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Sensors 2014, 14(5), 8485-8504; doi:10.3390/s140508485
Article

Novel Calibration Algorithm for a Three-Axis Strapdown Magnetometer

1,2,* , 2
,
2
 and
2
1 College of Automation, Beijing Union University, Beijing 100101, China 2 School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
* Author to whom correspondence should be addressed.
Received: 27 February 2014 / Revised: 27 April 2014 / Accepted: 28 April 2014 / Published: 14 May 2014
(This article belongs to the Section Physical Sensors)
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Abstract

A complete error calibration model with 12 independent parameters is established by analyzing the three-axis magnetometer error mechanism. The said model conforms to an ellipsoid restriction, the parameters of the ellipsoid equation are estimated, and the ellipsoid coefficient matrix is derived. However, the calibration matrix cannot be determined completely, as there are fewer ellipsoid parameters than calibration model parameters. Mathematically, the calibration matrix derived from the ellipsoid coefficient matrix by a different matrix decomposition method is not unique, and there exists an unknown rotation matrix R between them. This paper puts forward a constant intersection angle method (angles between the geomagnetic field and gravitational field are fixed) to estimate R. The Tikhonov method is adopted to solve the problem that rounding errors or other errors may seriously affect the calculation results of R when the condition number of the matrix is very large. The geomagnetic field vector and heading error are further corrected by R. The constant intersection angle method is convenient and practical, as it is free from any additional calibration procedure or coordinate transformation. In addition, the simulation experiment indicates that the heading error declines from ±1° calibrated by classical ellipsoid fitting to ±0.2° calibrated by a constant intersection angle method, and the signal-to-noise ratio is 50 dB. The actual experiment exhibits that the heading error is further corrected from ±0.8° calibrated by the classical ellipsoid fitting to ±0.3° calibrated by a constant intersection angle method.
Keywords: constant intersection angle assumption; ellipsoid fitting; restricted least squares solution; rotation matrix constant intersection angle assumption; ellipsoid fitting; restricted least squares solution; rotation matrix
This 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.

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Liu, Y.X.; Li, X.S.; Zhang, X.J.; Feng, Y.B. Novel Calibration Algorithm for a Three-Axis Strapdown Magnetometer. Sensors 2014, 14, 8485-8504.

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