Guaranteed state and parameter estimation for one-dimensional chaotic system

In this article, the problem of state and parameter estimation is considered for an one-dimensional chaotic system. Based on the guaranteed approach and interval computations, the proposed algorithm finds interval estimates (information sets) of unknown variables. Common estimation techniques (least squares method, modifications of the Kalman filter for nonlinear systems) can be combined with the proposed guaranteed algorithm to overcome the difficulties related with a small number of available observations and nonlinearity. The numerical example is given for the logistic map.