Magnetic field recovery technique based on distance weighting multipole expansion method

A space-borne gravitational wave detector requires the test mass (TM) to be in an ultra-low disturbance state. However, magnetic field fluctuations will disturb the TM and produce acceleration noise. To assess the influence of the magnetic field on the TM, it is necessary to monitor and reconstruct the magnetic field near the TM in real time. In this paper, a distance weighting multipole expansion (DWME) method was proposed, and its magnetic field reconstruction accuracy was analyzed. The results demonstrated that the proposed DWME method significantly improved the reconstruction precision compared to traditional methods. It reduced the average reconstruction error of the sensitive axial magnetic field from 1.2% to 0.8% and the maximum error from 16% to 8%. In the in-orbit situation, the DWME method also outperforms traditional methods.