Codes and Expansions (CodEx) Seminar

Ido Hadi (Tel Aviv University)
SE(d) synchronization via spectral decomposition on Clifford algebras

The goal in synchronization problems is to estimate elements of a group from noisy measurements of their ratios. It is possible to extract the group elements from eigenvectors of a block matrix formed from the measurements. As not every basis of the relevant eigenspace is a valid synchronization solution, the eigenvectors must be projected, or “rounded”, onto the group. In this talk, we will demonstrate the benefits of realizing this approach on the algebra of dual quaternions for synchronization problems over \(SE(3)\), the group of rigid motions of \(R^3\), a non-compact group. Our approach significantly reduces the eigenspace-synchronization gap and yields superior computational performance. We'll explain and demonstrate numerically how this approach can be generalized to \(SE(d)\) synchronization by embedding these groups in Clifford algebras.