  We explore the ability of a qubit probe to characterize unknown parameters of
its environment. By resorting to quantum estimation theory, we analytically
find the ultimate bound on the precision of estimating key parameters of a
broad class of ubiquitous environmental noises ("baths") which the qubit may
probe. These include the probe-bath coupling strength, the correlation time of
generic bath spectra, the power laws governing these spectra, as well as their
dephasing times T2. Our central result is that by optimizing the dynamical
control on the probe under realistic constraints one may attain the maximal
accuracy bound on the estimation of these parameters by the least number of
measurements possible. Applications of this protocol that combines dynamical
control and estimation theory tools to quantum sensing are illustrated for a
nitrogen-vacancy center in diamond used as a probe.
