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In quantum metrology schemes, one generally needs to prepare $m$ copies of$N$ entangled particles, such as entangled photon states, and then they aredetected in a destructive process to estimate an unknown parameter. Here, wepresent a novel experimental scheme for estimating this parameter by usingrepeated indirect quantum nondemolition measurements in the setup called"photon box". This interaction-based scheme is able to achieve the phasesensitivity scaling as $1/N$ with a Fock state of $N$ photons. Moreover, weonly need to prepare one initial $N$-photon state and it can be usedrepetitively for $m$ trials of measurements. This new scheme is shown tosustain the quantum advantage for a much longer time than the damping time ofFock state and be more robust than the common strategy with exotic entangledstates. To overcome the $2\pi/N$ periodic error in the estimation of the trueparameter, we can employ a cascaded strategy by adding a real-time feedbackinterferometric layout.

Quantum Metrology via Repeated Quantum Nondemolition Measurements in "Photon Box"