Model-free Unscented Kalman Filter with the Modified Method of Analogues

It is well known that the state estimation of nonlinear systems with noise is efficiently performed by unscented Kalman filters. However, they assume that the dynamics of the system is known in advance. Hence, this paper focuses on the state estimation problem of unknown chaotic dynamical systems with the recurrent property, and proposes a model-free unscented Kalman filter method for such systems, where the modified method of analogues developed in the field of nonlinear time series analysis is used. Effectiveness of this method is shown by numerical simulations.