In this paper, we address the problem of estimating the rotational extrinsics, as well as the scale factors of two gyroscopes rigidly mounted on the same device. In particular, we formulate the problem as a least-squares minimization and introduce a direct algorithm that computes the estimated quantities without any iterations, hence avoiding local minima and improving efficiency. Furthermore, we show that the rotational extrinsics are observable while the scale factors can be determined up to global scale for general configurations of the gyroscopes. To this end, we also study special placements of the gyroscopes where a pair, or all, of their axes are parallel and analyze their impact on the scale factors' observability. Lastly, we evaluate our algorithm in simulations and real-world experiments to assess its performance as a function of key motion and sensor characteristics.

翻译：本文研究了同一设备上刚性安装的两个陀螺仪旋转外参及比例因子的估计问题。具体而言，我们将该问题表述为最小二乘最小化问题，并提出一种无需迭代即可直接计算估计量的算法，从而避免局部极小值并提升效率。此外，我们证明旋转外参是可观测的，而比例因子在一般陀螺仪配置下仅能确定至全局尺度。为此，我们进一步研究了陀螺仪特殊安装情况（如存在一对或全部轴平行时），并分析了其对比例因子可观测性的影响。最后，通过仿真与真实世界实验评估了算法性能随关键运动及传感器特性变化的规律。