Towards a Factor Graph-Based Method using Angular Rates for Full Magnetometer Calibration and Gyroscope Bias Estimation

TL;DR

The paper tackles magnetometer–gyroscope calibration for MEMS-based AHRS under limited motion and GPS-denied settings. It proposes MAGYC, a factor-graph–based framework that uses three-axis angular-rate data to jointly estimate soft-iron and hard-iron magnetometer effects and gyroscope bias without relying on knowledge of the local magnetic field or attitude, with batch (MAGYC-BFG) and online (MAGYC-IFG) variants. The key contributions include a single-state-node factor-graph formulation, unary residuals from a nonlinear model, a unit-norm constraint on the soft-iron parameters, an averaging window to manage complexity, and the use of the RISE optimizer for robust online sparse nonlinear least-squares estimation. Across numerical simulations and field experiments (underwater vehicle), MAGYC significantly improves heading accuracy, outperforming TWOSTEP, Ellipsoid Fit, and MagFactor3, especially in constrained-motion scenarios, thereby enabling accurate, real-time calibration for low-cost MEMS AHRS with strong practical impact for underwater, aerial, and ground navigation.

Abstract

MEMS Attitude Heading Reference Systems are widely employed to determine a system's attitude, but sensor measurement biases limit their accuracy. This paper introduces a novel factor graph-based method called MAgnetometer and GYroscope Calibration (MAGYC). MAGYC leverages three-axis angular rate measurements from an angular rate gyroscope to enhance calibration for batch and online applications. Our approach imposes less restrictive conditions for instrument movements required for calibration, eliminates the need for knowledge of the local magnetic field or instrument attitude, and facilitates integration into factor graph algorithms within Smoothing and Mapping frameworks. We evaluate the proposed methods through numerical simulations and in-field experimental assessments using a sensor installed on an underwater vehicle. Ultimately, our proposed methods reduced the underwater vehicle's heading error standard deviation from 6.21 to 0.57 degrees for a standard seafloor mapping survey.

Figures (4)

• Figure 1: Diagram illustrating an underwater vehicle's dead reckoning position using different magnetic field sources for the heading estimation with the corresponding trajectories represented with dashed lines.
• Figure 2: Simulated magnetometer data for three datasets: (a) WAM, (b) MAM, and (c) LAM. The 3D plots show blue dots for magnetometer data, gray spheres for the true magnetic field, and orange ellipsoids for the distorted magnetic field.
• Figure 3: Evaluation results: (a) Performance comparison of five calibration methods on three simulated datasets. The hard-iron error $|m_b - m_b^*|$, soft-iron error $|A - A^*|$, and gyroscope bias error $|w_b - w_b^*|$ are analyzed for the WAM (green), MAM (yellow), and LAM (orange) datasets. Red dashed lines indicate instances where the method failed to estimate the parameters for a particular dataset, and gray-shaded zones, show the raw data value. (b) Heading error on field data for calibration parameters estimated with EXP1 and evaluated with EXP2.
• Figure 4: In-field magnetic data for two datasets: (a) EXP1 and (b) EXP2. The 3D plots show blue dots for magnetometer data and gray spheres for true magnetic field.