High spatiotemporal resolution maps of surface vegetation from remote sensing data are desirable for vegetation and disturbance monitoring. However, due to the current limitations of imaging spectrometers, remote sensing datasets of vegetation with high temporal frequency of measurements have lower spatial resolution, and vice versa. In this research, we propose a space-time dynamic linear model to fuse high temporal frequency data (MODIS) with high spatial resolution data (Landsat) to create high spatiotemporal resolution data products of a vegetation greenness index. The model incorporates the spatial misalignment of the data and models dependence within and across land cover types with a latent multivariate Matérn process. To handle the large size of the data, we introduce a fast estimation procedure and a moving window Kalman smoother to produce a daily, 30-m resolution data product with associated uncertainty.