Distributed methods for synchronization of orthogonal matrices over graphs
  This paper addresses the problem of synchronizing orthogonal matrices over
directed graphs. For synchronized transformations (or matrices), composite
transformations over loops equal the identity. We formulate the synchronization
problem as a least-squares optimization problem with nonlinear constraints. The
synchronization problem appears as one of the key components in applications
ranging from 3D-localization to image registration. The main contributions of
this work can be summarized as the introduction of two novel algorithms; one
for symmetric graphs and one for graphs that are possibly asymmetric. Under
general conditions, the former has guaranteed convergence to the solution of a
spectral relaxation to the synchronization problem. The latter is stable for
small step sizes when the graph is quasi-strongly connected. The proposed
methods are verified in numerical simulations.
