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Drowsiness is a leading cause of accidents on the road as it negatively affects the driver's ability to safely operate a vehicle. Neural activity recorded by EEG electrodes is a widely used physiological correlate of driver drowsiness. This paper presents a novel dynamical modeling solution to estimate the instantaneous level of the driver drowsiness using EEG signals, where the PERcentage of eyelid CLOSure (PERCLOS) is employed as the ground truth of driver drowsiness. Applying our proposed modeling framework, we find neural features present in EEG data that encode PERCLOS. In the decoding phase, we use a Bayesian filtering solution to estimate the PERCLOS level over time. A data set that comprises 18 driving tests, conducted by 13 drivers, has been used to investigate the performance of the proposed framework. The modeling performance in estimation of PERCLOS provides robust and repeatable results in tests with manual and automated driving modes by an average RMSE of 0.117 (at a PERCLOS range of 0 to 1) and average High Probability Density percentage of 62.5%. We further hypothesized that there are biomarkers that encode the PERCLOS across different driving tests and participants. Using this solution, we identified possible biomarkers such as Theta and Delta powers. Results show that about 73% and 66% of the Theta and Delta powers which are selected as biomarkers are increasing as PERCLOS grows during the driving test. We argue that the proposed method is a robust and reliable solution to estimate drowsiness in real-time which opens the door in utilizing EEG-based measures in driver drowsiness detection systems. [ABSTRACT FROM AUTHOR]