Attitude-Aided Linear Calibration of Triaxial Accelerometers
Authors: Yongqiang Yu, Tian Huang, Yipeng Yang
Organizations: 1Independent researcher · 2Harbin Institute of Technology
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.
Attitude estimation based on inertial sensing requires measurements of local angular velocities and local gravity via gyroscopes and accelerometers. However, during the motion of a mobile system the inertial measurement unit (IMU) will be subject to additional accelerations which skews the measurement of local gravity. This effect gets amplified the further away the IMU is from the base of the system. Many attitude estimation filters, such as "Madgwick" or "Mahony", account for this by relying more on gyroscope integration for periods of high angular velocity. However, this approach is prone to accumulate long term error especially around the gravity vector. In this work we utilize the gyroscope measurements to compensate the additional accelerations induced by the motion of the system, i.e., centripetal- and tangential-accelerations. Additionally, we introduce a calibration method that estimates intrinsic IMU parameters such as axes misalignment, bias, scale, as well as the extrinsic base-to-IMU vector without the necessity for additional external equipment. Our evaluation in simulation as well as in the real-world shows that this method improves any attitude filter that relies on the direction of gravity. Furthermore we demonstrate the effectivenes on highly dynamic systems, and systems that are unable to put the IMU at the center of rotation, using our real-world spherical mobile mapping system.
ALS boresight calibration has relied for two decades on dedicated flight patterns over structured scenes containing planar surfaces of varied aspect and slope. While reliable, this approach imposes constraints on the scene content and operations, which limits its applicability to boresight recovery within routine mapping missions. We present a practical approach that substantially relaxes these requirements by replacing plane-based constraints with scene-agnostic point-to-point correspondences extracted automatically from overlapping ALS strips. Two complementary formulations are proposed to estimate boresight with laser vector observations: (i) a simpler parametric adjustment utilizing INS/GNSS trajectory; (ii) a rigorous formulation treating GNSS and raw inertial data within an existing factor-graph, i.e. a dynamic network, where boresight is added as an additional parameter. Both formulations are evaluated across four operational ALS flights equipped with five inertial systems, covering a wide range of flight altitudes, overlap geometries, terrain types and inertial sensor classes. The analysis draws a clear boundary between the legacy plane-based conditioning that falls short outside the calibration scenario and the proposed formulations, which either recover or absorb boresight effects under conventional mapping geometry. Among them, the lightweight formulation is sufficient for boresight recovery using tactical and navigation grade inertial sensors, while the general factor-graph approach is clearly superior when the inertial sensor errors are less observable within an optimal smoother. This supports the hypothesis that, for INS/GNSS trajectory of sufficient quality, the boresight calibration can be performed without particular scene prerequisites during routine mapping operations using a minimum of 3-4 overlapping strips, with either proposed formulation...
Accurate and robust attitude estimation is a key challenge for autonomous vehicles, particularly in GNSS-denied conditions and during highly accelerated flight. In such conditions, Inertial Measurement Units (IMUs) alone are insufficient for reliable tilt estimation due to the ambiguity between gravitational and inertial accelerations. Although auxiliary velocity sensors such as GNSS, Pitot tubes, Doppler radar, or Visual Inertial Odometry are commonly used, they may be unavailable, intermittent, or costly. This paper introduces a barometer-aided attitude estimation architecture that exploits barometric altitude measurements to provide complementary information on the vehicle's vertical motion, thereby enhancing attitude estimation within nonlinear observers on SO(3). The contributions are twofold. First, we design a deterministic Riccati observer cascaded with a complementary filter, ensuring almost-global asymptotic stability (AGAS) under a uniform observability (UO) condition while preserving the geometric structure of the attitude dynamics. Second, we propose a nonlinear observer evolving on SO(3)xR2, which integrates IMU measurements as inputs and barometer and magnetometer measurements as outputs within a unified framework, guaranteeing local exponential stability (LES) under relaxed uniform observability conditions. The proposed approaches are validated using both simulated and real flight data. The results demonstrate that barometer-aided estimation provides a lightweight, reliable, and effective complementary sensing modality for attitude estimation in minimal-sensing configurations, offering a practical alternative when conventional velocity measurements are unavailable or degraded.