Abstract
Currently, when the existing magnetic dipole inversion methods are used, the classification process heavily relies on the localization results, and the localization error can significantly deteriorate the classification results. In order to address this problem, the present study proposes a novel magnetic dipole inversion method based on tensor geometric invariants, in which localization and classification processes are mutually independent. First, based on tensor geometric invariants, it was proved that the cross product between the intermediate eigenvectors at any two measurement points in the dipole magnetic field is either in the same direction as the magnetic moment vector or in the opposite direction. Accordingly, the direction of the magnetic moment vector could be directly obtained. Next, based on tensor geometric invariants, nonlinear equations including the position parameters of the dipole were constructed so as to derive the position of the dipole. By employing the proposed method, localization and classification were found to be two mutually independent processes, both of which are relatively insensitive to attitude changes of the measurement system. The present simulation results demonstrate that the proposed method is superior to the scalar triangulation and ranging (STAR) method, the Nara improved method, and the STAR improved method in both classification and localization performance. Moreover, the proposed method exhibits the strongest noise immunity and can be effectively used for real-time inversion.
Highlights
Ferromagnetic substances can induce a magnetic anomaly in the earth’s magnetic field, which has extensive applications for inverting certain parameters, such as the position and magnetic moment of a magnetic target.1 Significant research efforts have been devoted to the study of the magnetic anomaly detection in many domains, such as unexploded ordnance detection,2,3 underwater magnetic tracking,4,5 geophysics exploration,6,7 intruder detection,8 biomedical applications,9 and indoor localization10 with substantial progress
Based on tensor geometric invariants, it was proved that the cross product between the intermediate eigenvectors of any two measurement points in the dipole magnetic field is either in the same direction as the magnetic moment vector or in the opposite direction
Based on tensor geometric invariants, this study found a novel dipole inversion method, in which localization and classification processes are independent
Summary
Ferromagnetic substances can induce a magnetic anomaly in the earth’s magnetic field, which has extensive applications for inverting certain parameters, such as the position and magnetic moment of a magnetic target. Significant research efforts have been devoted to the study of the magnetic anomaly detection in many domains, such as unexploded ordnance detection, underwater magnetic tracking, geophysics exploration, intruder detection, biomedical applications, and indoor localization with substantial progress. Wiegert et al. proposed the scalar triangulation and ranging (STAR) method, capable of realizing real-time localization of magnetic targets using the regular hexahedral magnetic gradient tensor measurement system This method effectively overcomes the disturbance of the geomagnetic field, and has rotation invariability and can be applied to mobile-carrier platforms. According to the perpendicular geometric relationship between the intermediate eigenvector of dipole and the dipolemeasurement point displacement vector, Yin et al established a related equation, which simplified the structure of a third-order gradient tensor measurement array, and achieved single-point localization of the dipole.18 This method can effectively inhibit the disturbance caused by the geomagnetic field and provide an accurate localization result; a higher-order gradient tensor is dramatically affected by the measurement noise, requiring very high instrument precision. Simulations were performed in order to test the proposed method
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