Calibration of three-axis fluxgate magnetometers with nonlinear least square method

Pang, Hongfeng; Li, Ji; Chen, Dixiang; Pan, Mengchun; Luo, Siqiang; Zhang, Qi; Luo, Fei

doi:10.1016/j.measurement.2012.11.001

Cited by 55 publications

(26 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, the magnetic disturbance field is very complicated. Mathematically, these magnetic disturbance errors can be modeled as soft‐iron magnetic distortions and hard‐iron magnetic distortions . A mathematical model of the three‐axis magnetometer considering the distortion magnetic fields can be expressed by

([], \begin{matrix} H_{mx} \\ H_{my} \\ H_{mz} \end{matrix}) = ([], \begin{matrix} r_{xx} & r_{xy} & r_{xz} \\ r_{yx} & r_{yy} & r_{yz} \\ r_{zx} & r_{zy} & r_{zz} \end{matrix}) ([], \begin{matrix} H_{ex} \\ H_{ey} \\ H_{ez} \end{matrix}) + ([], \begin{matrix} H_{px} \\ H_{py} \\ H_{pz} \end{matrix})

where H m = ( H mx , H my , H mz ) T are the measured values of the three‐axis magnetometer to be compensated, H e = ( H ex , H ey , H ez ) T are the true values of geomagnetic field components in the three‐axis magnetometer coordinate, and H p = ( H px , H py , H pz ) T are hard‐iron offset values.…”

Section: Compensation Theorymentioning

confidence: 99%

“…In practice, the achievable accuracy of the geomagnetic field measurement is highly dependent on the quality of the three‐axis magnetometer (biases, different scalar factors, non‐orthogonality of three axes) and the external magnetic distortion sources . The magnetometer error can be calibrated beforehand . However, the magnetic disturbance fields are closely related to its own ferromagnetic parts and other electric equipment such as the inertial navigation system (INS) system, cabling, and the power circuit module.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Magnetic disturbance field compensation of a geomagnetic vector measuring instrument

Liu

Zhang

Pan

et al. 2017

IEEJ Transactions Elec Engng

Self Cite

View full text Add to dashboard Cite

Magnetic disturbance field from ferromagnetic structural parts is a dominant factor that influences the accuracy of a geomagnetic vector measuring instrument. In this paper, a new vector compensation method for a three-axis magnetometer is proposed. In the first step, combined with posture information from inertial sensors, the dataset of the three-axis magnetometer outputs in different postures is utilized to construct linear equations of the error parameters; then the soft-iron parameters are determined with singular value decomposition. In the second step, the hard-iron parameters are estimated by changing the fixing direction of the three-axis magnetometer. Simulations and experiments are performed to assess the performance of the proposed method. The results show that the error parameters can be accurately estimated, and the measurement errors of geomagnetic field vectors and magnitude are suppressed greatly. After compensation, the standard deviations of the errors of the magnetic vector components decrease from hundreds of nT to tens of nT. The main advantages of this proposed method are as follows: (i) it can compensate not only the scalar error but also the vector error, and (ii) it compensates the errors of vectors and magnitude with higher accuracy.

show abstract

([], \begin{matrix} H_{mx} \\ H_{my} \\ H_{mz} \end{matrix}) = ([], \begin{matrix} r_{xx} & r_{xy} & r_{xz} \\ r_{yx} & r_{yy} & r_{yz} \\ r_{zx} & r_{zy} & r_{zz} \end{matrix}) ([], \begin{matrix} H_{ex} \\ H_{ey} \\ H_{ez} \end{matrix}) + ([], \begin{matrix} H_{px} \\ H_{py} \\ H_{pz} \end{matrix})

Section: Compensation Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magnetic disturbance field compensation of a geomagnetic vector measuring instrument

Liu

Zhang

Pan

et al. 2017

IEEJ Transactions Elec Engng

Self Cite

View full text Add to dashboard Cite

show abstract

“…A simple and very fast scalar calibration procedure to determine the calibration coefficients including directions was presented, and the rms error and component difference through calibration were reduced from several hundreds nano-Tesla down to several nano-Tesla and from  1400nT down to  30nT [20]. Pang built a nonlinear error model and estimated detailed error parameters using nonlinear least square method [21]. Wu introduced a constrained total least-squares calibration without assuming a priori knowledge of the noise distribution, but the detailed parameters were not calculated [22].…”

Section: Review Of Calibration Techniquesmentioning

confidence: 99%

Two-Step Complete Calibration of Magnetic Vector Gradiometer Based on Functional Link Artificial Neural Network and Least Squares

Huang

2016

IEEE Sensors J.

