This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding quaternion parameters. We then explore applications of these constraints by formulating efficient methods for related problems. Finally, from this theoretical foundation, we propose two novel continuous representations for learning rotations in neural networks. Extensive experiments validate the effectiveness of the proposed methods.

翻译：本文从特殊酉矩阵的视角重新审视旋转估计问题。首先，我们利用$SU(2)$重新表述Wahba问题，推导出多个解，从而获得对应四元数参数的线性约束。随后，我们探索这些约束在相关问题中的应用，通过构建高效方法来实现。最后，基于这一理论基础，我们提出两种新的连续表示方法，用于神经网络中的旋转学习。大量实验验证了所提方法的有效性。