Analysis of Orientation Errors in Triaxial Fluxgate Sensors and Research on Their Calibration Methods

Hu, Xiujuan; He, Shaopeng; Tian, Qin; Mamatemin, Alimjan; Guo, Pengkun; Chang, Guoping

doi:https://doi.org/10.5194/gi-2024-5

Preprints

https://doi.org/10.5194/gi-2024-5

Preprints

06 Jun 2024

| 06 Jun 2024

Status: a revised version of this preprint was accepted for the journal GI and is expected to appear here in due course.

Analysis of Orientation Errors in Triaxial Fluxgate Sensors and Research on Their Calibration Methods

Xiujuan Hu, Shaopeng He, Qin Tian, Alimjan Mamatemin, Pengkun Guo, and Guoping Chang

Abstract. Three-axis magnetic flux gate sensors are widely used in Chinese geomagnetic observatories, but due to their directional errors, it is necessary to study error correction methods to improve measurement accuracy. Firstly, the mechanism of directional errors produced by three-axis magnetic flux gate sensors is analyzed, followed by the development of measurement tools for conducting directional error measurement experiments on the high-precision three-axis magnetic flux gate sensors of the Chinese FGM-01 series. Experimental results show that correcting the Z-axis and D-axis directional errors is essential. The observation data after error correction, whether in terms of the standard deviation of its all-day baseline values or the relative difference magnitude with the reference instrument, significantly decrease, demonstrating the clear correction effect and proving the effectiveness of this correction method.

Received: 29 May 2024 – Discussion started: 06 Jun 2024

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Xiujuan Hu, Shaopeng He, Qin Tian, Alimjan Mamatemin, Pengkun Guo, and Guoping Chang

Status: closed

RC1:
'Comment on gi-2024-5', Anonymous Referee #1, 16 Jun 2024

The work is devoted to calibration of three-axis fluxgate sensors intended for long-term magnetic field monitoring in geomagnetic observatories.
General note concerning methodology of sensor correction.
It is well known that 3-axis fluxgate magnetometers (FGM) need to be corrected for non-orthogonality and biases. Generally accepted method consists in rotation of the sensor in homogeneous magnetic field and calculation of non-orthogonality correction matrix 3x3 and bias correction matrix 3x1. This method gives excellent results for non-suspended sensors. (As far as I know, your GM4 device is of that type of instrument)
To my mind, there is a total confusion between bias and directional errors in your explanations. In lines 86-89 we see: “Furthermore, due to residual magnetism in the magnetic core, even if the spatial magnetic field intensity where the sensor is located is 0, there will still be a small offset output, causing the output value of the D-magnetic axis orientation to actually contain an offset value. This error is referred to as the D-magnetic axis directional error.”
By the way, what is: “spatial magnetic field intensity where the sensor is located is 0”? You, probably, mean an inhomogeneity of external magnetic field in sensor location?
Concerning your method of rotation of the sensor installed on turntable platform. Line 126: “We continued adjusting the three base screws to make the Z element's output values as close as possible at different positions.” In this case, you just aligned Z-axis of the magnetometer with rotation axis of the turntable. This direction is not a geo-vertical direction. So, you need to carefully explain your method.

Citation: https://doi.org/10.5194/gi-2024-5-RC1
- AC1:
  'Reply on RC1', xiujuan hu, 05 Jul 2024
  Dear Reviewers,
  
  Thank you very much for your valuable comments on the article. The responses are as follows:
  
  The main focus of this paper is the analysis and experimentation of errors generated during the directional installation of instruments, and it does not involve the analysis of instrument orthogonality. During the experiments, it is assumed that the three axes of the instruments are in an ideal state of complete orthogonality. Due to the lack of detailed descriptions in the original text, there is a tendency to confuse the concepts of directionality and orthogonality. We have now added relevant explanations about the directional errors and principles of the instruments in the text and have removed the confusing statements to make the content more detailed and complete, and the expression more accurate.
  
  The original text lacked an introduction to the non-magnetic rotating platform and a description of the platform's state during the experiment. Since this platform can achieve absolute level by adjusting the theodolite dial, and the measurement data are conducted based on the horizontal plane, adjusting the base screw of the instrument so that the Z-axis output values are close at different positions indicates that the Z-axis is perpendicular to the platform and therefore in the direction of geographic vertical. The original text has been supplemented with relevant descriptions.
  
