A Direct Algorithm for Multi-Gyroscope Infield Calibration

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.