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, 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 consider the errors in the TAM 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 and least squares according to its response to an external magnetic vector field. The procedure and the 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 the 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 the $x$ -, $y$ -, and $z$ -directions decrease from 74.655, 90.617, and 162.39 nT before calibration to 18.793, 20.095, and 13.671 nT after calibration, respectively.