A third-order magnetic gradient tensor optimization algorithm based on the second-order improved central difference method

An improved method based on the second order improved central difference method is proposed to improve the third-order magnetic gradient tensor, which is affected by noise and characterized by poor stability. The third-order magnetic gradient tensor at the center point is calculated by using the three-component magnetic field at four points along a single route; this approach effectively improves the stability of the third-order magnetic gradient tensor data. In this paper, the errors of the traditional method and the new method in calculating the third-order magnetic gradient tensor are given by the Taylor series. Based on the traditional third-order magnetic gradient tensor system, a new third-order magnetic gradient tensor system and the corresponding measurement method are presented. Through simulations, in the case of noise, it is verified that the proposed method exhibits better stability by comparing the components of the third-order magnetic gradient tensor with the positioning results. In experiments, the root-mean-square error is used to compare the positioning results before and after noise addition. The traditional method changes the root-mean-square error of the positioning results from (1.3626, 3.6573, 0.5766 m) to (3.3661, 9.5966, 1.9465 m), and the root-mean-square error obtained with the new method displays no obvious change.