaker
Time
Friday, October 10, 2025 3:00 PM - 4:00 PM
Venue
A3-2-303
Online
Zoom 435 529 7909
(BIMSA)
Abstract
The nonlinear filtering problem, which dates back to the 1600s, aims to infer reliable state estimates from stochastic measurements. The introduction of the Kalman filter in the 1960s revolutionized fields such as aerospace engineering and navigation. Nevertheless, achieving optimal state estimation hinges on computing the conditional density, governed by the Duncan-Mortensen-Zakai (DMZ) equation introduced in the 1970s. In 1981 International Congress of Mathematician, the well known Brockett-Mitter program was proposed classify finite dimensional filter by using Wei-Norman approach. One of the most important tool is estimation algebra. Since 1990, through about 2 decades, Yau and his collaborator have made significant progress in classifying maximal rank filter. In this talk we shall review the most recent progress made by speaker about the complicated extension to classification on non-maximal rank filters. Followed by this theoretical results, speaker shall then talk about numerical approximation on the FDF by utilizing powerful deep learning technique and Yau-Yau filter.
Speaker Intro
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.