The existing magnetic target localization methods are greatly affected by the geomagnetic field and exist approximation errors. In this paper, a two-point magnetic gradient tensor localization model is established by using the spatial relation between the magnetic target and the observation points derived from magnetic gradient tensor and tensor invariants. Based on the model, the equations relating to the position vector of magnetic target are constructed. Solving the equations, a new magnetic target localization method using only a two-point magnetic gradient tensor and no approximation errors is achieved. To accurately evaluate the localization accuracy of the method, a circular trajectory that varies in all three directions is proposed. Simulation results show that the proposed method is almost error-free in the absence of noise. After adding noise, the maximum relative error percentage is reduced by 28.4% and 2.21% compared with the single-point method and the other two-point method, respectively. Furthermore, the proposed method is not affected by the variation in the distance between two observation points. At a detection distance of 20 m, the maximum localization error is 1.86 m. In addition, the experiments also verify that the new method can avoid the influence of the geomagnetic field and the variation in the distance, and achieve high localization accuracy. The average relative error percentage in the y-direction is as low as 3.78%.

In the field of high-precision physical field detection, measurements based on magnetic signals are crucial due to their exceptional accuracy, sensitivity, and stability. Superconducting Quantum Interference Devices (SQUIDs), with their ultra-high sensitivity, have become key in detecting minute changes in magnetic flux. However, with increasing demands for higher precision, further enhancing device performance under quantum constraints remains a significant challenge. This study improved the precision of SQUID sensors by optimizing the geometry of microscale washers using the physical response of superconducting films under micromachining technologies and quantum constraints. Our research extensively examined the effects of square, octagonal, and circular washers on the magnetic field response, shielding currents, and inductance. Experimental results showed that, compared to traditional square washers, octagonal washers significantly enhanced sensor sensitivity and efficiency by minimizing edge magnetic flux and optimizing current distribution. Notably, all observed inductance values exceeded predictions based on traditional empirical formulas, with square washers showing the highest average relative error of 80.8%, while circular and octagonal washers had errors of 65.31% and 66.43%, respectively. This breakthrough not only lays a new theoretical foundation for the design of SQUID sensors but also provides robust evidence for enhancing magnetic field detection through microscale technological innovation.

In practical application, existing two-point magnetic gradient tensor (MGT) localization methods have a maximum detection distance of only 2.5 m, and the magnetic moment vectors of measured targets are all unknown. In order to realize remote, real-time localization, a new two-point magnetic localization method based on self-developed, ultra-sensitive superconducting quantum interference device (SQUID) magnetometers and MGT invariants is proposed. Both the magnetic moment vector and the relative position vector can be directly calculated based on the linear positioning model, and a quasi-Newton optimization algorithm is adopted to further improve the interference suppression capability. The simulation results show that the detection distance of the proposed method can reach 500 m when the superconducting MGT measurement system is used. Compared with Nara’s single-point tensor (NSPT) method and Xu’s two-point tensor (XTPT) method, the proposed method produces the smallest relative localization error (i.e., significantly less than 1% in the non-positioning blind area) without sacrificing real-time characteristics. The causes of and solutions to the positioning blind area are also analyzed. The equivalent experiments, which were conducted with a detection distance of 10 m, validate the effectiveness of the localization method, yielding a minimum relative localization error of 4.5229%.

Vector magnetometer arrays are essential for ferromagnetic target detection and MGT measurement, but their performance is limited by proportional factor errors, triaxial non-orthogonality, soft/hard iron interference, and inconsistent array orientations. Traditional rotation-based scalar calibration requires magnetic-free turntables or manual multi-orientation operations, introducing mechanical noise, orientation perturbations, and poor repeatability. This paper proposes an in situ rapid calibration method for MGT systems using triaxial Helmholtz coils. By generating three-dimensional magnetic field sequences of constant magnitude and random directions while keeping the sensors stationary, the method replaces conventional rotational excitation. A two-stage rapid calibration algorithm is developed to achieve individual sensor error modeling and array relative calibration. Experimental results show substantial improvements. The tensor invariant C_T decreased from 6287.84 nT/m to 7.57 nT/m, with variance reduced from 1.46 × 10⁶ to 13.47 nT²/m²; inter-sensor output differences were suppressed to 1–3 nT; and the magnetic field magnitude error dropped from ~940 nT to 3 × 10⁻⁴ nT, achieving a 5–6-order-of-magnitude enhancement. These results verify the method’s effectiveness in eliminating rotational errors, improving array consistency, and enabling high-precision in situ calibration with strong engineering value.

Accurate calibration is essential for ensuring the performance of magnetic gradient tensor (MGT) arrays. Existing calibration methods generally rely on mechanical rotation to obtain magnetic responses under multiple orientations. However, for large-scale cubic MGT arrays, rotating the entire array using a high-precision non-magnetic turntable is often costly and impractical, while manual rotation is difficult to control and may introduce array-center offsets. To address these limitations, this paper proposes a rotation-free scalar calibration framework for cubic MGT arrays, in which a tri-axial Helmholtz coil system generates constant-magnitude magnetic fields with randomized orientations while compensating for ambient magnetic drifts. Based on the acquired data, a hierarchical calibration algorithm is developed to estimate sensor-level intrinsic errors and array-level misalignment errors. Experimental results show that the proposed method reduces the joint tensor invariant $C_T$ from $9.07\times {10}^3$ nT/m to 11.51 nT/m, corresponding to a 99.87% reduction. In addition, compared with a conventional rotation-based fast calibration method, the proposed framework further decreases the mean and RMS of the joint $C_T$ by 62.7% and 63.1%, respectively. These results demonstrate that the proposed framework improves the spatial consistency of the MGT array and provides a practical calibration solution for large-scale MGT array systems.