  In realistic metrology, entangled probes are more sensitive to noise,
especially for a correlated environment. The precision of parameter estimation
with entangled probes is even lower than that of the unentangled ones in a
correlated environment. In this paper, we propose a measurement scheme with
only one auxiliary qubit, which can selectively offset the impact of
environmental noise under this situation. We analyse the estimation precision
of our scheme and find out that it approaches the Heisenberg limit when
prepared in a proper auxiliary state. We further discuss employing auxiliary
states to improve the precision of measurement in other environment models such
as a partially-correlated environment. In order to verify our scheme, we apply
a recently-developed quantum algorithm to simulate the quantum dynamics of our
proposal and show that it outperform the other proposals with less resources.
