  Experimental noise often contains valuable information on the interactions of
a system with its environment but establishing a relation between the measured
time fluctuations and relevant physical observables is rarely apparent. Here,
we leverage a multi-dimensional and multi-sensor analysis of spectral diffusion
to investigate the dynamics of carriers in charge traps surrounding color
center clusters in diamond. Working with nitrogen-vacancy (NV) centers sharing
the same diffraction-limited volume, we establish statistical correlations in
the spectral changes we measure as we recursively probe the optical resonances
of the cluster, which we subsequently exploit to unveil proximal traps. By
simultaneously co-monitoring the spectra of multiple NVs in the set, we show
the ability to deterministically induce Stark shifts in the observed optical
resonances, hence allowing us to identify electrostatically coupled sets of
emitters. These cross-correlated measurements allow us to determine the
relative three-dimensional positions of interacting NVs in a cluster as well as
the location and charge sign of proximal traps. Our results can be generalized
to other color centers and open intriguing opportunities for the microscopic
characterization of photo-carrier dynamics in semiconductors and for the
manipulation of nanoscale spin-qubit clusters connected via electric fields.
