synchronization of matrices; graph theory; spectral methods
Abstract :
[en] This paper addresses synchronization of invertible matrices over graphs. The matrices represent pairwise transformations between n euclidean coordinate systems. Synchronization means that composite transformations over loops are equal to the identity. Given a set of measured matrices that are not synchronized, the synchronization problem amounts to fining new synchronized matrices close to the former. Under the assumption that the measurement noise is zero mean Gaussian with known covariance, we introduce an iterative method based on linear subspace projection. The method is free of step size determination and tuning and numerical simulations show significant improvement of the solution compared to a recently proposed direct method as well as the Gauss-Newton method.
Disciplines :
Mathematics
Author, co-author :
THUNBERG, Johan ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
COLOMBO, Nicolo ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
YUE, Zuogong ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Life Science Research Unit
GONCALVES, Jorge ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
External co-authors :
yes
Language :
English
Title :
An Iterative Projection method for Synchronization of Invertible Matrices Over Graphs
Publication date :
2016
Event name :
22nd International Symposium on Mathematical Theory of Networks and Systems
Event date :
July 12-15
Audience :
International
Main work title :
22nd International Symposium on Mathematical Theory of Networks and Systems
Peer reviewed :
Peer reviewed
FnR Project :
FNR8864515 - Set Convergence In Nonlinear Multi-agent Systems, 2014 (01/02/2015-31/01/2017) - Johan Thunberg
