Distributed methods for synchronization of orthogonal matrices over graphs
This work addresses synchronization issues in distributed systems for applications such as 3D-localization and image registration, but it appears incremental as it builds on existing spectral relaxation methods.
The paper tackles the problem of synchronizing orthogonal matrices over directed graphs, which is crucial for applications like 3D-localization and image registration, by introducing two novel algorithms with guaranteed convergence under specific graph conditions and verifying them through numerical simulations.
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.