Full Magnetometer Calibration and Gyroscope Bias Estimation Using Angular Rates: A Factor Graph Approach

Concepts de base

This paper presents a novel factor graph-based method called MAGYC for calibrating magnetometers and estimating gyroscope biases in AHRS, leveraging angular rate measurements to improve accuracy and enable calibration in scenarios with limited angular motion.

Résumé

Bibliographic Information:

Rodríguez-Martínez, S., & Troni, G. (2024). Towards a Factor Graph-Based Method using Angular Rates for Full Magnetometer Calibration and Gyroscope Bias Estimation. arXiv preprint arXiv:2410.13827.

Research Objective:

This research paper aims to address the limitations of existing magnetometer and gyroscope calibration methods for AHRS, particularly in situations where extensive angular motion is infeasible. The authors propose a novel method using factor graphs and angular rate measurements to enable accurate calibration under constrained movements.

Methodology:

The authors develop a factor graph-based method called MAGYC (MAgnetometer and GYroscope Calibration) that leverages angular rate measurements from a gyroscope to estimate the full calibration parameters of a three-axis magnetometer (hard-iron and soft-iron biases) and the gyroscope bias. They formulate a nonlinear system model independent of the instrument's attitude and utilize unary factors to represent the residual errors and constraints within the factor graph. Two methods are proposed: MAGYC-BFG, a batch processing approach, and MAGYC-IFG, an incremental approach for real-time calibration. The performance of the proposed methods is evaluated through numerical simulations and in-field experiments using data collected from an underwater vehicle equipped with a MEMS IMU and a high-end INS for ground truth.

Key Findings:

• The proposed MAGYC methods, both in batch (MAGYC-BFG) and incremental (MAGYC-IFG) modes, consistently outperformed benchmark methods (TWOSTEP, Ellipsoid Fit, MagFactor3) in simulations and field experiments, particularly in scenarios with limited angular motion.
• MAGYC methods demonstrated robustness to constrained angular movements, successfully converging and providing accurate calibration even when benchmark methods failed.
• In field experiments, MAGYC methods significantly reduced heading error, highlighting their effectiveness in real-world applications.

Main Conclusions:

The MAGYC methods offer a robust and accurate solution for calibrating magnetometers and estimating gyroscope biases in AHRS, particularly in situations where extensive angular motion is impractical. The methods' ability to handle constrained movements makes them highly suitable for applications involving full-scale vehicles and platforms with limited maneuverability.

Significance:

This research contributes to the field of sensor calibration by introducing a novel factor graph-based approach that overcomes limitations of existing methods. The proposed MAGYC methods have the potential to improve the accuracy and reliability of attitude estimation in various applications, including robotics, navigation, and autonomous systems.

Limitations and Future Research:

While the proposed methods demonstrate significant improvements, future research could explore incorporating additional sensor measurements or exploring the integration of MAGYC within SLAM frameworks for enhanced performance and broader applicability.

Stats

The underwater vehicle's heading error standard deviation was reduced from 6.21° to 0.57° for a standard seafloor mapping survey.
The simulated magnetometer measurements had noise with a standard deviation of 1 mG.
The simulated angular rate sensor measurements had noise with a standard deviation of 5 mrad/s.
The local magnetic field had a magnitude of 479 mG during the field experiments.
The Kearfott SeaDeViL INS used as ground truth provides a precision of 0.05° and 0.03° in heading and pitch/roll, respectively.
The Vectornav VN100 MEMS-based IMU used in the experiments has a magnetometer noise level of 1 mG and an angular-rate gyroscope noise level of 0.5 mrad/s.

Citations

Idées clés tirées de

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

by Seba... à arxiv.org 10-18-2024

https://arxiv.org/pdf/2410.13827.pdf

Questions plus approfondies

How can the MAGYC methods be adapted for use with other types of sensors or in different application domains beyond AHRS calibration?

The MAGYC methods, while specifically designed for AHRS calibration, present a versatile framework adaptable to other sensor types and applications. The core principle lies in leveraging known relationships between sensor measurements to estimate biases and calibration parameters. Here's how it can be extended:
1. Different Sensor Combinations:

Accelerometer Calibration: Instead of magnetometer readings, gravity can act as the reference vector. By maneuvering the system through rotations and measuring the accelerometer output, similar factor graph formulations can be derived to estimate accelerometer biases and scale factors.
Camera-IMU Calibration: The known geometric constraints between a camera and an IMU during motion can be exploited. By tracking visual features and fusing the information with IMU data in a factor graph, extrinsic calibration parameters (relative pose) and temporal synchronization can be estimated.
Multi-Robot Calibration: In multi-robot systems, relative measurements between robots (e.g., distances, bearings) can be combined with individual odometry in a factor graph. This allows for the estimation of inter-robot calibration parameters, improving collaborative localization and mapping.
2. Beyond Calibration:

Geomagnetic Navigation: In environments with known magnetic field variations, the MAGYC framework can be extended to estimate the system's position by treating the magnetic field as a spatially varying signal. This is akin to terrain-based navigation but using magnetic features.
Sensor Fault Detection: Deviations from the expected sensor behavior, as modeled in the factor graph, can indicate sensor faults. By monitoring residuals and uncertainties during operation, the MAGYC framework can be used for online fault detection and isolation.
Key Considerations for Adaptation:

Sensor Model: A precise mathematical model capturing the sensor's behavior and its relationship with other measurements is crucial.
Reference Signal: A known or partially known signal (like Earth's magnetic field in MAGYC) is needed to establish constraints within the factor graph.
Motion Excitation: Sufficient motion that excites the system dynamics is essential for accurate parameter estimation.

