磁梯度张量不变量的椭圆误差消除方法研究

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

基于磁梯度张量不变量定位方法,可以实现对目标的单点实时定位,且定位目标不限于静止目标,这一方法目前得到了人们的广泛关注,但该方法由于存在着椭圆系数导致目标定位误差较大的问题.针对该问题,提出了一种基于正六面体磁梯度张量测量系统的单点实时定位改进方法,该方法通过消除原定位方法中不变量存在的椭圆系数,从而克服椭圆误差对定位精度的影响.具体做法是通过求解测量系统中正六面体的六个平面中心点处磁梯度张量的特征值,并把这些特征值按照一定关系进行组合来消除椭圆系数,来获得六个平面的新不变量,再对这些新不变量求其梯度值,根据这些梯度值对目标进行定位,这样该定位方法可以有效的克服椭圆误差,可对目标进行单点实时定位.对改进定位方法进行了仿真实验分析,结果表明改进方法可以实现目标的单点实时定位,定位的平均相对误差较现有方法减少10.9%.改进方法对所搭载平台的机动性要求较低,其平台可做直线或曲线运动对目标实现单点实时定位.

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.