  We investigate the problem of estimating the tunneling frequency of a
two-level atomic system embedded in a dissipative environment by employing a
numerically rigorous hierarchical equations of motion method. The effect of
counter-rotating-wave terms on the attainable precision of the noisy quantum
metrology is systematically studied beyond the usual framework of perturbative
treatments. We find the counter-rotating-wave terms are able to boost the noisy
quantum metrological performance in the intermediate and strong coupling
regimes, whether the dissipative environment is composed of bosons or fermions.
The result presented in this paper may pave a guideline to design a
high-precision quantum estimation scenario under practical decoherence.
