title: Estimability and dependency analysis of model parameters based on delay coordinates.
abstract: In data-driven system identification, values of parameters and not observed variables of a given model of a dynamical system are estimated from measured time series. We address the question of estimability and redundancy of parameters and variables, that is, whether unique results can be expected for the estimates or whether, for example, different combinations of parameter values would provide the same measured output. This question is answered by analyzing the null space of the linearized delay coordinates map. Examples with zero-dimensional, one-dimensional, and two-dimensional null spaces are presented employing the Hindmarsh-Rose model, the Colpitts oscillator, and the Rössler system.
authors.affiliation: Biomedical Physics Group, 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: J
authors.initials: J
authors.lastname: Schumann-Bischoff
authors.affiliation: Biomedical Physics Group, 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: S
authors.initials: S
authors.lastname: Luther
authors.affiliation: Biomedical Physics Group, 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: U
authors.initials: U
authors.lastname: Parlitz