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.
Highlights
Accurate measurement of the geomagnetic field has been widely applied in geophysical research, space magnetic measurement, military defense, mineral resources exploration, and drilling practice [1].Common magnetometers include a helium optical-pumping magnetometer, a proton magnetometer, a three-axis flux gate magnetometer, and an anisotropic magnetoresistive magnetometer
This paper provides a constant intersection angle method to solve the rotation matrix R
In the calculation process according to the method proposed in [6] we find the problem that the condition number of matrix is larger, which decrease the estimation accuracy of the rotation matrix
Summary
Accurate measurement of the geomagnetic field has been widely applied in geophysical research, space magnetic measurement, military defense, mineral resources exploration, and drilling practice [1]. Magnetometer data can be compensated for sensor errors and the presence of magnetic distortions by mapping an ellipsoid of data to a sphere; the rotation of the sphere is unknown [5,6] The essence of this difference discloses the failure to clarify the three-axis misalignment error. The transition matrix defined in [12] between the sensor coordinate system and body system contains six unknown parameters This matrix completely describes the non-orthogonal error and misalignment error and adopts the “three-step” algorithm in magnetometer pre-calibration before flight, without reference to any direction information. This paper is based on the constant intersection angle between the geomagnetic field vector and gravitation field vector [14], without additional independent calibration and coordinate system conversion, and seeks to derive a rotation matrix more conveniently, furthering the compensation of magnetic field measurement error and heading error
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
