2014 Rice Oil & Gas HPC

The Kalman Filter uses a sequence of noisy observations of a system over time to produce a sequence of approximations of the state of the system. Many variations of the original Kalman Filter have been proposed and applied in a wide variety of sciences and engineering fields, such as aerospace, meteorology, geophysics, oceanology, and reservoir simulation. However, often no connections between newly proposed variants and existing ones are made and no comparisons are given. I will evaluate and compare the efficiency of recently proposed Krylov space approximate Kalman filters and of the Ensemble Kalman filter on large-scale time dependent partial differential equation models. In addition, my work establishes theoretical connections between different variations of the Kalman filter, identifies their relative advantages and weaknesses, and exposes opportunities for algorithmic improvements. Future work will include analysis and implementation of these algorithmic improvements to increase the efficiency of Kalman Filter for large-scale nonlinear problems.