  The revised article has been sent to the journal's editorial office.The modifications made in the text have been marked with blue lines.
  
  Best regards.
  
  Citation: https://doi.org/10.5194/gi-2024-5-AC1
- AC2:
  'Reply on RC1', xiujuan hu, 05 Jul 2024
  Dear Reviewers,
  
  Thank you very much for your valuable comments on the article. The responses are as follows:
  
  The main focus of this paper is the analysis and experimentation of errors generated during the directional installation of instruments, and it does not involve the analysis of instrument orthogonality. During the experiments, it is assumed that the three axes of the instruments are in an ideal state of complete orthogonality. Due to the lack of detailed descriptions in the original text, there is a tendency to confuse the concepts of directionality and orthogonality. We have now added relevant explanations about the directional errors and principles of the instruments in the text and have removed the confusing statements to make the content more detailed and complete, and the expression more accurate.
  
  The original text lacked an introduction to the non-magnetic rotating platform and a description of the platform's state during the experiment. Since this platform can achieve absolute level by adjusting the theodolite dial, and the measurement data are conducted based on the horizontal plane, adjusting the base screw of the instrument so that the Z-axis output values are close at different positions indicates that the Z-axis is perpendicular to the platform and therefore in the direction of geographic vertical. The original text has been supplemented with relevant descriptions.
  
  The revised article has been sent to the journal's editorial office.The modifications made in the text have been marked with blue lines.
  
  Best regards.
  
  Citation: https://doi.org/10.5194/gi-2024-5-AC2
RC2:
'Comment on gi-2024-5', Anonymous Referee #2, 07 Jul 2024

The comment was uploaded in the form of a supplement: https://gi.copernicus.org/preprints/gi-2024-5/gi-2024-5-RC2-supplement.pdf

Citation: https://doi.org/10.5194/gi-2024-5-RC2
- AC3:
  'Reply on RC2', xiujuan hu, 18 Jul 2024
  Dear Reviewers,
  
  Thank you very much for your valuable comments on the article. The revisions have been made based on your suggestions, and the changes are highlighted in blue in the text.
  
  The article cites "Guide for Magnetic Measurements and Observatory Practice" by Jankowski and Sucksdorff. See Page4, Line 142-144 and Page 9 , Line 297-299.
  
  After calculating the D magnetic axis offset, it can be converted from nT to degrees using a formula. See Page5, Line 176-179.
  
  Descriptions of the accuracy and installation positions of the two additional water bubbles on the sensor have been added. See Page4, Line 135-141.
  
  During the verticality adjustment of the Z magnetic axis, an explanation was given for the result of the Z output values differing by 22nT at positions 180° apart. See Page4,5, Line 162-173.
  
  The textual descriptions between Figure 5, Figure 5(a), and Figure 5(b) have been revised. See Page 6, Line 220-222.
  
  The selection times for five quiet days and five disturbed days before and after calibration have been rephrased. See Page 6, Line 229-242. The header of Table 2 has been revised. See Page 7, Line 254-255.
  
  One reference with an incorrect format has been revised. See Page 9, Line 304-305. The DOIs of two other references have been verified; the data is correct, but they cannot be accessed for unknown reasons. Should the DOI data be deleted or retained? See Page 9, Line 294-296. See Page 9, Line 320-322. Best regards
  
  Citation: https://doi.org/10.5194/gi-2024-5-AC3
  - AC4: 'Reply on AC3', xiujuan hu, 18 Jul 2024
    
    Dear Reviewers,
    
    Thank you very much for your valuable comments on the article. The revisions have been made based on your suggestions, and the changes are highlighted in blue in the text.
    
    The article cites "Guide for Magnetic Measurements and Observatory Practice" by Jankowski and Sucksdorff. See Page4, Line 142-144 and Page 9 , Line 297-299.
    
    After calculating the D magnetic axis offset, it can be converted from nT to degrees using a formula. See Page5, Line 176-179.
    
    Descriptions of the accuracy and installation positions of the two additional water bubbles on the sensor have been added. See Page4, Line 135-141.
    
    During the verticality adjustment of the Z magnetic axis, an explanation was given for the result of the Z output values differing by 22nT at positions 180° apart. See Page4,5, Line 162-173.
    
    The textual descriptions between Figure 5, Figure 5(a), and Figure 5(b) have been revised. See Page 6, Line 220-222.
    
