Application of Gauss–Newton method in magnetic dipole model

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.