Multi-Factor Error Modeling and Analysis of Magnetic Source Inversion
Lin Shengxin1, Li Yi1, Jin Yinxi1,2, Pan Donghua1,2,3, Li Liyi1,2
1. School of Electrical Engineering Harbin Institute of Technology Harbin 150001 China; 2. Laboratory for Space Environment and Physical Sciences Harbin Institute of Technology Harbin 150028 China; 3. Zhengzhou Research Institute Harbin Institute of Technology Zhengzhou 450000 China
Abstract：High-precision magnetic source inversion is critical for applications such as biomagnetic navigation, vehicle tracking, and buried object detection. Accurate error modeling and in-depth analysis are crucial for identifying error sources and formulating effective compensation strategies. Existing studies frequently overlook the impact of the target's position and posture, and they often lack analysis of the coupling effects between multiple factors. This work establishes a comprehensive, multi-factor error model that considers position, posture, background magnetic interference and sensor array errors. To overcome the limitations of traditional magnetic source information functions, a novel Dual-Sphere Function is proposed, introducing complete position,posture parameters and decoupling them via their relative angles for a more accurate representation of the magnetic source. A diamond grid tessellation method is introduced for uniform sampling on the spherical surfaces, ensuring analysis accuracy while reducing computational time by over 75% compared to conventional tessellation. Based on the multi-factor error model constructed earlier, a multi-factor error analysis was conducted using the controlled variable method, with the scalar triangulation and ranging (STAR) method and Wang-STAR (WS) method as the research objects. Firstly, the analysis of inversion system parameters revealed that as the inversion distance and the baseline distance of the sensor array increase, the global positioning accuracy first improves and then declines.The WS method is more sensitive to magnetic sensor resolution, and when the resolution exceeds 5 nT, its accuracy becomes inferior to that of the STAR method. Secondly, the analysis of background magnetic interference showed that a uniform magnetic field has no significant impact on positioning accuracy.The WS method is more sensitive to magnetic noise—if the noise exceeds 2 nT, its accuracy is lower than that of the STAR method.In the geomagnetic environment, the accuracy of the two algorithms decreases by 506% and 3758% respectively compared with that in the zero-magnetic environment. Finally, in the study of sensor array errors, the zero bias error exerts the most significant impact on positioning accuracy, while the influence of other errors is comparable. After correction using the calibration model, the positioning errors of the STAR method and WS method are reduced by 76.68% and 94.65% respectively. Calibration of the sensor array was conducted in a magnetic shielding room (MSR) with an internal space of 3.6 m×3.6 m×3.6 m, and experimental verification was carried out on this basis. The results show that the measured positioning errors under different magnetic source postures are highly consistent with the model predictions. For the STAR method, the positioning error is 0.026 9 m in the simulation model and 0.027 7 m in the experiment. For the WS method, the positioning error is 0.013 1 m in the simulation model and 0.013 4 m in the experiment. The deviation between the experimental and the calculation results of the error model does not exceed 2.9%, which verifies the accuracy and reliability of the proposed multi-factor error model and analysis method. This research outcome provides a solid theoretical foundation for the optimization of error compensation and the design of sensor arrays in magnetic source inversion systems.
林生鑫, 李弋, 金银锡, 潘东华, 李立毅. 磁源反演的多因素误差建模与分析[J]. 电工技术学报, 2026, 41(19): 6437-6448.
Lin Shengxin, Li Yi, Jin Yinxi, Pan Donghua, Li Liyi. Multi-Factor Error Modeling and Analysis of Magnetic Source Inversion. Transactions of China Electrotechnical Society, 2026, 41(19): 6437-6448.
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2026, Vol. 41 
