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A Novel Calibration Method for Tri-axial Magnetometers Based on an Expanded Error Model and a Two-step Total Least Square Algorithm

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Abstract

Magnetometer plays an important role in strap-down navigation system, but the measurement results are influenced by various kinds of errors. All combined time-invariance effect inferences are compensated directly by the calibration algorithm, including biases, scale factors, and sensor non-orthogonal errors, as well as soft iron, hard iron, and misalignment errors. This paper proposes a novel magnetometer calibration method based on an expanded magnetometer error model (EM) and a two-step total least square algorithm (TLS) in the magnetic domain. In the method, the EM is derived to achieve calibration directly, and the two-step TLS algorithm is used to calculate the expanded magnetometer EM coefficients. Then, the simulations and experiments are performed to evaluate the proposed method’s performance. The proposed method is compared with the direct least square (DLS) algorithm, which is based on a traditional EM and the least square algorithm (LSA) based on an expanded EM. The results indicate that the proposed algorithm can improve heading accuracy by approximately 13.67% compared with that of the DLS algorithm. Moreover, the proposed algorithm is easy to implement and has resistance to noise interference.

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References

  1. Fang J, Sun H, Cao J, Zhang X, Tao Y (2011) A novel calibration method of magnetic compass based on ellipsoid fitting. IEEE Inst Meas 60:2053–2061

    Article  Google Scholar 

  2. Grivon D, Vezzetti E, Violante M (2013) Development of an innovative low-cost MARG sensors alignment and distortion compensation methodology for 3D scanning applications. Robot Auton Syst 61:1710–1716

    Article  Google Scholar 

  3. Luinge H, Veltink P, Baten C (2007) Ambulatory measurement of arm orientation. J Biomech 40:78–85

    Article  Google Scholar 

  4. Vasconcelos F, Elkaim G, Silvestre C, Oliveira P, Cardeira B (2011) Geometric approach to strapdown magnetometer calibration in sensor frame. IEEE Aerospace Electron Syst 47:1293–1306

    Article  Google Scholar 

  5. Gebre-Egziabher D, Elkaim H, Powell D, Parkinson W (2001) A non-linear, two-step estimation algorithm for calibrating solid-state strapdown magnetometers. In 8th International St Petersburg Conference on Navigation Systems IEEE/AIAA

  6. Lv C, Chen X, Huang H et al (2015) Study on calibration method for tri-axial accelerometers, in Metrology for Aerospace conference IEEE: 15–20

  7. Gebre-Egziabher D, Elkaim H, Powell D, Parkinson W, Parkinson W (2006) Calibration of strapdown magnetometers in magnetic field domain. J Aerosp Eng 19:87–102

    Article  Google Scholar 

  8. Foster C, Elkaim G (2008) Extension of a two-step calibration methodology to include nonorthogonal sensor axes. IEEE Aerospace Electron Syst 44:1070–1078

    Article  Google Scholar 

  9. Zhang Z (2015) Two-step calibration methods for miniature inertial and magnetic sensor units. IEEE Trans Ind Electron 62:3714–3723

    Google Scholar 

  10. Zhang Y (2021) A multiple input deep convolutional attention network for Covid-19 diagnosis based on chest CT and chest X-ray. Pattern Recogn Lett 150:8–16

    Article  Google Scholar 

  11. Zhu R, Zhou Z (2006) Calibration of three-dimensional integrated sensors for improved system accuracy. Sensors Actuators A Phys 127:340–344

    Article  Google Scholar 

  12. Jurman D, Jankovec M, Kamnik R, Topic M (2007) Calibration and data fusion solution for the miniature attitude and heading reference system. Sensors Actuators A Phys 138:411–420

    Article  Google Scholar 

  13. Bonnet S, Bassompierre C, Godin C, Lesecq S, Barraud A (2009) Calibration methods for inertial and magnetic sensors. Sensors Actuators A Phys 156:302–311

    Article  Google Scholar 

  14. Včelák J, Ripka P, Kubik J, Platil A, Kašpar P (2005) AMR navigation systems and methods of their calibration. Sensors Actuators A Phys 123:122–128

    Article  Google Scholar 

  15. Včelák J, Ripka P, Kubik J, Platil A, Kašpar P (2006) Errors of AMR compass and methods of their compensation. Sensors Actuators A Phys 129:53–57

    Article  Google Scholar 

  16. Wu Y, Zou D, Liu P et al (2018) Dynamic magnetometer calibration and alignment to inertial sensors by Kalman filtering. IEEE Trans Control Syst Technol 26:716–723

    Article  Google Scholar 

  17. Renaudin V, Afzal H, Lachapelle G (2010) New method for magnetometers based orientation estimation. In Position Location and Navigation Symposium, IEEE: 348–356

  18. Zhang X, Zhang Y (2009) New auto-calibration and compensation method for vehicle magnetic field based on ellipse restriction. Chin J Sci Instrum 30:2439–2443

