Anotation:
Local state estimation approaches for nonlinear stochastic systems are treated. The unscented transformation and the Stirling’s polynomial interpolation, used in the design of the derivative-free Kalman filters, are briefly discussed. These approximation techniques are exploited to the design of the derivative-free smoothers and predictors. Some aspects of the different types of the derivative-free smoothers are analysed. The estimation qualities of the proposed estimators are illustrated in a numerical example.