Computational Optimal Transport and Filtering on Riemannian Manifolds

被引：4

作者：

Grange, Daniel ^{[1
]}

Al-Jarrah, Mohammad ^{[2
]}

Baptista, Ricardo ^{[3
]}

Taghvaei, Amirhossein ^{[2
]}

Georgiou, Tryphon T. ^{[4
]}

Phillips, Sean ^{[5
]}

Tannenbaum, Allen ^{[1
]}

机构：

[1] SUNY Stony Brook, Dept Comp Sci, Bellmore, NY 11794 USA

[2] Univ Washington, Dept Aeronaut & Astronaut, Seattle, WA 98195 USA

[3] CALTECH, Dept Comp & Math Sci, Pasadena, CA 91125 USA

[4] Univ Calif Irvine, Dept Mech & Aerosp Engn, Irvine, CA 92697 USA

[5] Air Force Res Lab, Space Vehicles Directorate, Albuquerque, NM 87116 USA

来源：

IEEE CONTROL SYSTEMS LETTERS | 2023年 / 7卷

关键词：

Optimal transportation; optimal control; nonlinear filtering; Riemannian manifolds; OPTIMAL MASS-TRANSPORT; POLAR FACTORIZATION; ATTITUDE;

D O I：

10.1109/LCSYS.2023.3331834

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this letter we extend recent developments in computational optimal transport to the setting of Riemannian manifolds. In particular, we show how to learn optimal transport maps from samples that relate probability distributions defined on manifolds. Specializing these maps for sampling conditional probability distributions provides an ensemble approach for solving nonlinear filtering problems defined on such geometries. The proposed computational methodology is illustrated with examples of transport and nonlinear filtering on Lie groups, including the circle S1, the special Euclidean group SE(2), and the special orthogonal group SO(3).

引用

页码：3495 / 3500

页数：6

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