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| Research on Analytical Positioning Method of Magnetic Sensors for Inversion Modeling of Electromagnetic Devices |
| Jin Yinxi1,2, Li Liyi1,2,3, Chen Chen4, Pan Donghua1,2,5, Lin Shengxin1,2 |
1. State Key Laboratory of Space Environment Interation with Matters Harbin Institute of Technology Harbin 150001 China;
2. School of Electrical Engineering and Automation Harbin Institute of Technology Harbin 150001 China;
3. Institute of Space Environment and Material Science Harbin Institute of Technology Harbin 150001 China;
4. No. 710 R &D Institute CSSC Yichang 443003 China;
5. Zhengzhou Research Institute Harbin Institute of Technology Zhengzhou 450018 China |
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Abstract The inverse problem of the electromagnetic field refers to the reverse calculation of an equivalent mathematical model from the measurement data of the electromagnetic field generated by the electromagnetic equipment. This method is widely applied in fields such as deep space magnetic detection, geological exploration, and geophysical detection. Among them, the positioning accuracy of the magnetic sensor directly affects the inversion accuracy of the magnetic characteristics of the electromagnetic equipment. The positioning method of magnetic sensors based on the nonlinear least square optimization algorithm is relatively complex, involves a large amount of computation, and may obtain local optimal solutions. Meanwhile, the traditional analytical positioning algorithm is easily affected by random magnetic interference due to insufficient test data, resulting in relatively low measured positioning accuracy. To address the aforementioned issue, a novel analytical positioning method of magnetic sensors based on a magnetic beacon is proposed.
Firstly, a combination of five permanent magnets was taken as the equipment to be tested, and its equivalent model was established by using the spherical harmonic function method. Through this model, the influence of the positioning error of the magnetic sensor on its modeling accuracy was quantitatively analyzed.
Subsequently, in order to achieve high-precision positioning of the magnetic sensor, the magnetic field distribution generated by the magnetic beacon was obtained through the rotation test method and the corresponding Fourier coefficients were calculated. Then, the expression of the Fourier coefficients was simplified and calculated, and the explicit expression of the spatial coordinates of the magnetic sensor was derived.
Finally, the accuracy of the magnetic sensor positioning algorithm based on the magnetic beacon was verified respectively by the finite element method and experimental tests, thereby supporting the further improvement of the inversion accuracy of the magnetic characteristics of electromagnetic equipment.
The following conclusions can be drawn: (1) By combining the spherical harmonic function expression of the magnetic beacon and the Fourier coefficients of the magnetic measurement data, the explicit expression of the spatial coordinates of the magnetic sensor was derived. This overcame the limitations of local optimal solutions or correlation with the initial values in the nonlinear least squares optimization algorithm and exhibited stronger anti-random interference ability compared with the traditional analytical positioning algorithm. (2) Verified by the finite element method, the magnetic sensor positioning algorithm has a standard deviation of 1.058 mm under Gaussian noise with a variance of 10 nT after 1 000 repeated calculations. (3) Through experimental tests for inverting the magnetic moment of an energized coil, it was found that after accurately positioning the sensor position, the inversion error of the magnetic moment on the x-axis decreased from 2.61% to 2.44%, the inversion error of the magnetic moment on the y-axis decreased from 0.45% to 0.30%, the inversion error of the magnetic moment on the z-axis decreased from 1.65% to 1.04%, and the synthetic inversion error decreased from 3.12% to 2.67%. The results show that the positioning algorithm proposed in this paper can further improve the inversion accuracy of the magnetic characteristic model of electromagnetic equipment.
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Received: 06 May 2025
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2026, Vol. 41 
