  In quantum metrology schemes, one generally needs to prepare $m$ copies of
$N$ entangled particles, such as entangled photon states, and then they are
detected in a destructive process to estimate an unknown parameter. Here, we
present a novel experimental scheme for estimating this parameter by using
repeated indirect quantum nondemolition measurements in the setup called
"photon box". This interaction-based scheme is able to achieve the phase
sensitivity scaling as $1/N$ with a Fock state of $N$ photons. Moreover, we
only need to prepare one initial $N$-photon state and it can be used
repetitively for $m$ trials of measurements. This new scheme is shown to
sustain the quantum advantage for a much longer time than the damping time of
Fock state and be more robust than the common strategy with exotic entangled
states. To overcome the $2\pi/N$ periodic error in the estimation of the true
parameter, we can employ a cascaded strategy by adding a real-time feedback
interferometric layout.
