The miniaturization of inertial measurement units (IMUs) facilitates their widespread use in a growing number of application domains. Orientation estimation is a prerequisite for most further data processing steps in inertial motion tracking, such as position/velocity estimation, joint angle estimation, and 3D visualization. Errors in the estimated orientations severely affect all further processing steps. Recent systematic comparisons of existing algorithms show that out-of-the-box accuracy is often low and that application-specific tuning is required to obtain high accuracy. In the present work, we propose and extensively evaluate a quaternion-based orientation estimation algorithm that is based on a novel approach of filtering the acceleration measurements in an almost-inertial frame and that includes extensions for gyroscope bias estimation and magnetic disturbance rejection, as well as a variant for offline data processing. In contrast to all existing work, we perform an extensive evaluation, using a large collection of publicly available datasets and eight literature methods for comparison. The proposed method consistently outperforms all literature methods and achieves an average RMSE of 2.9°, while the errors obtained with literature methods range from 5.3° to 16.7°. Since the evaluation was performed with one single fixed parametrization across a very diverse dataset collection, we conclude that the proposed method provides unprecedented out-of-the-box performance for a broad range of motions, sensor hardware, and environmental conditions. This gain in orientation estimation accuracy is expected to advance the field of IMU-based motion analysis and provide performance benefits in numerous applications. The provided open-source implementation makes it easy to employ the proposed method.