Time-domain approach to inverse modeling of respiratory system requires estimation of the parameters from the noisy observation. In this work, states and parameters of the linear lung models are estimated simultaneously by dual Kalman filter where the algorithm use two-observation forms. We also employ Kalman smoother for fine tuning the parameters. It is found that the state estimates are more robust to initial filter parameters than the model parameter convergences. Both viscoelastic and the Mead models yielded encouraging results and compatible estimator variances.