Multi-Target Magnetic Positioning Using SAFCM Clustering and Invariants-Improved Tilt Angle

The positioning of multiple magnetic sources with different depths, distributions, and magnetic moments is extremely difficult. The improved tilt angle (TA) for target area recognition can be well adapted to the self-adaptive fuzzy
$c$
-means (SAFCM) clustering algorithm for the grid measurement of magnetic gradient tensors (MGTs), which provides a feasible solution to solve the complex problem of multi-target inversion. First, we improve the TA with the normalized source strengths and the tensor contraction (TC), which can accurately identify the 2-D area boundary of objects with different buried depths regardless of the magnetization direction. The grid measurements of MGT systems (MGTS) enable this process. Then, with the tensor spacial invariant relations, we calculate the source initial position coordinates corresponding to each node in the recognition area, thereby forming a dense point cloud in the space near the target real position. Finally, we introduce a penalty function into the clustering validity function (CVF) to eliminate the monotonous decreasing trend of the cluster number optimization process; thus, the SAFCM algorithm can accurately and automatically detect the number and position of centroids. The simulation shows that with the Gaussian noise of 0 mean and 5-nT/m variance, the targets number recognition accuracy of 20 magnetic dipoles is 97.6%, and the horizontal position and buried depth estimation accuracy are greater than 91.7% and 85.6%, respectively. In the real survey areas of 2.1
$\times $
2.1 and 1.2
$\times $
1.2 m, the coordinates’ estimation deviation (ED) of nine small magnets is less than 0.091 m.