High resolution direction-of-arrival (DOA) estimation is an important problem in many array signal processing applications. This paper proposes an augmented covariance estimator for DOA estimation. The new method exploits the periodicity of the covariance lags when the DOAs are assumed on a discrete grid with a certain resolution. Then, it achieves twice the resolution of typical methods such as the direct augmentable approach or forward backward spatial smoothing. When the sources are not on the discrete grid, an interpolated array manifold technique is proposed to mitigate the grid mismatch error.