Estimating a Rotation Matrix R by using Higher-Order Matrices RN with Application to Supervised Pose Estimation

T. Tamaki, B. Raytchev, K. Kaneda, and T. Amano (Japan)


Rotation matrix, pose estimation, EDM, polar decomposition, higher-order rotation matrices


In this paper, we show that a more accurate estimation of a 3 × 3 rotation matrix R can be achieved by appropriately decomposing higher-order rotation matrices: R2, R3, and so on. First we discuss an angle estimation of a 2 × 2 rotation matrix inspired by the Electronic Distance Measurement. Then we reformulate the problem for a 3 × 3 rotation matrix: if noise-contaminated measurement matrices R, R2 , . . . , Rn are given, find an appropriate rotation matrix R. In the proposed method, the given measurement matrices are first transformed to rotation matrices by using the polar decomposition. Then the rotation angles are obtained by using an eigen decomposition of the rotation matrices. Finally, the ambiguity of the obtained rotation angle is removed. Experimental results show that the use of Rn results in more accurate estimates than when R itself is used.

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