This paper explores rotation estimation from the perspective of special unitary matrices. First, multiple solutions to Wahba's problem are derived through special unitary matrices, providing linear constraints on quaternion rotation parameters. Next, from these constraints, closed-form solutions to the problem are presented for minimal cases. Finally, motivated by these results, we investigate new representations for learning rotations in neural networks. Numerous experiments validate the proposed methods.

翻译：本文从特殊酉矩阵的视角探讨旋转估计问题。首先，通过特殊酉矩阵推导了Wahba问题的多重解，为四元数旋转参数提供了线性约束条件。其次，基于这些约束条件，针对最小配置情况给出了该问题的闭式解。最后，受这些结果的启发，我们研究了神经网络中学习旋转的新表示方法。大量实验验证了所提方法的有效性。