An algorithm to compute averages on matrix Lie groups

Authors:
Simone Fiori;Toshihisa Tanaka
Affiliations:
Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni, Università Politecnica delle Marche, Ancona, Italy;Department of Electrical and Electronic Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

Averaging is a common way to alleviate errors and random fluctuations in measurements and to smooth out data. Averaging also provides a way to merge structured data in a smooth manner. The present paper describes an algorithm to compute averages on matrix Lie groups. In particular, we discuss the case of averaging over the special orthogonal group of matrices, the unitary group of matrices and the group of symmetric positive-definite matrices.