Satellite-based aerosol optical depth (AOD) data are widely used to estimate land surface ${\mathrm{PM}}_{2.5}$ concentrations in areas not covered by ground ${\mathrm{PM}}_{2.5}$ monitoring stations. However, AOD data obtained from satellites are typically at coarse spatial resolutions, limiting their applications on small or medium scales. In this paper, we propose a new two-step approach to estimate 1-km-resolution ${\mathrm{PM}}_{2.5}$ concentrations in Shanghai using high spatial resolution AOD retrievals from MODIS. In the first step, AOD data are refined to a $1\times 1{\mathrm{km}}^2$ resolution via a Bayesian AOD retrieval method. In the second step, a hierarchical Gaussian process model is used to estimate ${\mathrm{PM}}_{2.5}$ concentrations. We evaluate our approach by model fitting and out-of-sample cross-validation. Our results show that the proposed approach enjoys accurate predictive performance in estimating ${\mathrm{PM}}_{2.5}$ concentrations.