Attitude-Aided Linear Calibration of Triaxial Accelerometers

Abstract: Triaxial MEMS accelerometers are widely used for inertial sensing, navigation, and sensor fusion, but existing calibration methods often rely on costly reference setups or nonlinear iterative optimization, limiting their efficiency and applicability to low-cost or self-calibrating systems. We present attitude-aided linear accelerometer calibration (ALAC), a method that operates on any platform providing orientation information, such as turntables, robotic arms, or inertial measurement units. ALAC constructs a combined error matrix (CEM) to represent sensor errors in a unified calibration model and enables linear least-squares estimation. The bias and gravity vector are jointly estimated, implicitly accounting for platform misalignment, and matrix decomposition of the CEM recovers scale, non-orthogonality, and alignment rotation parameters. Under static gravity, calibration is formulated as a constrained homogeneous least-squares (CHLS) problem and solved in closed form using standard linear algebra. Only five arbitrarily oriented measurements are required, and a recursive extension supports online or in-field calibration. Experiments on a stationary robot-mounted accelerometer and a quasi-static public IMU trajectory show that ALAC, in both offline and online modes, outperforms reference-based and online baselines in accuracy and robustness to sensor noise. On the same dataset, it matches iterative self-calibration under filtered conditions and surpasses all evaluated baselines on raw measurements. These results demonstrate a robust and practical calibration scheme for MEMS-based inertial platforms, especially low-cost IMUs and online calibration scenarios.