Magnetic Dipole Two-Point Tensor Positioning Based on Magnetic Moment Constraints

Huan, Liu; Wang, Xiaobin; Zhao, Changfeng; Ge, Jianhua; Dong, Haobin; Liu, Zheng

doi:10.1109/tim.2021.3105264

Cited by 19 publications

(9 citation statements)

References 23 publications

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“…When the distance between the magnetic target and the measurement point is 2.5 times or more relative to the size of the target, it can be simplified as a magnetic dipole [7,22,23]. The equivalent relationship between the target position vector and magnetic field data is established based on the magnetic dipole model.…”

Section: Location Principle Of Magnetic Gradient Tensormentioning

confidence: 99%

“…However, this method does not calibrate the measurement system, resulting in a significant positioning error. Liu explored a new two-point tensor positioning method based on the magnetic moment constraint [23]. This method introduced a particle swarm optimization algorithm to optimize objective functions and achieve better positioning performance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Magnetic target nonlinear positioning method based on planar regular octagon tensor system

Chen,

Li,

Zhang

et al. 2024

Meas. Sci. Technol.

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The magnetic target location technology based on the principle of magnetic gradient tensor has broad engineering application prospects. However, commonly used target positioning methods are easily interfered with by the geomagnetic environment. We proposed a magnetic target nonlinear positioning method to achieve precise localization of magnetic objects. An ellipsoid fitting method based on the total least square algorithm is proposed to correct the measurement system’s magnetic interference and array error. The results show that the algorithm can reduce the root mean square error of the total magnetic field strength by 93.05% to 0.1007 uT. The tensor components are all limited to 100 nT m−1. Then, a target positioning function is constructed with the magnetic moment information introduced as a constraint term, and the location of the magnetic target is optimally calculated using the Levenberg–Marquardt algorithm. The field experimental results indicate when the magnetic targets are located at (5,0,0) and (10,−5,0), the positioning errors are 5.11% and 6.62%. This technology can also achieve high-precision path tracking of magnetic targets.

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Section: Location Principle Of Magnetic Gradient Tensormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magnetic target nonlinear positioning method based on planar regular octagon tensor system

Chen,

Li,

Zhang

et al. 2024

Meas. Sci. Technol.

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show abstract

“…The optimization model described above does not include magnetic field vector terms; hence, it is not affected by geomagnetic field estimation errors. Research in [20] has shown that the optimization of the aforementioned objective function faces the challenge of potential convergence to false solutions, leading to a lower success rate and larger localization errors. Numerous studies suggest that introducing constraints into the objective function can more effectively address these issues [29].…”

Section: Principle Of Magnetic Gradient Tensor Localizationmentioning

confidence: 99%

“…The success rate of optimization is low, and it is greatly affected by the initial values. Liu Huan [20] introduced a constraint term, magnetic moment constraints, to the aforementioned optimization algorithm, reducing localization errors. However, the issue of easily falling into a local optimum still persists.…”

Section: Introductionmentioning

confidence: 99%

Two-Point Localization Algorithm of a Magnetic Target Based on Tensor Geometric Invariant

Chi,

Wang,

Tao

et al. 2024

Sensors

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Currently, magnetic gradient tensor-based localization methods face challenges such as significant errors in geomagnetic field estimation, susceptibility to local optima in optimization algorithms, and inefficient performance. In addressing these issues, this article propose a two-point localization method under the constraint of overlaying geometric invariants. This method initially establishes the relationship between the target position and the magnetic gradient tensor by substituting an intermediate variable for the magnetic moment. Exploiting the property of the eigenvector corresponding to the minimum absolute eigenvalue being perpendicular to the target position vector, this constraint is superimposed to formulate a nonlinear system of equations of the target’s position. In the process of determining the target position, the Nara method is employed for obtaining the initial values, followed by the utilization of the Levenberg–Marquardt algorithm to derive a precise solution. Experimental validation through both simulations and experiments confirms the effectiveness of the proposed method. The results demonstrate its capability to overcome the challenges faced by a single-point localization method in the presence of some errors in geomagnetic field estimation. In comparison to traditional two-point localization methods, the proposed method exhibits the highest precision. The localization outcomes under different noise conditions underscore the robust noise resistance and resilience of the proposed method.

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“…Most importantly, it has not been experimentally verified. Liu [29] constructed an objective function based on magnetic moment constraints to achieve magnetic target localization, and designed a two-point tensor measurement system composed of two cross-tensor structures arranged vertically. This method has the advantages of high environmental noise tolerance and low sensor accuracy requirements, but it used the PSO algorithm to identify the parameters, resulting in poor real-time performance.…”

Section: Introductionmentioning

confidence: 99%

A New Magnetic Target Localization Method Based on Two-Point Magnetic Gradient Tensor

et al. 2022

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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%.

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Magnetic Dipole Two-Point Tensor Positioning Based on Magnetic Moment Constraints

Cited by 19 publications

References 23 publications

Magnetic target nonlinear positioning method based on planar regular octagon tensor system

Magnetic target nonlinear positioning method based on planar regular octagon tensor system

Two-Point Localization Algorithm of a Magnetic Target Based on Tensor Geometric Invariant

A New Magnetic Target Localization Method Based on Two-Point Magnetic Gradient Tensor

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