BIMSA > Seminar on Control Theory and Nonlinear Filtering Estimation of the Linear System via Optimal Transportation and Its Application for Missing Data Observations
Estimation of the Linear System via Optimal Transportation and Its Application for Missing Data Observations
Organizer
Shing Toung Yau
Speaker
Jia Yi Kang
Time
Monday, May 1, 2023 3:00 PM - 3:30 PM
Venue
Online
Abstract
This paper presents a unified framework for particle data fusion using optimal transportation. We address prediction, filtering, and smoothing problems by representing particle methods as paths on the Wasserstein space. We use optimal transportation to develop robust and stable algorithms for prediction and filtering, known as optimal transportation particle prediction and optimal transportation particle filtering. We derive optimal transportation particle smoothing using Mayne-Fraser's two-filter formula. We derive equations for empirical mean and covariance, equivalent to the explicit solution of filtering and smoothing. We provide detailed convergence results for our proposed algorithms. Finally, we test our algorithms on missing observation processes, requiring a hybrid data fusion approach.