Data Assimilation Methods for Dynamical Systems With Poor Observability

Daniel Rey, University of California, San Diego

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State and parameter estimation is a fundamental process that involves the transfer of information from measured data to a mathematical model developed to describe a complex dynamical system. The result is an estimate for the initial state of the system, which is needed to validate the model or make a quantitative prediction. This search becomes especially difficult when the model is chaotic and the number of observations at any given time is insufficient. Such conditions are quite typical in practice. We show how to use the concept of time delay embedding, familiar from nonlinear dynamics, to augment the set of available measurements and further stabilize the estimation process. The idea is general enough to be applied to a variety of filtering algorithms (such as the Kalman filter and its nonlinear extensions) to improve their stability and convergence.

Abstract Author(s): Daniel Rey, Henry D.I. Abarbanel