Research on the asphericity error elimination of the invariant of magnetic gradient tensor

Abstract

Real-time, point-by-point localization of magnetic targets such as ferrous unexploded ordnance can be achieved by the cube magnetic gradiometer system designed by the Naval Surface Warfare Center. The localization method uses the Frobenius norm of the magnetic gradient tensor to calculate the location of the magnetic target. This method assumes that the potential field of the Frobenius norm of the magnetic gradient tensor is a prefect sphere. But the Frobenius norm of the magnetic gradient tensor has an asphericity parameter, and its potential field is an ellipsoid, which can cause asphericity error. Since the current localization method can be affected seriously by the asphericity error, an improved method is proposed in this paper to eliminate the asphericity error. The improved method is based on a new invariant, which does not contain asphericity parameter. The new invariant can be obtained by the combination of the Frobenius norm and eigenvalues of the magnetic gradient tensor. In detail the procedure is as follows: first, the magnetic gradient tensor of the center point of the regular hexahedron's six planes can be measured by the cube magnetic gradiometer system, then these eigenvalues can be calculated and combined according to a certain relationship to eliminate the asphericity parameter, then the new invariants of the six planes can be obtained, and the spatial gradient of the new invariant can be calculated from the six new invariants, then the localization of the magnetic target can be calculated from the spatial gradient of the new invariant. This improved method can overcome the asphericity error effectively, and it can be used for real-time, point-by-point localization and detection of unexploded ordnance. Simulation experiments show that the localization error of the improved method is much smaller than that of the original method, the average relative error can be reduced by 10.9%. The improved method can be deployed on the highly maneuverable platform. The platform motion will not be constrained, and the improved method will be made more effectively in detection and localization of the magnetic targets. Thus the improved method can be widely applied in naval mines localization, mineral exploration, ferrous resources exploration, moving magnetic target tracking, and other fields.