We introduce a new method to estimate the integrated volatility (IV) based on noisy high-frequency data. Our method employs the ReMeDI approach introduced by Li and Linton (2021a) to estimate the moments of the microstructure noise and thereby eliminate their influence, and the pre-averaging method to target the volatility parameter. The method is robust: it can be applied when the efficient price exhibits stochastic volatility and jumps, the observation times are random and endogenous, and the noise process is nonstationary, autocorrelated and dependent on the efficient price. We derive the limit distribution for the proposed estimators under infill asymptotics in a general setting. Our simulation and empirical studies demonstrate the robustness, accuracy and computational efficiency of our estimators compared to several alternatives recently proposed in the literature.