  We propose an efficient quantum measurement protocol for the hyperfine
interaction between the electron spin and the $^{15}$N nuclear spin of a
diamond nitrogen-vacancy center. In this protocol, a sequence of quantum
operations of successively increasing duration is utilized to estimate the
hyperfine interaction with successively higher precision approaching the
quantum metrology limit. This protocol does not need the preparation of the
nuclear spin state. In the presence of realistic operation errors and electron
spin decoherence, the overall precision of our protocol still surpasses the
standard quantum limit.
