A system for magnetic detection of an external magnetic field is described. The system includes a nitrogen vacancy (NV) diamond material having a plurality of crystallographic axes, a radio frequency (RF) excitation source, an optical excitation source, an optical detector, and a controller. The RF radio frequency excitation source is configured to provide RF excitations to the NV diamond material to excite electron spin resonances corresponding to the RF excitations. The controller determines the spectral position corresponding to some of the electron spin resonances, determines a measured four-dimensional projection of a magnetic field based on the determined spectral positions of a subset of all of the plurality of spin resonances, where the number of spin resonances in the subset is one half of a total number of the spin resonances, and determines an estimated three-dimensional magnetic field based on the measured four-dimensional magnetic field projections.
