Background: The study of cerebral activity during sleep using the electroencephalograph (EEG) is a major research field in neuroscience. Despite the rich literature in this field, the automatic and accurate categorization of wake-sleep stages remains an open problem. New Method: A robust model-based Kalman filtering scheme is proposed for tracking the poles of a second order time-varying autoregressive model fitted over the EEG acquired during different wake/sleep stages. The pole angle/phase is regarded as the dominant frequency of the EEG spectrum (known as the instantaneous frequency in literature). The frequency resolution is improved by splitting the wide frequency band to subbands corresponding to well-known brain rhythms. Using recent findings in field of EEG phase/frequency tracking, the instantaneous envelope of the narrow-band signal's analytic form is also tracked as a complementary feature. Results: The minimal set of instantaneous frequency and envelope features is employed in three classification schemes, using training labels from R&k and AASM sleep scoring standards. The LDA classifier resulted in the highest performance using the proposed feature set. Comparison with Existing Methods: The proposed method resulted in a higher mean decoding accuracy and a lower standard deviation on the entire dataset, as compared with state-of-the-art techniques. Conclusions: The accurate tracking of the instantaneous frequency and envelope are highly informative for sleep stage scoring. The proposed method is shown to have additional applications, including the prediction of wake-sleep transition, which can be used for drowsiness detection from the EEG.