View full text Add to dashboard Cite

Magnetic vector gradiometers are frequently used for the detection of ferrous metals, the detection of unexploded ordinance (UXO) and defense applications. A magnetic vector gradiometer, which is under consideration in this paper, consists of two tri-axial magnetometers (TAMs). It requires a calibration procedure in order to take into account the errors in the TAM(tri-axial magnetometer) itself and the spatial misalignment of the magnetometers that will deteriorate the measurement precision of the gradiometer. This paper reports a two-step calibration algorithm of magnetic vector gradiometer based on functional link artificial neural network (FLANN) and least squares according to its response to an external magnetic vector field. The procedure and steps to identify the coefficients related to the measurement error are given. The calibration algorithm with good convergence proved by the numerical simulations decreased the relative error of magnetic vector gradient, in the case when the TAM is used in earth field, from 6.2340 down to 0.0187 and the parameters can be identified with the maximum inaccuracy of 5.35%. The efficiency of two-step calibration is also validated through experimental tests of two TAMs of type Mag03-MSB100 strapped on a nonmagnetic turntable. The calibrated coefficients are a good match with those specified by the manufacturer of the TAMs; the standard deviations of the increments of magnetic vector components in x, y and z directions decrease from 74.655nT, 90.617nT and 162.39nT before calibration down to 18.793nT, 20.095nT and 13.671nT after calibration, respectively.

show abstract

“…We propose another measurement strategy to solve this problem. The DM-050 magnetometer measured data at 36 different static poses, and these poses are distributed uniformly in three dimensions using nonmagnetic rotation equipment [19]. The measurement strategy is compared with the rotation measurement strategy.…”

Section: The Influence Of Measurement Strategy In Thismentioning

confidence: 99%

Improvement of magnetometer calibration using Levenberg-Marquardt algorithm

Pang

Chen

Pan

et al. 2014

IEEJ Trans Elec Electron Eng

Self Cite

View full text Add to dashboard Cite

The algorithm, the model, and the measurement strategy are important for the calibration of three‐axis magnetometers. A new calibration model with clear physical meaning is proposed, and scale factors, offsets, and nonorthogonal angles are directly illustrated. One limitation of traditional iteration calibration algorithms is the influence of the initial parameters. In this paper, the Levenberg–Marquardt algorithm is proposed to solve the troublesome procedure of initial parameter selection, so that it can improve the calibration performance of three‐axis magnetometers. The validity of this method is proved by simulation, and the estimated parameters are found to be close to the prearranged parameters. The experimental system mainly consists of a three‐axis fluxgate magnetometer (DM‐050), two‐dimensional nonmagnetic rotation equipment, and a proton magnetometer. The magnetic field intensity is obtained by the proton magnetometer. Experimental results show that the root‐mean‐square error is reduced from 84.177 to 4.076 nT. In addition, the influence of the initial parameters and measurement strategy is analyzed. Experimental results show that the Levenberg–Marquardt algorithm is not sensitive to the initial parameters and the 36 static measurements strategy is more reliable than the rotation measurement strategy. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

show abstract

Calibration of three-axis fluxgate magnetometers with nonlinear least square method

Cited by 55 publications

References 18 publications

Magnetic disturbance field compensation of a geomagnetic vector measuring instrument

Magnetic disturbance field compensation of a geomagnetic vector measuring instrument

Two-Step Complete Calibration of Magnetic Vector Gradiometer Based on Functional Link Artificial Neural Network and Least Squares

Improvement of magnetometer calibration using Levenberg-Marquardt algorithm

Contact Info

Product

Resources

About