Joint Magnetometer-IMU Calibration via Maximum A Posteriori Estimation

TL;DR

The paper addresses the challenge of jointly calibrating magnetometers and IMUs under in-situ conditions by formulating calibration as a maximum a posteriori estimation problem. It introduces a joint MAP framework that estimates both calibration parameters and the orientation trajectory, employing optimization on manifolds with closed-form derivatives for efficiency. The work compares the proposed approach to two prior methods, demonstrates superior calibration accuracy in simulations, and validates practical benefits with real-world data, including significant reductions in position drift for magnetic field-aided navigation. The method is computationally efficient and scalable, and the authors provide public datasets and code to support reproducibility and further research.

Abstract

This paper presents a new approach for jointly calibrating magnetometers and inertial measurement units, focusing on improving calibration accuracy and computational efficiency. The proposed method formulates the calibration problem as a maximum a posteriori estimation problem, treating both the calibration parameters and orientation trajectory of the sensors as unknowns. This formulation enables efficient optimization with closed-form derivatives. The method is compared against two state-of-the-art approaches in terms of computational complexity and estimation accuracy. Simulation results demonstrate that the proposed method achieves lower root mean square error in calibration parameters while maintaining competitive computational efficiency. Further validation through real-world experiments confirms the practical benefits of our approach: it effectively reduces position drift in a magnetic field-aided inertial navigation system by more than a factor of two on most datasets. Moreover, the proposed method calibrated 30 magnetometers in less than 2 minutes. The contributions include a new calibration method, an analysis of existing methods, and a comprehensive empirical evaluation. Datasets and algorithms are made publicly available to promote reproducible research.

Figures (6)

• Figure 1: The reference (big axes sets) and sensors' coordinate frames (small axes sets). The Z-axis in the reference frame is aligned with the local gravity vector, $\text{g}$, the Y--Z plane is parallel to the local magnetic field, $m(\alpha)$, with its horizontal component pointing in the positive Y-axis direction. The dip angle of the magnetic field $\alpha$ is the angle between the magnetic field and the horizontal plane. The misalignment of the magnetometer frame (m-frame) with the inertial sensor frame (IMU-frame) is represented by the rotation matrix $R_D$.
• Figure 2: The reference (big axes sets) and magnetometer's coordinate frames (small axes sets) used in the intrinsic calibration. The Z-axis in the reference frame is aligned with the local magnetic field, $m$. The orientation of the m-frame can be parameterized with only roll ($\phi$) and pitch ($\gamma$) angles, since the yaw ($\psi$) angle represents a rotation around the magnetic field direction (in green), which does not change the relative inclination of the sensor to the field.
• Figure 3: Comparison of the computation time and RMSE of the estimated calibration parameters on datasets with different sampling frequencies.
• Figure 4: Comparison of the computation time and RMSE of the estimated calibration parameters on datasets with different sampling rate ratios. The horizontal axis is the ratio of the IMU sampling rate to the magnetometer sampling rate.
• Figure 5: The sensor board used in the experiment. It has 30 PNI https://www.pnicorp.com/rm3100/ magnetometers and an Osmium MIMU 4844 IMU mounted on the bottom side.