This paper contributes to an understudied category of traffic state estimation approaches, i.e. using a Godunov-type discrete traffic flow model (e.g. the Cell Transmission Model, CTM) to simultaneously estimate traffic flow parameters and traffic densities. Our main estimation algorithm is based on the CTM and the extended Kalman filter (EKF). Compared to previous studies, this study has two features. First, we take into account the effect of capacity drop, a factor that is largely ignored by previous studies in traffic state estimation. Second, a separate, supervisory observer capturing the capacity drop mode is attached to the main algorithm. Such a treatment enables the main estimation algorithm to more accurately switch between functions of free-flow regime and congested regime. It thus avoids mismatches between the applied models and the measurements, a common pitfall in conventional CTM-EKF approaches, hence can potentially enhance the quality of estimation. The proposed method was tested using micro-simulation data and showed a satisfactory performance in tracking variations of traffic flow parameters and estimating traffic densities in real time.