Ambient field suppression is critical for accurate magnetic field measurements, and a requirement for certain low-field sensors to operate. The difference in magnitude between noise and signal (up to 10$^9$) makes the problem challenging, and solutions such as passive shielding, post-hoc processing, and most active shielding designs do not address it completely. Zero field active shielding (ZFS) achieves accurate field suppression with a feed-forward structure in which correction coils are fed by reference sensors via a matrix found using data-driven methods. Requirements are a sufficient number of correction coils and reference sensors to span the ambient field at the sensors, and to zero out the coil-to-reference sensor coupling. The solution assumes instantaneous propagation and mixing, but it can be extended to handle convolutional effects. Precise calculations based on sensor and coil geometries are not necessary, other than to improve efficiency and usability. The solution is simulated here but not implemented in hardware.

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