  This paper presents the first certifiably correct algorithm for distributed
pose-graph optimization (PGO), the backbone of modern collaborative
simultaneous localization and mapping (CSLAM) and camera network localization
(CNL) systems. Our method is based upon a sparse semidefinite relaxation that
we prove provides globally-optimal PGO solutions under moderate measurement
noise (matching the guarantees enjoyed by state-of-the-art centralized
methods), but is amenable to distributed optimization using the low-rank
Riemannian Staircase framework. To implement the Riemannian Staircase in the
distributed setting, we develop Riemannian block coordinate descent (RBCD), a
novel method for (locally) minimizing a function over a product of Riemannian
manifolds. We also propose the first distributed solution verification and
saddle escape methods to certify the global optimality of critical points
recovered via RBCD, and to descend from suboptimal critical points (if
necessary). All components of our approach are inherently decentralized: they
require only local communication, provide privacy protection, and are easily
parallelizable. Extensive evaluations on synthetic and real-world datasets
demonstrate that the proposed method correctly recovers globally optimal
solutions under moderate noise, and outperforms alternative distributed
techniques in terms of solution precision and convergence speed.
