Computational Foundation for Optimal Transport Ensemble Kalman Filter

Abstract

This thesis is concerned with novel filtering algorithms that are constructedbased on the recently introduced optimal transportation formulation of the Bayes’ formula. The problem involves solving a stochastic optimization problem to find the optimal map that transports the prior distribution to the posterior distribution at each time-step. An insightful case is obtained when the functions are restricted to be quadratic, leading to a variation of ensemble Kalman filter (EnKF), called optimal transport EnKF(OT-EnKF). The thesis includes development of computational algorithms for OT-EnKF and performing numerical experiments for evaluation and comparison with the original EnKF algorithm.