linear system.

We evaluate our algorithm with synthetic and real data. Extensive experimental results show that recovering the local minimal is essential, especially when the number of correspondences $N$ is small. For a small $N$, our algorithm significantly outperforms previous works [@olsson2006registration; @olsson2009branch; @briales2017convex; @wientapper2018universal]. Besides, experimental results verify that our algorithm can converge to the global minimizer with the same accuracy as the previous work with guaranteed globally optimality [@olsson2009branch; @briales2017convex], however, our algorithm is much faster.

Related Works
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This paper focuses on the pose estimation from point-to-point, point-to-line and point-to-plane correspondences correspondences. Pose estimation from point-to-point correspondences has been solved in early works [@arun1987least; @horn1987closed; @horn1988closed]. There exist closed-form solutions for this problem. However, estimating pose from point-to-line and point-to-plane correspondences is more complicated. These 3D correspondences actually yield similar distance function, which is employed by previous works to construct a general cost function [@olsson2006registration; @olsson2008solving; @olsson2009branch; @wientapper2016unifying; @briales2017convex; @wientapper2018universal]. The difference of various cost functions lies in the parameterization of the rotation matrix. The raw rotation matrix is adopted in [@olsson2008solving; @briales2017convex], and the quaternion [@horn1987closed] is used in [@olsson2006registration; @olsson2009branch; @wientapper2016unifying; @wientapper2018universal]. Previous works mainly focus on finding the global minimizer of the resulting cost 