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
Friday, March 3, 2023 9:30 PM - 10:00 PM
Venue
Online
Abstract
In this report, we present a unified framework for particle data fusion based on optimal transportation. The sequence data fusion can be considered as three different types, prediction problems, filtering problem and smoothing problem. We summarise the different particle methods as the paths on the Wasserstein space. However, there are infinite-many flow models corresponding to the same path. Firstly, we design the tangent flow by using the optimal transportation so that this flow model is unique, deterministic and optimal in the sense of Wasserstein space. The tangent flow of PDE can be used to solve the prediction/sampling problem. The tangent flow of SPDE can be used to solve the filtering problem. Finally, we extend the filtering algorithm as smoothing algorithm by using the forward-backward duality of Mayne–Fraser two-filter formula.