In studies of volatility estimation based on high-frequency data, existing literature most often assumes the market microstructure noise is random and additive on log prices. Research for situations where the market microstructure noise is due to rounding to the price grids is also available. However, despite the practical relevance of co-presence of random noise and rounding, the existing methods only focus on one type of noise and hence suffer from biases when both types of noise are present. This paper is the first attempt to complete the literature by a unified approach for volatility estimation in the presence of either one or both rounding and random market microstructure noise. The proposed volatility estimation method enjoys superior asymptotic properties. Numerical studies via simulation and empirical analysis show that compared with existing popular estimation methods, the performance of our proposed method can be substantially better in terms of finite sample bias, standard error and robustness over different sampling frequencies. Based on Joint work with Zhiyuan Zhang and Yichu Li