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We propose a protocol to estimate magnetic fields using a single nitrogen-vacancy (N-V) center in diamond, where the estimate precision scales inversely with time, δB~1/T, rather than the square-root of time, δB~1/√T. The method is based on converting the task of magnetometry into phase estimation, performing quantum phase estimation on a single N-V nuclear spin using either adaptive or nonadaptive feedback control, and the recently demonstrated capability to perform single-shot readout within the N-V [ P. Neumann et al. Science 329 542 (2010)]. We present numerical simulations to show that our method provides an estimate whose precision scales close to ~1/T (T~ the total estimation time), and moreover will give an unambiguous estimate of the static magnetic field experienced by the N-V. By combining this protocol with recent proposals for scanning magnetometry using an N-V, our protocol will provide a significant decrease in signal acquisition time while providing an unambiguous spatial map of the magnetic field.
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