Upper bounds for Rao distance on the manifold of multivariate elliptical distributions. (July 2021)

• Record Type: Journal Article
• Authors: Chen, Xiangbing; Zhou, Jie; Hu, Sanfeng
• Is Part Of: Automatica. Volume 129(2021)
• Publication Date: 2021-07
• Subjects: Multivariate elliptical distribution -- Fisher information matrix -- Rao distance -- Manhattan distance -- Upper bound; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109604
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: As a natural intrinsic measure on the manifold of probability distributions, Rao distance has received a lot of attentions and been applied successfully to many fields. However, the closed form of Rao distance on the manifold of multivariate elliptical distributions (MEDs) is still absent. In this paper, a class of Manhattan distances (MHDs) with single parameter on MED manifold is constructed by deducing explicit expressions of the geodesic and Rao distance on a specified submanifold of MED manifold. Then, three MHDs in such class, namely ordinary MHD, minimal MHD and quasi-minimal MHD, are provided as upper bounds of Rao distance on MED manifold by specifically, optimally and sub-optimally specifying parameter respectively. The second one can be efficiently computed numerically owing to its convexity with respect to the scalar parameter, and the third one has an explicit form. The performance of the proposed MHDs for approximating Rao distance is illustrated by examples. An application to distributed estimation fusion based on MHD for dynamic system with heavy-tailed process and observation noises is provided.