Accurate magnetic field estimation in fiber-coupled nanodiamond NV ensembles using model-assisted regression

Fiber-coupled ensembles of nanodiamonds containing nitrogen-vacancy (NV) centers are widely used for microscopic magnetic field measurements. However, the random distribution of NV crystal axes in nanodiamond ensembles causes resonance frequencies from differently oriented NV centers to overlap in the ODMR spectrum, distorting the spectral line shape and breaking the linear mapping between frequency shift and magnetic field. As a result, conventional magnetic field measurements based on Lorentzian fitting suffer from significant systematic errors. Here, we establish a fiber-nanodiamond ensemble model to analyze the impact of random NV orientations on the ODMR linear response and define an effective ensemble-averaged linear response coefficient K. Fisher information analysis identifies an information-optimal intrinsic magnetic field of approximately 640 µT, at which the ensemble response can be reliably approximated as linear in its vicinity. Building on this condition, we propose a model-assisted regression scheme, in which the physical fiber-nanodiamond ensemble model defines the optimal operating condition and the associated linear frequency-field scaling, while intrinsic-field-guided Gaussian regression (IFGGR) extracts magnetic-field-induced frequency shifts from distorted ensemble ODMR spectra, enabling accurate magnetic field estimation via the response coefficient K. Under identical acquisition conditions, the proposed method reduces the RMSE from 37.21 µT to 8.99 µT and significantly suppresses systematic bias, while achieving an absolute sensitivity approaching the shot-noise limit at optimal averaging time. The relative slope error reduction (≈15.6-fold) further confirms improved local linearity near the optimal operating point.