Dynamic estimation, the assimilation of data over time, is an important scientific issue in remote sensing, image processing, and computer vision, to name a few.; The main motivation for this thesis is large-scale 2-D dynamic estimation problems related to remote sensing. For such problems, number of variables to be estimated can reach to the order of millions. As a result, direct application of conventional estimation algorithm, i.e., the Kalman filter, becomes totally impractical from two technical aspects: computational and storage demands. In this thesis, we propose a new method for large-scale 2-D estimation problems that emulates the Kalman filter, but with more efficient computational and storage demands.; Using parameterized error models to model the huge error covariance matrices is the main contribution of this thesis. Under this scope, we develop a new approximate error prediction step and a new approximate large-scale update step.; We studied the performance of the proposed method in the context of small synthetic 2-D diffusion processes. In addition, we applied our method to a large-scale remote sensing problem: the estimation of the ocean surface temperature based on sparse satellite measurements.
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