  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.
