To deal with such scenario while keeping a low computational complexity, we propose a prioritized progressive voting for translation in Algorithm \[voting\]. The main idea is that we progressively vote on the three dimensions, but there is a priority, i.e. number of votes, for early termination. The experimental results show that the computational complexity of prioritized progressive voting is almost similar to the dimension-wise voting. Otherwise, it is also possible to use 3D BnB translation search for better accuracy, but it is slower because of the coupled multi-dimensional solution space. Finally, we apply nonlinear refinement to achieve the best accuracy when the maximum consensus set is found.

Initialize best estimation $E^{*}=0$.\
$S_x = Voting(\{\hat{t}_{k,x}\}, \{\underline{t}_{k,x}\}, \{\overline{t}_{k,x}\})$.\
Sort $S_x$ in decreasing cardinality.\

Experimental Results
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In the experiments, we evaluate the proposed consensus maximization solver on (i) the feasibility and effectiveness of the subproblem solvers, (ii) the accuracy and robustness compared with existing methods, and (iii) the performance in real world visual inertial localization applications. We implement the proposed solver in MATLAB on a desktop with CPU Intel i7-7700 3.60GHz and 8G RAM.

Ablation study
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We build the synthetic world consisting of 3D points and lines in the cube $[-1,1]^3$. 