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

Ali Shakerian; Saoussen Bilel; René Jr. Landry

doi:doi:10.11648/j.ijssn.20231101.13

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

Ali Shakerian, Saoussen Bilel, René Jr. Landry

Published in International Journal of Sensors and Sensor Networks (Volume 11, Issue 1)

Received: 6 July 2023 Accepted: 20 July 2023 Published: 9 August 2023

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Abstract

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.

Published in	International Journal of Sensors and Sensor Networks (Volume 11, Issue 1)
DOI	10.11648/j.ijssn.20231101.13
Page(s)	18-24
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Magnetometer Calibration, Magnetic Interferences, Instrumentation Errors, Ellipsoid Fitting

References

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[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.
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[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.
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[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.
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APA Style

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. https://doi.org/10.11648/j.ijssn.20231101.13

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ACS Style

Ali Shakerian; Saoussen Bilel; René Jr. Landry. Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm. Int. J. Sens. Sens. Netw. 2023, 11(1), 18-24. doi: 10.11648/j.ijssn.20231101.13

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AMA Style

Ali Shakerian, Saoussen Bilel, René Jr. Landry. Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm. Int J Sens Sens Netw. 2023;11(1):18-24. doi: 10.11648/j.ijssn.20231101.13

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@article{10.11648/j.ijssn.20231101.13,
  author = {Ali Shakerian and Saoussen Bilel and René Jr. Landry},
  title = {Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm},
  journal = {International Journal of Sensors and Sensor Networks},
  volume = {11},
  number = {1},
  pages = {18-24},
  doi = {10.11648/j.ijssn.20231101.13},
  url = {https://doi.org/10.11648/j.ijssn.20231101.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssn.20231101.13},
  abstract = {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.},
 year = {2023}
}

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TY  - JOUR
T1  - Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm
AU  - Ali Shakerian
AU  - Saoussen Bilel
AU  - René Jr. Landry
Y1  - 2023/08/09
PY  - 2023
N1  - https://doi.org/10.11648/j.ijssn.20231101.13
DO  - 10.11648/j.ijssn.20231101.13
T2  - International Journal of Sensors and Sensor Networks
JF  - International Journal of Sensors and Sensor Networks
JO  - International Journal of Sensors and Sensor Networks
SP  - 18
EP  - 24
PB  - Science Publishing Group
SN  - 2329-1788
UR  - https://doi.org/10.11648/j.ijssn.20231101.13
AB  - 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.
VL  - 11
IS  - 1
ER  -

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Author Information

Ali Shakerian

Department of Electrical Engineering, LASSENA Laboratory, Ecole de Technologie Superieure, Montreal, Canada
Saoussen Bilel

Department of Electrical Engineering, LASSENA Laboratory, Ecole de Technologie Superieure, Montreal, Canada
René Jr. Landry

Department of Electrical Engineering, LASSENA Laboratory, Ecole de Technologie Superieure, Montreal, Canada

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APA Style

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. https://doi.org/10.11648/j.ijssn.20231101.13

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ACS Style

Ali Shakerian; Saoussen Bilel; René Jr. Landry. Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm. Int. J. Sens. Sens. Netw. 2023, 11(1), 18-24. doi: 10.11648/j.ijssn.20231101.13

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AMA Style

Ali Shakerian, Saoussen Bilel, René Jr. Landry. Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm. Int J Sens Sens Netw. 2023;11(1):18-24. doi: 10.11648/j.ijssn.20231101.13

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@article{10.11648/j.ijssn.20231101.13,
  author = {Ali Shakerian and Saoussen Bilel and René Jr. Landry},
  title = {Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm},
  journal = {International Journal of Sensors and Sensor Networks},
  volume = {11},
  number = {1},
  pages = {18-24},
  doi = {10.11648/j.ijssn.20231101.13},
  url = {https://doi.org/10.11648/j.ijssn.20231101.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssn.20231101.13},
  abstract = {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.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Calibration of 3-Axis Low-Cost Magnetometer Using the Least Square Ellipsoid Fitting Algorithm
AU  - Ali Shakerian
AU  - Saoussen Bilel
AU  - René Jr. Landry
Y1  - 2023/08/09
PY  - 2023
N1  - https://doi.org/10.11648/j.ijssn.20231101.13
DO  - 10.11648/j.ijssn.20231101.13
T2  - International Journal of Sensors and Sensor Networks
JF  - International Journal of Sensors and Sensor Networks
JO  - International Journal of Sensors and Sensor Networks
SP  - 18
EP  - 24
PB  - Science Publishing Group
SN  - 2329-1788
UR  - https://doi.org/10.11648/j.ijssn.20231101.13
AB  - 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.
VL  - 11
IS  - 1
ER  -

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