Dimensional Reduction for Filters of Nonlinear Systems with Time-Scale Separation
Final rept. 15 Apr 2008-30 Nov 2011
BOARD OF TRUSTEES OF THE UNIV OF ILLINOIS CHAMPAIGN
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This project outlines a collection of problems which combine techniques of model reduction and filtering. The basis of this work is a collection of limit theories for stochastic processes which model dynamical systems with multiple time scales. These different time scales often allow one to find effective behaviors of the fast time scales. When the rates of change of different variables differ by orders of magnitude, efficient data assimilation can be accomplished by constructing nonlinear filtering equations for the coarse-grained signal. In particular, we study how scaling interacts with filtering via stochastic averaging. We combine our study of stochastic dimensional reduction and nonlinear filtering to provide a rigorous framework for identifying and simulating filters which are specifically adapted to the complexities of the underlying multi-scale dynamical system.
- Statistics and Probability
- Operations Research