    Google Scholar 

  19. Valérie R, Afzal MH, Gérard L (2010) Complete triaxis magnetometer calibration in the magnetic domain. J Sensors 1:23–59

    Google Scholar 

  20. Pang H, Pan M, Chen J et al (2016) Integrated calibration and magnetic disturbance compensation of three-axis magnetometers. Measurement 93:409–413

    Article  Google Scholar 

  21. Zhang Y (2021) Improving ductal carcinoma in situ classification by convolutional neural network with exponential linear unit and rank-based weighted pooling. Complex Intell Syst 7:1295–1310

    Article  Google Scholar 

  22. Zhu X, Zhao T, Cheng D et al (2017) A three-step calibration method for tri-axial field sensors in a 3D magnetic digital compass. Meas Sci Technol 28:055106

    Article  Google Scholar 

  23. Crassidis L, Lai L, Harman R (2005) Real-time attitude-independent three-axis magnetometer calibration. J Guid Control Dyn 28:115–120

    Article  Google Scholar 

  24. Soken H, Sakai S (2020) Attitude estimation and magnetometer calibration using reconfigurable TRIAD+filtering approach. Aerosp Sci Technol 99:105754

    Article  Google Scholar 

  25. Wang J, Chen X, Yang P (2021) Adaptive h-infinite kalman filter based on multiple fading factors and its application in unmanned underwater vehicle. ISA Trans 108:295–304

    Article  Google Scholar 

  26. Wang J, Ma Z, Chen X (2021) Generalized dynamic fuzzy nn model based on multiple fading factors sckf and its application in integrated navigation. IEEE Sensors J 21:3680–3693

    Article  Google Scholar 

  27. Zhang Y (2020) Advances in multimodal data fusion in neuroimaging: overview, challenges, and novel orientation. Inf Fusion 64:149–187

    Article  Google Scholar 

  28. Liu S, Liu D, Srivastava G et al (2021) Overview and methods of correlation filter algorithms in object tracking. Complex Intell Syst 7:1895–1917

    Article  Google Scholar 

  29. Tabatabaei S, Gluhak A, Tafazolli R (2013) A fast calibration method for triaxial magnetometers. IEEE Trans Instrum Meas 62:2929–2937

    Article  Google Scholar 

  30. Wu Y, Zhu M, Yu W (2019) An efficient method for gyroscope-aided full magnetometer calibration. IEEE Sensors J 15:1–1

    Google Scholar 

  31. Liu J, Li X, Zhang Y et al (2021) A comprehensive strapdown triaxial magnetometer calibration method considering temporal misalignment error. Measurement 175:109092

    Article  Google Scholar 

  32. Bowditch N (1984) The American Pratical Navigator. Hydrographic /Topographic Center, Defense Mapping Agency

    Google Scholar 

  33. Liu S, Bai W, Srivastava G et al (2020) Property of self-similarity between baseband and modulated signals. Mobile Netw Appl 25:1537–1547

    Article  Google Scholar 

  34. Fitzgibbon A, Pilu M, Fisher R (1999) Direct least square fitting of ellipses. IEEE Patt Anal Mach Intell 21:476–480

    Article  Google Scholar 

  35. Zhang H, Huang J, Fan W (1995) Total least square method and its application to parameter estimation. Acta Automat Sin 21:40–47

    MATH  Google Scholar 

  36. Liu S, Liu X, Wang S et al (2021) Fuzzy-aided solution for out-of-view challenge in visual tracking under IoT assisted complex environment. Neural Comput Applic 33:1055–1106

    Article  Google Scholar 

  37. Chen X, Ma Z, Yang P (2021) Integrated modeling of motion decoupling and flexure deformation of carrier in transfer alignment. Mech Syst Signal Process 159:107690

    Article  Google Scholar 

Download references

Funding

This work was partly supported by the NSFC (Grant Nos. 61873064, 61803175, 51375087,41204025) and the Ocean Special Funds (Grant no. 201205035–09).

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Authors and Affiliations

  1. Key Laboratory of Micro -Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing, 210096, China

    Xiyuan Chen, Xiaotian Zhang, Min Zhu & Caiping Lv

  2. School of Electrical Engineering, University of Jinan, Jinan, 250022, China

    Yuan Xu

  3. Institute of Space Science and Technology, Nanchang University, Nanchang, 330031, China

    Hang Guo

Authors
  1. Xiyuan Chen
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  2. Xiaotian Zhang
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  3. Min Zhu
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  4. Caiping Lv
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  5. Yuan Xu
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  6. Hang Guo
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Correspondence to Xiyuan Chen, Yuan Xu or Hang Guo.

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Chen, X., Zhang, X., Zhu, M. et al. A Novel Calibration Method for Tri-axial Magnetometers Based on an Expanded Error Model and a Two-step Total Least Square Algorithm. Mobile Netw Appl 27, 794–805 (2022). https://doi.org/10.1007/s11036-021-01898-z

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  • DOI: https://doi.org/10.1007/s11036-021-01898-z

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