Over the past few decades, short term Dst index prediction using different techniques have been proposed since effects of space weather cause many problems on operational systems on Earth. Using input-output methods, the coupling function between solar wind parameters and Dst index is found to be nonlinear. In practice, observed data have been provided in almost real time but this is very noisy. To address noisy data and nonlinear dynamics, Kalman filtering techniques are used. Furthermore, the measurement noise which is derived from the error between provisional Dst and quick look Dst is found to be non white and modelled using an ARMA structure. Four existing models are chosen and a new model using NARX structure is proposed. Parameter estimation using joint and dual estimation techniques is studied. A comparison between models with Kalman filtering techniques and models alone is made and it is found that Kalman filtering methods can improve prediction performance and reduce prediction error.