Cost-effective magnetic localization using permanent magnets

Abstract

This paper presents a novel approach to enhance the accuracy of 3D magnetic localization using a single magnetometer and permanent magnets (PMs). Our proposed solution is inexpensive and compact (with a significantly reduced size) compared to traditional methods that rely on multiple sensors. To accurately calculate the magnetic field generated by the PMs, and to address the potential errors due to magnetometer inaccuracies and misalignment with the PMs, we implement a two-step calibration process. This process corrects for magnetometer errors such as body frame misalignment, scale factors, non-orthogonality, biases, and soft and hard iron effects, as well as errors related to the magnetometer-PM system, including offsets in effective points, uncertainties in the magnetic dipole, and misalignment between the components. To further improve the signal-to-noise ratio (SNR) and localization accuracy, we utilized four PMs. We explore three different methods for modelling magnetic field of the PM: Magnetic Dipole (MD), Circular Current Loop (CCL), and Idealized Solenoid (IS). Our findings revealed that while each model provided distinct predictions, the overall results were consistent, suggesting that there are systematic errors in the mathematical models compared to the real-world magnetic field generated by the PMs. To address these errors, we introduce a symmetric matrix to effectively eliminate these errors and enhance the accuracy of each model. The proposed method offers a promising solution for improving the accuracy, stability, and reliability of magnetic localization systems. Our results demonstrate that the proposed method achieves a root mean square error (RMSE) in the region of 1-3 millimeters (an improvement of 78%), outperforming traditional methods at a fraction of the cost and complexity. • Introduces a novel, low-cost approach to 3D magnetic localization using a single magnetometer and permanent magnets. • Outperforms traditional methods in terms of accuracy and cost-effectiveness. • Implements a two-step calibration process to address various magnetometer inaccuracies and errors related to the magnetometer-PM interaction. • Ensures precise magnetic field calculations and improves localization accuracy. • Explores three different models for approximating the magnetic field generated by permanent magnets. • Identifies and addresses systematic errors in the mathematical models. • Achieves a root mean square error (RMSE) of 1-3 millimeters, significantly improving localization accuracy compared to traditional methods. • Offers a promising solution for applications requiring precise 3D localization. • Robotics • Autonomous vehicles • Indoor navigation systems • Other applications demanding accurate 3D localization.