title: Estimation of parameters and unobserved components for nonlinear systems from noisy time series.
abstract: We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.
authors.affiliation: Center for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Sitz
authors.forename: U
authors.initials: U
authors.lastname: Schwarz
authors.forename: J
authors.initials: J
authors.lastname: Kurths
authors.forename: H U
authors.initials: HU
authors.lastname: Voss