  Permitting a more precise measurement to physical quantities than the
classical limit by using quantum resources, quantum metrology holds a promise
in developing many revolutionary technologies. However, the noise-induced
decoherence forces its superiority to disappear, which is called no-go theorem
of noisy quantum metrology and constrains its application. We propose a scheme
to overcome the no-go theorem by Floquet engineering. It is found that, by
applying a periodic driving on the atoms of the Ramsey spectroscopy, the
ultimate sensitivity to measure their frequency characterized by quantum Fisher
information returns to the ideal $t^2$ scaling with the encoding time whenever
a Floquet bound state is formed by the system consisting of each driven atom
and its local noise. Combining with the optimal control, this mechanism also
allows us to retrieve the ideal Heisenberg-limit scaling with the atom number
$N$. Our result gives an efficient way to avoid the no-go theorem of noisy
quantum metrology and to realize high-precision measurements.
