Technical Report: Pose Graph Optimization over Planar Unit Dual Quaternions: Improved Accuracy with Provably Convergent Riemannian Optimization

It is common in pose graph optimization (PGO) algorithms to assume that noise in the translations and rotations of relative pose measurements is uncorrelated. However, existing work shows that in practice these measurements can be highly correlated, which leads to degradation in the accuracy of PGO solutions that rely on this assumption. Therefore, in this paper we develop a novel algorithm derived from a realistic, correlated model of relative pose uncertainty, and we quantify the resulting improvement in the accuracy of the solutions we obtain relative to state-of-the-art PGO algorithms. Our approach utilizes Riemannian optimization on the planar unit dual quaternion (PUDQ) manifold, and we prove that it converges to first-order stationary points of a Lie-theoretic maximum likelihood objective. Then we show experimentally that, compared to state-of-the-art PGO algorithms, this algorithm produces estimation errors that are lower by 10% to 25% across several orders of magnitude of noise levels and graph sizes.