Presently used magnetic target location methods are greatly affected by geomagnetism and involve complex solution processes. To address these problems, herein, a linear location method based on the two-point magnetic gradient full tensor is proposed. Moreover, the principle of single-point magnetic gradient full tensor positioning is analyzed in detail. Based on this principle, a two-point magnetic gradient full tensor location model is constructed. A linear location method is proposed. Measuring the magnetic gradient full tensor at two locations and using a linear method for the calculation of the positioning model, a more precise location of the magnetic target is achieved. The simulation results show that the proposed method significantly reduces the relative error percentages in the three magnet field directions, with the minimum value being 0.0021% in the X-direction. The maximum X-direction error of the proposed method is reduced by 18.66% compared with that of the single-point magnetic gradient full tensor positioning method. In addition, the positioning accuracy of the method is experimentally verified. The Z-direction error value is reduced to 5.48%.

In this paper, the ship’s rotating propeller is a considered as rotating magnetic dipole. The shaft-rate magnetic field is modeled, and an inversion calculation is utilized to realize the magnetic target localization. The low frequency of the shaft-rate magnetic field provides long propagation distance, high stability, and low interference by sea conditions and other noises. The magnetic field signal has an important role in target and location detection. In the developed model, the magnetic moment of the rotating magnetic dipole is decomposed into three orthogonal magnetic moments indicated by mp, mf and ml. The mentioned moments can be obtained through a three-component integration of the measured magnetic field of the rotating dipole at a point. The relation between the eigenvectors of these orthogonal magnetic moments and the coordinates of the observation position is employed to obtain the coordinates and the magnetic target position. In the simulation, the relative and absolute errors of the location method are analyzed, while the measurement noise confines the positioning distance. Finally, the rotating magnetic field of 80 points is measured, and the feasibility of the rotating magnetic model is verified. Besides, the relative mean error of 80 points is equal to 3.7%, demonstrating the feasibility of the location method. However, due to some experiment limitations, including the measurement distance, measurement error, and the experimental equipment sensitivity, the maximum relative error is obtained as 7.4% which is higher than its theoretical value.

The structural characteristics of the magnetic gradient full tensor measurement system are important factors affecting the accuracy of the magnetic gradient full tensor measurement. In order to analyze the measurement error of the cross-shaped magnetic gradient full tensor measurement system, the theoretical framework and structural configuration of the tensor system that is based on the magnetic dipole model are introduced. Four factors including the resolution, baseline length, target distance, and magnetic moment direction that cause measurement errors are simulated and analyzed. The simulation results show that the resolution, baseline length, and target distance have a great influence on the error of the measurement system. In contrast, the influence caused by the change in the magnetic moment direction is not significant. In a certain area, the resolution increases from 1 nT to 1 fT, and the error percentage of the tensor component B_yy decreases the most, reaching 2.1370%. When designing the system structure, it is necessary to comprehensively consider the measurement purpose, design cost, measurement error, and other factors. It is important to select the fluxgate according to actual needs and coordinate the relationship between the baseline length and the measurement distance, which can be effective to decrease the error. The research conclusion can provide theoretical guidance for the design of the cross-shaped magnetic gradient full tensor measurement system.

In this Study, the application of wavelet threshold denoising in weak signal detection of underwater targets under complex sea conditions is discussed. Firstly, the basic principle and steps of wavelet threshold denoising method based on Mallat decomposition are analyzed. Then a new threshold function is proposed to overcome the shortcomings of traditional Donoho hard and soft thresholds. The denoising effects of wavelet and wavelet packet threshold denoising methods under hard threshold, soft threshold and new threshold functions are simulated, and the signal-to-noise ratio (SNR) and mean square error (MSE) after denoising are taken as evaluation indexes. The results show that the improved threshold denoising method outperforms the traditional threshold denoising methods.

The magnetic gradient full-tensor measurement system is diverse, and the magnetometer array structure is complex. Aimed at the problem, seven magnetic gradient full-tensor measurement system models are studied in detail. The full-tensor measurement theories of the tensor measurement arrays are analyzed. Under the same baseline distance, the magnetic dipole model is used to simulate the measurement system. Based on different measurement systems, the paper quantitatively compares and analyzes the error of the structure. A more optimized magnetic gradient full-tensor measurement system is suggested. The simulation results show that the measurement accuracy of the planar measurement system is slightly higher than that of the stereo measurement system. Among them, the cross-shaped and square measurement systems have relatively smaller structural errors and higher measurement accuracy.

In order to comprehensively analyze the effect of error factors on the magnetic gradient tensor, an integrated error model of the magnetic gradient tensor is established. It integrates five error factors, including three-axis non-orthogonal (TANO), three-axis sensitivity inconsistency (TASI), zero offset (ZO), coordinate system misalignment (CSM) and three-axis non-common point (TANCP). In addition, an iterative orthogonal experiment method is proposed to analyze the values of error caused by these factors and determine the calibration priority of all factors. The simulation result shows that the five error factors on the magnetic tensor from great to small is: TASI, TANO, CSM, ZO, TANCP. At the same time, the error factor which has a greater effect has a higher calibration priority level. When the circumstances occur, in which not all errors need be calibrated, error factors with higher priority should be calibrated first.