Dynamic Data-Driven Adaptive Observations in Data Assimilation for Multi-scale Systems

This chapter considers several research topics that encompass the area of Dynamic Data Driven Applications Systems (DDDAS), and describes the multidisciplinary methods required for the analysis and prediction of complex systems. It focuses on developing new algorithms and tools for the collection, assimilation and harnessing of data by threading together ideas from random dynamical systems to information theory. A general overview of the multi-scale signal and observation processes, the multidisciplinary methods required for their analysis, and a new particle filtering algorithm that combines homogenization with filtering theory are presented. Importance sampling and control methods are then used as a basic and flexible tool for the construction of the proposal density inherent in particle filtering for approximating the real time filtering of chaotic signals. Finally the chapter describes an information theoretic method, which follows naturally from the expected uncertainty minimization criterion, for dynamic sensor selection in filtering problems. It is compared with a strategy based on finite-time Lyapunov exponents of the dynamical system, which provide insight into error growth due to signal dynamics.