Multi-point magnetic field compensation for matrix coils based on sparse Bayesian learning

The stable operation of a spin-exchange relaxation-free (SERF) atomic magnetometer array requires a near-zero magnetic-field environment. However, non-uniform magnetic fields within the measurement region can still cause interference. Conventional compensation coils generate a fixed magnetic field distribution, making it difficult to simultaneously suppress residual magnetic fields at multiple points. Matrix coils composed of multiple independently driven units enable active compensation at multiple points. However, when the number of observation points is limited and noise or unmodeled errors are present, the current-inversion problem can become ill-conditioned, leading to solution instability or abnormal current amplification. To address this issue, this paper proposes a current inversion method for matrix-coil compensation based on a sparse Bayesian learning (SBL) framework. The method incorporates an automatic relevance determination (ARD) prior to adaptively suppress redundant coil channels and employs joint marginal likelihood maximization to estimate prior parameters and noise precision. Additionally, an incremental current update strategy is adopted to smooth current transitions and reduce the risk of overshoot caused by abrupt current changes. Experimental results show that when the amplitude of the disturbance magnetic field to be compensated does not exceed 3 nT, the residual magnetic field at the four target probes can be suppressed to within approximately ±0.25 nT, with a suppression rate exceeding 90%. These results indicate that the proposed method provides a promising solution for constructing near-zero magnetic environments in future SERF atomic magnetometer array systems.