Parameter identification for nonlinear systems: Guaranteed confidence regions through LSCR

In this paper we consider the problem of constructing confidence regions for the parameters of nonlinear dynamical systems. The proposed method uses higher order statistics and extends the LSCR (leave-out sign-dominant correlation regions) algorithm for linear systems introduced in Campi and Weyer [2005, Guaranteed non-asymptotic confidence regions in system identification. Automatica   41(10), 1751–1764. Extended version available at 〈〈http://www.ing.unibs.it/∼∼campi〉〉]. The confidence regions contain the true parameter value with a guaranteed probability for any finite number of data points. Moreover, the confidence regions shrink around the true parameter value as the number of data points increases. The usefulness of the proposed approach is illustrated on some simple examples.