Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

Abstract

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust.

A method for estimating magnetic target location by employing total field and its gradients data

“…As can be seen in Eq. ( 2 ), | B | can be seen as a rotational invariant 20 . | B | only includes the magnitude of r and bearing information of the magnetic target can’t be obtained.…”

Design and optimization of sensor array for magnetic gradient tensor system

“…The Cartesian coordinate system is established as shown in Figure 1, and the distance from each magnetic sensor to the origin of the coordinates is d. The shortdistance difference method is used to estimate the magnetic gradient tensor in the direction j of the coordinate axis as G ij % DB i /d j , where i, j = 1, 2, 3 represent x, y and z in the Cartesian coordinate system, DB i is the component difference of two Figure 1 The structure of planar orthogonal magnetic gradient tensor system magnetic sensors in the direction i of the coordinate axis, d j is the distance of the two magnetic sensors in the direction j. Then, the magnetic field vector B o and the magnetic gradient tensor matrix G at the origin of the coordinate can be obtained as follows (Li et al, 2018):…”

“…Allen et al (2005) proposed a planar crossshaped tensor system with significantly reduced structural error. Because of a number of advantages such as simple layout and minimum structural error, the planar cross-shaped array is widely used for gradient-based magnetic localization algorithms (Gang et al, 2016;Li et al, 2018). Therefore, in the simulation and experiment, we choose the planar cross-shaped structure as the comparison of the proposed arrays.…”

Preprocessed Method and Application of Magnetic Gradient Tensor Data

“…The system consisted of four mag-03 tri-axial fluxgate magnetometers and a cross-type plastic bracket. The baseline distance between the two magnetometers was 0.4 m. The nonorthogonality error of the sensor and the misalignment error between the sensors are corrected by nonlinear least squares [24]. Besides, the measured magnetic gradient tensor, NSS data, and magnetic gradient tensor invariant are shown in Fig.…”