title: Quantifying uncertainty in state and parameter estimation.
abstract: Observability of state variables and parameters of a dynamical system from an observed time series is analyzed and quantified by means of the Jacobian matrix of the delay coordinates map. For each state variable and each parameter to be estimated, a measure of uncertainty is introduced depending on the current state and parameter values, which allows us to identify regions in state and parameter space where the specific unknown quantity can(not) be estimated from a given time series. The method is demonstrated using the Ikeda map and the Hindmarsh-Rose model.
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization Am Faßberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen, Germany.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Parlitz
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization Am Faßberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen, Germany.
authors.forename: Jan
authors.initials: J
authors.lastname: Schumann-Bischoff
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization Am Faßberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Luther
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics