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DY: Fachverband Dynamik und Statistische Physik
DY 17: Modeling and Data Analysis
DY 17.6: Talk
Tuesday, March 17, 2015, 10:45–11:00, BH-N 333
State estimation and observability analysis employing delay coordinates — •Ulrich Parlitz1,2, Jan Schumann-Bischoff1,2, and Stefan Luther1,2 — 1Max Planck Institute for Dynamics and Selforganization, Göttingen, Germany — 2Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Germany
For many dynamical processes in physics and other fields of science a model is known, but some of its variables and parameter values are difficult to observe or measure directly. In this case one may try to estimate the unknown quantities by adapting the model to time series generated by the process of interest. We shall revisit this problem by addressing the question whether the estimation problem is solvable in principle (observability) [1,2] and how synchronization based estimation methods can be improved to achieve good estimates based on few observables, only [3]. For both tasks delay coordinates will be employed and the main concepts will be illustrated using examples including the Lorenz-96 model and other chaotic systems.
[1] U. Parlitz, J. Schumann-Bischoff, and S. Luther, Phys. Rev. E 89, 050902(R) (2014).
[2] U. Parlitz, J. Schumann-Bischoff, and S. Luther, Chaos 24, 024411 (2014).
[3] D. Rey, M. Eldridge, M. Kostuk, H.D.I. Abarbanel, J. Schumann-Bischoff, U. Parlitz, Physics Letters A 378, 869-873 (2014).