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

Abstract

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.

Error Calibration of Cross Magnetic Gradient Tensor System with Total Least-Squares Method

“…Vector calibration [10,11] needs a rigorous calibration magnetic feld and a high-precision tri-axial nonmagnetic platform, the calibration equipment is very expensive, and the calibration procedure is complicated, so vector calibration is not suitable for practical applications. However, on the other hand, scalar calibration [12][13][14] is usually described as the "poor man's" calibration method, because scalar calibration only needs a high-precision proton magnetometer to monitor the background geomagnetic feld, and the calibration procedure is simple and easy to perform. Yu et al [12,13] proposed a calibration method for a magnetic vector gradiometer, but two or higher-order small quantities were omitted in this method, and the precision of the corrected outs was reduced.…”

Compounded Calibration Based on FNN and Attitude Estimation Method Using Intelligent Filtering for Low Cost MEMS Sensor Application

“…For triaxial magnetometers, a two-step calibration algorithm based on functional link artificial neural network and least squares is reported. The coefficients could be identified according to optimal weights [4]. The attitude estimation based on gyros is constrained to time varying bias drift and noise [5].…”

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

“…The magnetic gradient tensor systems comprised of magnetometers with differencing are generally composed of multiple three-axis fluxgate sensors in accordance with a certain shape combination array [ 4 ]. Many measurement factors exist that give rise to errors in measurements performed using a magnetic gradient tensor system [ 5 , 6 ]; because of manufacturing technology and process limitations, fluxgate sensors will always exhibit systematic errors, such as triaxial scalar output deviation and differences of sensitivity and nonorthogonality; displacement and rotation misalignment errors also arise between the different sensor axes when multiple magnetic sensors are used to arrange the tensor system. In addition, the sensor itself exhibits a core temperature coefficient and magnetic hysteresis, and hard and soft magnetic interference in the background field can also affect the measurement accuracy.…”