Theoretical Investigation on the Linear Location Algorithm of the Magnetic Gradient Tensor Ranging by Use of Cuboid Triaxial Magnetometer Array

The passive magnetic detection and localization technology of the magnetic field has the advantages of good concealment, continuous detection, high efficiency, reliable use, and rapid response. It has important application in the detection and localization of submarines and mines. The conventional location algorithm needs magnetic gradient tensor system moving to other points, we propose a kind of linear location algorithm with a unique solution based on a single measurement of the cuboid tri-axial magnetometer array. The magnetic gradient tensor of the magnetic target is first calculated at the center points of the six rectangles of the cuboid array, and then the distance between the magnetic target and the rectangle center of the cuboid array is calculated. Finally, according to the square difference of the distances of the three pairs of parallel rectangles, a linear equation set about the position coordinates of the magnetic dipole is formed and then these position coordinates are calculated fast. We derive an analytical formula of the location error for the linear location algorithm. The simulation shows that the position of the target can be calculated accurately and the relative error of the position is <1%, and the location errors are positively correlated with the noise standard deviation of the three-axis magnetometer, and more they are proportional to the non-orthogonality between every two axes, sensitivity deviation and bias of the three-axis magnetometer. The location errors of the linear location algorithm through numerical simulations are consistent with the location errors calculated by the analytical formula.