报告题目： Nonlinear Filtering Based on Third-Degree Approximation via Sequential Homotopy

报 告 人：胡三丰

研究方向：信息处理与融合

摘 要: In order to develop an effective nonlinear filter for nonlinear dynamic systems in the linear minimum mean square error (LMMSE) estimation framework, third-degree approximation of the moments of nonlinearly transformed random variable without symmetric distribution assumption is addressed in this paper. The construction of deterministic points, named tau points, to match the first three moments of random variables, is formulated first as a constrained third-order symmetric tensor decomposition problem. Inspired by the idea of homotopy, a simple problem with easy solution is proposed, and then a novel approach is developed for solving the decomposition problem by tracing sequential zero paths emanating from a solution of the simple problem. The propagated tau points through nonlinear transformations are used to approximate the moments in the LMMSE estimation framework, and thus a new filter is derived. The involved moments are estimated more accurately through third-degree approximation. The effectiveness of the developed filter is demonstrated through simulation studies, compared with some popular nonlinear filters.

报告题目：Geometric Properties of Statistical Models and Their Applications

报 告 人：唐梦皎

研究方向：应用统计、信息几何、统计信号处理

摘 要：Information geometry is an interdisciplinary field that applies the techniques of differential geometry to the study of probability theory and statistics. It investigates statistical manifolds, where the points correspond to probability distributions. In this talk, I will introduce some information geometric concepts, research issues, and applications.

时 间：2023年3月24日周五14：00——16：00

地 点：数学与统计学院格物楼3103报告厅

欢迎广大师生参加！