Abstract
An improved method based on the second order improved central difference method is proposed to improve the third-order magnetic gradient tensor, which is affected by noise and characterized by poor stability. The third-order magnetic gradient tensor at the center point is calculated by using the three-component magnetic field at four points along a single route; this approach effectively improves the stability of the third-order magnetic gradient tensor data. In this paper, the errors of the traditional method and the new method in calculating the third-order magnetic gradient tensor are given by the Taylor series. Based on the traditional third-order magnetic gradient tensor system, a new third-order magnetic gradient tensor system and the corresponding measurement method are presented. Through simulations, in the case of noise, it is verified that the proposed method exhibits better stability by comparing the components of the third-order magnetic gradient tensor with the positioning results. In experiments, the root-mean-square error is used to compare the positioning results before and after noise addition. The traditional method changes the root-mean-square error of the positioning results from (1.3626, 3.6573, 0.5766 m) to (3.3661, 9.5966, 1.9465 m), and the root-mean-square error obtained with the new method displays no obvious change.
Highlights
Magnetic detection technology has rapidly developed in recent years due to its low cost, low system attitude requirements, and high accuracy
In practice, an abnormal magnetic field is much smaller than the magnetic field of Earth, and this difference can lead to large errors
Yin11 derived an approximate formula for the thirdorder magnetic gradient tensor based on the research by Nara, and single-point locations were directly obtained through a high-order Euler deconvolution formula with unique results
Summary
Magnetic detection technology has rapidly developed in recent years due to its low cost, low system attitude requirements, and high accuracy. Nara used the relative position vector of a magnetic dipole to relate magnetic gradient tensor data to magnetic field components and deduced a linear equation This process is equivalent to Euler deconvolution, a source-location method widely used in geophysics.. In this paper, based on the Yin method, a new method for calculating the third-order magnetic gradient tensor is proposed to enhance the poor stability of the third-order magnetic gradient component algorithm. The stability of the new method is verified based on a third-order magnetic gradient tensor component diagram and the root-mean-square error of the positioning results.
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