中国物理B ›› 2025, Vol. 34 ›› Issue (10): 100701-100701.doi: 10.1088/1674-1056/addcd1

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Application of Gauss-Newton method in magnetic dipole model

Junchen Gao(高骏琛)1, Chaobo Liu(刘超波)2, Jinjing Zhang(张津菁)1, Yu Duan(段宇)1, Hao-Ran Yang(杨浩冉)1, and Daqiang Gao(高大强)1,†   

  1. 1 College of Physical Science and Technology, Key Laboratory of Magnetism and Magnetic Materials, Ministry of Education, Lanzhou University, Lanzhou 730000, China;
    2 Beijing Institute of Spacecraft Environment Engineering, Beijing 100000, China
  • 收稿日期:2025-03-24 修回日期:2025-05-19 接受日期:2025-05-26 发布日期:2025-09-25
  • 通讯作者: Daqiang Gao E-mail:gaodqxz@sina.com
  • 基金资助:
    Project supported by the National Key Research and Development Program of China (Grant No. 2023YFC2206003).

Application of Gauss-Newton method in magnetic dipole model

Junchen Gao(高骏琛)1, Chaobo Liu(刘超波)2, Jinjing Zhang(张津菁)1, Yu Duan(段宇)1, Hao-Ran Yang(杨浩冉)1, and Daqiang Gao(高大强)1,†   

  1. 1 College of Physical Science and Technology, Key Laboratory of Magnetism and Magnetic Materials, Ministry of Education, Lanzhou University, Lanzhou 730000, China;
    2 Beijing Institute of Spacecraft Environment Engineering, Beijing 100000, China
  • Received:2025-03-24 Revised:2025-05-19 Accepted:2025-05-26 Published:2025-09-25
  • Contact: Daqiang Gao E-mail:gaodqxz@sina.com
  • Supported by:
    Project supported by the National Key Research and Development Program of China (Grant No. 2023YFC2206003).

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摘要： With the increasing accuracy requirements of satellite magnetic detection missions, reducing low-frequency noise has become a key focus of satellite magnetic cleanliness technology. Traditional satellite magnetic simulation methods have matured in static magnetic dipole simulations, but there is still significant room for optimization in the simulation and computation of low-frequency magnetic dipole models. This study employs the Gauss-Newton method and Fourier transform techniques for modeling and simulating low-frequency magnetic dipoles. Compared to the traditional particle swarm optimization (PSO) algorithm, this method achieves significant improvements, with errors reaching the order of 10$^{-13}$% under noise-free conditions and maintaining an error level of less than 0.5% under 10% noise. Additionally, the use of Fourier transform and the Gauss-Newton method enables high-precision magnetic field frequency identification and rapid computation of the dipole position and magnetic moment, greatly enhancing the computational efficiency and accuracy of the model.

关键词: magnetic dipole model, Gauss-Newton method, Fourier transform, inversion accuracy

Abstract: With the increasing accuracy requirements of satellite magnetic detection missions, reducing low-frequency noise has become a key focus of satellite magnetic cleanliness technology. Traditional satellite magnetic simulation methods have matured in static magnetic dipole simulations, but there is still significant room for optimization in the simulation and computation of low-frequency magnetic dipole models. This study employs the Gauss-Newton method and Fourier transform techniques for modeling and simulating low-frequency magnetic dipoles. Compared to the traditional particle swarm optimization (PSO) algorithm, this method achieves significant improvements, with errors reaching the order of 10$^{-13}$% under noise-free conditions and maintaining an error level of less than 0.5% under 10% noise. Additionally, the use of Fourier transform and the Gauss-Newton method enables high-precision magnetic field frequency identification and rapid computation of the dipole position and magnetic moment, greatly enhancing the computational efficiency and accuracy of the model.

Key words: magnetic dipole model, Gauss-Newton method, Fourier transform, inversion accuracy

中图分类号:  (Magnetometers for magnetic field measurements)

  • 07.55.Ge
02.30.Zz (Inverse problems) 41.20.Gz (Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems) 02.60.Pn (Numerical optimization)