    The selection times for five quiet days and five disturbed days before and after calibration have been rephrased. See Page 6, Line 229-242. The header of Table 2 has been revised. See Page 7, Line 254-255.
    
    One reference with an incorrect format has been revised. See Page 9, Line 304-305. The DOIs of two other references have been verified; the data is correct, but they cannot be accessed for unknown reasons. Should the DOI data be deleted or retained? See Page 9, Line 294-296. See Page 9, Line 320-322. Best regards
    
    Citation: https://doi.org/10.5194/gi-2024-5-AC4

Status: closed

RC1:
'Comment on gi-2024-5', Anonymous Referee #1, 16 Jun 2024

The work is devoted to calibration of three-axis fluxgate sensors intended for long-term magnetic field monitoring in geomagnetic observatories.
General note concerning methodology of sensor correction.
It is well known that 3-axis fluxgate magnetometers (FGM) need to be corrected for non-orthogonality and biases. Generally accepted method consists in rotation of the sensor in homogeneous magnetic field and calculation of non-orthogonality correction matrix 3x3 and bias correction matrix 3x1. This method gives excellent results for non-suspended sensors. (As far as I know, your GM4 device is of that type of instrument)
To my mind, there is a total confusion between bias and directional errors in your explanations. In lines 86-89 we see: “Furthermore, due to residual magnetism in the magnetic core, even if the spatial magnetic field intensity where the sensor is located is 0, there will still be a small offset output, causing the output value of the D-magnetic axis orientation to actually contain an offset value. This error is referred to as the D-magnetic axis directional error.”
By the way, what is: “spatial magnetic field intensity where the sensor is located is 0”? You, probably, mean an inhomogeneity of external magnetic field in sensor location?
Concerning your method of rotation of the sensor installed on turntable platform. Line 126: “We continued adjusting the three base screws to make the Z element's output values as close as possible at different positions.” In this case, you just aligned Z-axis of the magnetometer with rotation axis of the turntable. This direction is not a geo-vertical direction. So, you need to carefully explain your method.

Citation: https://doi.org/10.5194/gi-2024-5-RC1
- AC1:
  'Reply on RC1', xiujuan hu, 05 Jul 2024
  Dear Reviewers,
  
  Thank you very much for your valuable comments on the article. The responses are as follows:
  
  The main focus of this paper is the analysis and experimentation of errors generated during the directional installation of instruments, and it does not involve the analysis of instrument orthogonality. During the experiments, it is assumed that the three axes of the instruments are in an ideal state of complete orthogonality. Due to the lack of detailed descriptions in the original text, there is a tendency to confuse the concepts of directionality and orthogonality. We have now added relevant explanations about the directional errors and principles of the instruments in the text and have removed the confusing statements to make the content more detailed and complete, and the expression more accurate.
  
  The original text lacked an introduction to the non-magnetic rotating platform and a description of the platform's state during the experiment. Since this platform can achieve absolute level by adjusting the theodolite dial, and the measurement data are conducted based on the horizontal plane, adjusting the base screw of the instrument so that the Z-axis output values are close at different positions indicates that the Z-axis is perpendicular to the platform and therefore in the direction of geographic vertical. The original text has been supplemented with relevant descriptions.
  
  The revised article has been sent to the journal's editorial office.The modifications made in the text have been marked with blue lines.
  
  Best regards.
  
  Citation: https://doi.org/10.5194/gi-2024-5-AC1
- AC2:
  'Reply on RC1', xiujuan hu, 05 Jul 2024
  Dear Reviewers,
  
  Thank you very much for your valuable comments on the article. The responses are as follows:
  
  The main focus of this paper is the analysis and experimentation of errors generated during the directional installation of instruments, and it does not involve the analysis of instrument orthogonality. During the experiments, it is assumed that the three axes of the instruments are in an ideal state of complete orthogonality. Due to the lack of detailed descriptions in the original text, there is a tendency to confuse the concepts of directionality and orthogonality. We have now added relevant explanations about the directional errors and principles of the instruments in the text and have removed the confusing statements to make the content more detailed and complete, and the expression more accurate.
  
