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Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm

This paper presents a calibration method for low-cost 3-axis magnetometers using the least square ellipsoid fitting algorithm. The aim of the calibration process is to reduce noise and mitigate the effects of magnetic interferences and instrumentation errors, thereby enhancing the accuracy and reliability of magnetometer measurements. By collecting data while moving the sensor in arbitrary directions, the calibration parameters are estimated, including magnetic disturbances (soft iron and hard iron effects) and instrumental errors (scale factor, nonorthogonality, and bias). The measured data are modeled as a combination of these errors, and the calibration parameters are obtained by solving a quadratic form equation using the least square ellipsoid fitting algorithm. The results demonstrate that the proposed calibration method using the least square ellipsoid fitting algorithm provides a valuable contribution to the field of magnetometer calibration, with the calibrated data exhibiting a better fit to the surface of an ellipsoid compared to the original magnetometer data, indicating its effectiveness, achieving 90% accuracy in magnetometer calibration of module MPU-9250. The proposed calibration method offers several advantages, including its simplicity and cost-effectiveness. Furthermore, the real-time capability of the algorithm makes it suitable for applications that require continuous calibration, ensuring accurate and reliable measurements over time. The integration of the calibration method into the intelligent IMU Sensor (IIS) further enhances its practicality and applicability in real-world scenarios.

Magnetometer Calibration, Magnetic Interferences, Instrumentation Errors, Ellipsoid Fitting

Ali Shakerian, Saoussen Bilel, René Jr. Landry. (2023). Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm. International Journal of Sensors and Sensor Networks, 11(1), 18-24.

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. J. Andel, V. Šimák, A. Kanálikova, and R. Pirník, “GNSS Based Low-Cost Magnetometer Calibration,” Sensors, vol. 22, no. 21, p. 8447, Nov. 2022, doi: 10.3390/s22218447.
2. G. Cao, X. Xu, and D. Xu, “Real-Time Calibration of Magnetometers Using the RLS/ML Algorithm,” Sensors, vol. 20, no. 2, p. 535, Jan. 2020, doi: 10.3390/s20020535.
3. X. Hu et al., “Automatic calculation of the magnetometer zero offset using the interplanetary magnetic field based on the Wang-Pan method,” Earth Planet. Phys., vol. 6, no. 1, pp. 56–60, 2022, doi: 10.26464/epp2022017.
4. S. Li, D. Cheng, Y. Wang, and J. Zhao, “Calibration of strapdown magnetic vector measurement systems based on a plane compression method,” Meas. Sci. Technol., vol. 34, no. 5, p. 055115, May 2023, doi: 10.1088/1361-6501/acbab0.
5. X. Ru, N. Gu, H. Shang, and H. Zhang, “MEMS Inertial Sensor Calibration Technology: Current Status and Future Trends,” Micromachines, vol. 13, no. 6, p. 879, May 2022, doi: 10.3390/mi13060879.
6. V. Renaudin, M. H. Afzal, and G. Lachapelle, “Complete Triaxis Magnetometer Calibration in the Magnetic Domain,” J. Sens., vol. 2010, pp. 1–10, 2010, doi: 10.1155/2010/967245.
7. K. Styp-Rekowski, I. Michaelis, C. Stolle, J. Baerenzung, M. Korte, and O. Kao, “Machine learning-based calibration of the GOCE satellite platform magnetometers,” Earth Planets Space, vol. 74, no. 1, p. 138, Sep. 2022, doi: 10.1186/s40623-022-01695-2.
8. A. Abosekeen, A. Noureldin, T. Karamat, and M. J. Korenberg, “Comparative Analysis of Magnetic-Based RISS using Different MEMS-Based Sensors,” presented at the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, Nov. 2017, pp. 2944–2959. doi: 10.33012/2017.15120.
9. C. M. N. Brigante, N. Abbate, A. Basile, A. C. Faulisi, and S. Sessa, “Towards Miniaturization of a MEMS-Based Wearable Motion Capture System,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3234–3241, Aug. 2011, doi: 10.1109/TIE.2011.2148671.
10. J. Coulin, R. Guillemard, V. Gay-Bellile, C. Joly, and A. De La Fortelle, “Online Magnetometer Calibration in Indoor Environments for Magnetic field-based SLAM,” in 2022 IEEE 12th International Conference on Indoor Positioning and Indoor Navigation (IPIN), Beijing, China: IEEE, Sep. 2022, pp. 1–8. doi: 10.1109/IPIN54987.2022.9917514.
11. X. Chen, X. Zhang, M. Zhu, C. Lv, Y. Xu, and H. Guo, “A Novel Calibration Method for Tri-axial Magnetometers Based on an Expanded Error Model and a Two-step Total Least Square Algorithm,” Mob. Netw. Appl., vol. 27, no. 2, pp. 794–805, Apr. 2022, doi: 10.1007/s11036-021-01898-z.
12. M. A. Ouni and R. Landry, “Partide swarm optimization algorithm in calibration of MEMS-based low-cost magnetometer,” in 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS), Savannah, GA: IEEE, Apr. 2016, pp. 27–33. doi: 10.1109/PLANS.2016.7479679.
13. T. Pylvänäinen, “Automatic and adaptive calibration of 3D field sensors,” Appl. Math. Model., vol. 32, no. 4, pp. 575–587, Apr. 2008, doi: 10.1016/j.apm.2007.02.004.
14. R. Yan, F. Zhang, and H. Chen, “A MEMS-based Magnetometer Calibration Approach in AUV Navigation System,” in OCEANS 2019 - Marseille, Marseille, France: IEEE, Jun. 2019, pp. 1–6. doi: 10.1109/OCEANSE.2019.8867368.
15. A. Wahdan, J. Georgy, W. F. Abdelfatah, and A. Noureldin, “Magnetometer Calibration for Portable Navigation Devices in Vehicles Using a Fast and Autonomous Technique,” IEEE Trans. Intell. Transp. Syst., vol. 15, no. 5, pp. 2347–2352, Oct. 2014, doi: 10.1109/TITS.2014.2313764.
16. Teslabs Engineering, “A way to calibrate a magnetometer.”