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This paper presents a traffic state estimation and prediction model based on the cell transmission model (CTM). The nonlinear CTM is transcribed in a closed analytical state-space form for use within a general extended Kalman filtering framework. The state-space CTM switches implicitly between numerous possible linear modes. The paper provides measurement models for the traffic state and model parameters for automatically estimating traffic conditions and model parameters in an online context. The applicability of the approach is illustrated in a real and a simulated case study.