Datasets from remote-sensing platforms and sensor networks are often spatial, temporal, and very large. Processing massive amounts of data to provide current estimates of the (hidden) state from current and past data is challenging, even for the Kalman filter. A large number of spatial locations observed through time can quickly lead to an overwhelmingly high-dimensional statistical model. Dimension reduction without sacrificing complexity is our goal in this article. We demonstrate how a Spatio-Temporal Random Effects (STRE) component of a statistical model reduces the problem to one of fixed dimension with a very fast statistical solution, a methodology we call Fixed Rank Filtering (FRF). This is compared in a simulation experiment to successive, spatial-only predictions based on an analogous Spatial Random Effects (SRE) model, and the value of incorporating temporal dependence is quantified. A remote-sensing dataset of aerosol optical depth (AOD), from the Multi-angle Imaging SpectroRadiometer (MISR) i...

Spatial statistical analysis of massive amounts of spatial data can be challenging because computation of optimal procedures can break down. The Spatial Random Effects (SRE) model uses a fixed numb...