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Many important geometric estimation problems take the form of synchronizationover the special Euclidean group: estimate the values of a set of poses given aset of relative measurements between them. This problem is typically formulatedas a nonconvex maximum-likelihood estimation that is computationally hard tosolve in general. Nevertheless, in this paper we present an algorithm that isable to efficiently recover certifiably globally optimal solutions of thespecial Euclidean synchronization problem in a non-adversarial noise regime.The crux of our approach is the development of a semidefinite relaxation of themaximum-likelihood estimation whose minimizer provides an exact MLE so long asthe magnitude of the noise corrupting the available measurements falls below acertain critical threshold; furthermore, whenever exactness obtains, it ispossible to verify this fact a posteriori, thereby certifying the optimality ofthe recovered estimate. We develop a specialized optimization scheme forsolving large-scale instances of this relaxation by exploiting its low-rank,geometric, and graph-theoretic structure to reduce it to an equivalentoptimization problem on a low-dimensional Riemannian manifold, and design atruncated-Newton trust-region method to solve this reduction efficiently.Finally, we combine this fast optimization approach with a simple roundingprocedure to produce our algorithm, SE-Sync. Experimental evaluation on avariety of simulated and real-world pose-graph SLAM datasets shows that SE-Syncis able to recover certifiably globally optimal solutions when the availablemeasurements are corrupted by noise up to an order of magnitude greater thanthat typically encountered in robotics and computer vision applications, anddoes so more than an order of magnitude faster than the Gauss-Newton-basedapproach that forms the basis of current state-of-the-art techniques.

SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group