Could the reliance on a constant magnetic field assumption pose limitations in environments with dynamic magnetic disturbances, and how might the method be adapted to address such scenarios?

You are absolutely correct. The assumption of a constant magnetic field in the MAGYC methods poses a significant limitation in environments with dynamic magnetic disturbances. These disturbances can arise from various sources, including:

Ferromagnetic Materials: Moving metallic objects or structures containing iron, nickel, or cobalt can significantly alter the local magnetic field.
Electric Currents: Power lines, electric motors, and other current-carrying conductors generate magnetic fields that can interfere with measurements.
Temporal Variations: The Earth's magnetic field itself experiences natural temporal variations, although these are usually slow and small in magnitude.
Adaptation Strategies:

Dynamic Magnetic Field Modeling:

Spatial Mapping: If the magnetic disturbances are spatially localized, a map of the magnetic field variations can be created beforehand. This map can then be incorporated into the factor graph to compensate for the disturbances during calibration and operation.
Temporal Filtering: For time-varying disturbances, adaptive filtering techniques like Kalman filtering or particle filtering can be employed. These filters can estimate and track the magnetic field changes online, allowing for more accurate magnetometer measurements.

Sensor Fusion and Redundancy:

Integration with Other Sensors: Combining magnetometer data with other sensors less susceptible to magnetic interference, such as gyroscopes, accelerometers, or even GPS when available, can improve robustness. Sensor fusion techniques like Kalman filtering can effectively integrate these measurements.
Redundant Magnetometers: Using multiple magnetometers spatially separated on the vehicle can help distinguish between the Earth's magnetic field and local disturbances. Differential magnetometry techniques can then be applied to cancel out common-mode noise.

Robust Estimation Techniques:

Outlier Rejection: Robust estimation methods, such as RANSAC (Random Sample Consensus), can be incorporated into the factor graph optimization to identify and reject outlier measurements caused by magnetic disturbances.
Adaptive Noise Models: Instead of assuming constant measurement noise, adaptive noise models can be used to account for the increased uncertainty in magnetometer readings due to disturbances.

What are the potential implications of integrating the MAGYC methods with other estimation algorithms, such as Kalman filters or particle filters, for improved state estimation in robotic systems?

Integrating MAGYC methods with other estimation algorithms like Kalman filters (KF) or particle filters (PF) holds significant potential for enhancing state estimation in robotic systems. Here's a breakdown of the implications:
1. Improved Accuracy and Robustness:

Online Bias Estimation: KF and PF can incorporate the MAGYC framework to estimate sensor biases in real-time. This dynamic bias correction leads to more accurate state estimates, especially in the long term, as biases can drift over time.
Handling Non-Gaussian Noise: While MAGYC typically assumes Gaussian noise, PF can handle non-Gaussian noise distributions, which are common in real-world scenarios. This makes the estimation more robust to outliers and non-linearities.
Improved Data Fusion: KF and PF provide a principled framework for fusing data from multiple sensors, including those calibrated using MAGYC. This leads to more accurate and reliable state estimates by leveraging complementary information from different sources.
2. Enhanced Capabilities:

Simultaneous Localization and Mapping (SLAM): Integrating MAGYC within a KF or PF-based SLAM algorithm can improve the accuracy of both the robot's pose and the map. Accurate sensor calibration is crucial for consistent map building and precise localization.
Adaptive Control: Accurate state estimation is essential for robust control in robots. By integrating MAGYC, the control system can benefit from improved sensor measurements, leading to better trajectory following, stability, and overall performance.
Fault-Tolerant Navigation: By monitoring the residuals and uncertainties in the KF or PF framework, deviations from the expected sensor behavior can be detected. This enables fault detection and isolation, potentially allowing the system to switch to alternative sensors or implement fail-safe maneuvers.
Implementation Considerations:

Computational Complexity: Integrating MAGYC with KF or PF can increase computational demands. Efficient implementations and approximations might be necessary, especially for real-time applications.
Tuning and Parameter Selection: Proper tuning of the filter parameters and noise models is crucial for optimal performance. This might require extensive experimentation and validation.
In conclusion, integrating MAGYC methods with KF or PF offers a powerful approach for improving state estimation in robotic systems. This integration can lead to more accurate, robust, and reliable navigation, control, and perception capabilities, pushing the boundaries of what's achievable in robotics.