Nonlinear dynamical system identification with dynamic noise and observational noise

In this paper we consider the problem of whether a nonlinear system has dynamic noise and then estimate the level of dynamic noise to add to any model we build. The method we propose relies on a nonlinear model and an improved least squares method recently proposed on the assumption that observational noise is not large. We do not need any a priori knowledge for systems to be considered and we can apply the method to both maps and flows. We demonstrate with applications to artificial and experimental data. The results indicate that applying the proposed method can detect presence or absence of dynamic noise from scalar time series and give a reliable level of dynamic noise to add to the model built in some cases.