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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
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Facilities
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News
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Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Seminar on Control Theory and Nonlinear Filtering Non-Gaussian Bayesian Filtering by Density Parametrization Using Power Moments
Non-Gaussian Bayesian Filtering by Density Parametrization Using Power Moments
Organizer
Shing Toung Yau
Speaker
Jia Yi Kang
Time
Monday, July 10, 2023 3:00 PM - 3:30 PM
Venue
数学系理科楼A-203
Abstract
I will report a paper on Non-Gaussian Bayesian filtering. Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments to obtain a parameterization. Unlike the existing parametric estimation methods, our proposed algorithm does not require prior knowledge about the state to be estimated, e.g. the number of modes and the feasible classes of function. Moreover, the proposed algorithm is not required to store massive parameters during filtering as the existing nonparametric Bayesian filters, e.g. the particle filter. The parameters of the proposed parametrization can also be determined by a convex optimization scheme with moments constraints, to which the solution is proved to exist and be unique. A necessary and sufficient condition for all the power moments of the density estimate to exist and be finite is provided. The errors of power moments are analyzed for the density estimate being either light-tailed or heavy-tailed. Error upper bounds of the density estimate for the one-step prediction are proposed. Simulation results on different types of density functions of the state are given, including the heavy-tailed densities, to validate the proposed algorithm.
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