In this paper, we use the nonlinear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with a precision above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly efficient single photon detectors, it should be of practical interest until highly entangled many-photon states become more readily available.