Motion-Driven Automatic IMU Orientation Calibration via SO(3) Pattern Alignment

Calibration of body-worn inertial measurement units (IMUs) is essential for accurate motion estimation, yet sensor orientations may drift over time due to slippage or long-term integration errors. This causes an IMU to gradually lose alignment with the body segment on which it is mounted. In this paper, we develop a novel technique for Automatic Calibration-recovering this alignment during normal motion, without a dedicated calibration step. We implement automatic calibration by formulating it as the alignment of motion-induced orientation distributions on SO(3). When the activity being performed is known (e.g., walking), the distribution of orientations for a correctly calibrated IMU exhibits a characteristic and repeatable pattern on SO(3). Although sensor drift may rotate this distribution into a different orientation, the underlying pattern remains similar. Thus, we calibrate a drifted IMU by aligning its observed orientation distribution to a prior reference distribution obtained from the same activity, either from the same subject at an earlier time or from other subjects. To perform this alignment, we employ a correspondence-free spherical pattern matching method on SO(3) (SO3_SPMC), based on transformed basis vector distributions and spherical cross-correlation. We evaluate the proposed automatic calibration framework with N = 5 people wearing body-worn IMUs during activities of daily living, demonstrating calibration accuracy comparable to supervised single-frame calibration without requiring explicit calibration poses or user intervention. The activities of walking, typing, and using using a computer mouse were best for automatically calibrating a sensor on the wrist.