  The original text lacked an introduction to the non-magnetic rotating platform and a description of the platform's state during the experiment. Since this platform can achieve absolute level by adjusting the theodolite dial, and the measurement data are conducted based on the horizontal plane, adjusting the base screw of the instrument so that the Z-axis output values are close at different positions indicates that the Z-axis is perpendicular to the platform and therefore in the direction of geographic vertical. The original text has been supplemented with relevant descriptions.
  
  The revised article has been sent to the journal's editorial office.The modifications made in the text have been marked with blue lines.
  
  Best regards.
  
  Citation: https://doi.org/10.5194/gi-2024-5-AC2
RC2:
'Comment on gi-2024-5', Anonymous Referee #2, 07 Jul 2024

The comment was uploaded in the form of a supplement: https://gi.copernicus.org/preprints/gi-2024-5/gi-2024-5-RC2-supplement.pdf

Citation: https://doi.org/10.5194/gi-2024-5-RC2
- AC3:
  'Reply on RC2', xiujuan hu, 18 Jul 2024
  Dear Reviewers,
  
  Thank you very much for your valuable comments on the article. The revisions have been made based on your suggestions, and the changes are highlighted in blue in the text.
  
  The article cites "Guide for Magnetic Measurements and Observatory Practice" by Jankowski and Sucksdorff. See Page4, Line 142-144 and Page 9 , Line 297-299.
  
  After calculating the D magnetic axis offset, it can be converted from nT to degrees using a formula. See Page5, Line 176-179.
  
  Descriptions of the accuracy and installation positions of the two additional water bubbles on the sensor have been added. See Page4, Line 135-141.
  
  During the verticality adjustment of the Z magnetic axis, an explanation was given for the result of the Z output values differing by 22nT at positions 180° apart. See Page4,5, Line 162-173.
  
  The textual descriptions between Figure 5, Figure 5(a), and Figure 5(b) have been revised. See Page 6, Line 220-222.
  
  The selection times for five quiet days and five disturbed days before and after calibration have been rephrased. See Page 6, Line 229-242. The header of Table 2 has been revised. See Page 7, Line 254-255.
  
  One reference with an incorrect format has been revised. See Page 9, Line 304-305. The DOIs of two other references have been verified; the data is correct, but they cannot be accessed for unknown reasons. Should the DOI data be deleted or retained? See Page 9, Line 294-296. See Page 9, Line 320-322. Best regards
  
  Citation: https://doi.org/10.5194/gi-2024-5-AC3
  - AC4: 'Reply on AC3', xiujuan hu, 18 Jul 2024
    
    Dear Reviewers,
    
    Thank you very much for your valuable comments on the article. The revisions have been made based on your suggestions, and the changes are highlighted in blue in the text.
    
    The article cites "Guide for Magnetic Measurements and Observatory Practice" by Jankowski and Sucksdorff. See Page4, Line 142-144 and Page 9 , Line 297-299.
    
    After calculating the D magnetic axis offset, it can be converted from nT to degrees using a formula. See Page5, Line 176-179.
    
    Descriptions of the accuracy and installation positions of the two additional water bubbles on the sensor have been added. See Page4, Line 135-141.
    
    During the verticality adjustment of the Z magnetic axis, an explanation was given for the result of the Z output values differing by 22nT at positions 180° apart. See Page4,5, Line 162-173.
    
    The textual descriptions between Figure 5, Figure 5(a), and Figure 5(b) have been revised. See Page 6, Line 220-222.
    
    The selection times for five quiet days and five disturbed days before and after calibration have been rephrased. See Page 6, Line 229-242. The header of Table 2 has been revised. See Page 7, Line 254-255.
    
    One reference with an incorrect format has been revised. See Page 9, Line 304-305. The DOIs of two other references have been verified; the data is correct, but they cannot be accessed for unknown reasons. Should the DOI data be deleted or retained? See Page 9, Line 294-296. See Page 9, Line 320-322. Best regards
    
    Citation: https://doi.org/10.5194/gi-2024-5-AC4

Xiujuan Hu, Shaopeng He, Qin Tian, Alimjan Mamatemin, Pengkun Guo, and Guoping Chang

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Short summary

Nearly 200 sets of three-axis fluxgate magnetometers used in Chinese geomagnetic observatories, but due to their directional errors, it is necessary to study error correction methods to improve measurement accuracy. Experimental results show that correcting the Z-axis and D-axis directional errors is essential. The observation data after error correction demonstrating the clear correction effect. The measurement device used in the experiment is low-cost and easy to disseminate.


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