Multiscale and Uncertainty-Aware Targetless Hand-Eye Calibration via the Gauss–Helmert Model

The operational reliability of an autonomous robot depends crucially on extrinsic sensor calibration as a prerequisite for precise and accurate data fusion. Exploring the calibration of unscaled sensors (e.g., monocular cameras) and the effective utilization of uncertainties are difficult and often overlooked. The development of a solution for the simultaneous calibration of hand-eye sensors and scale estimation based on the Gauss–Helmert model aims to utilize the valuable information contained in the uncertainty of odometry. In this work, we propose a versatile and robust solution for batch calibration based on the analytical on-manifold approach for estimation. The versatility of our method is demonstrated by its ability to calibrate multiple unscaled and metric-scaled sensors while dealing with odometry failures and reinitializations. Importantly, all estimated parameters are provided with their corresponding uncertainties. The validation of our method and its comparison with five competing state-of-the-art calibration methods in both simulations and real-world experiments show its superior accuracy, with particularly promising results observed in high-noise scenarios.