Estimation of the Linear System via Optimal Transportation and Its Application for Missing Data Observations

Abstract

In this article, an optimal transportation particle method has been proposed to deal with the data fusion problem. The proposed method can handle prediction, filtering, and smoothing problems uniformly more robustly and stably than traditional algorithms. Our main idea is to approximate the trajectory in Wasserstein space, which is the set of probability distributions equipped with the Wasserstein metric. Recent literature has demonstrated the successful application of optimal transportation for prediction and filtering problems. In this article, we derive an optimal transportation particle for solving the smoothing problem utilizing Mayne–Fraser's formula (Mayne, 1966; Fraser and Potter, 1969). Detailed convergence results are presented, and the proposed algorithms are tested on missing observation processes, showcasing their ability to solve hybrid data fusion problems. This work introduces a new approach to particle methods, which expands their possibilities in data fusion applications.