Large-scale 2D dynamic estimation

Abstract

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 developed 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.