  We present a protocol to perform self-stabilizing measurements on noisy
qubits. We employ rapid purification in a rotating frame whose frequency is
estimated and periodically updated via a Bayesian estimation scheme. The
Bayesian estimation protocol employs the continuous measurement record to
improve the estimate, which in turn purifies the qubit more. This procedure
stabilizes the qubit. Such an adaptive measurement scheme serves the purpose of
purifying the state, while minimally interfering with the phase estimation.
