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Map based visual inertial localization is a crucial step to reduce the driftin state estimation of mobile robots. The underlying problem for localizationis to estimate the pose from a set of 3D-2D feature correspondences, of whichthe main challenge is the presence of outliers, especially in changingenvironment. In this paper, we propose a robust solution based on efficientglobal optimization of the consensus maximization problem, which is insensitiveto high percentage of outliers. We first introduce translation invariantmeasurements (TIMs) for both points and lines to decouple the consensusmaximization problem into rotation and translation subproblems, allowing for atwo-stage solver with reduced solution dimensions. Then we show that (i) therotation can be calculated by minimizing TIMs using only 1-dimensionalbranch-and-bound (BnB), (ii) the translation can be found by running1-dimensional search for three times with prioritized progressive voting.Compared with the popular randomized solver, our solver achieves deterministicglobal convergence without depending on an initial value. While compared withexisting BnB based methods, ours is exponentially faster. Finally, byevaluating the performance on both simulation and real-world datasets, ourapproach gives accurate pose even when there are 90\% outliers (only 2inliers).

Globally optimal consensus maximization for robust visual inertial localization in point and line map