As distributed parameter systems, dynamics of freeway traffic are dominated by the current traffic parameter and boundary fluxes from upstream/downstream sections or on/off ramps. The difference between traffic demand-supply and boundary fluxes actually reflects the congestion level of freeway travel. This paper investigates simultaneous traffic density and boundary flux estimation with data extracted from on-road detectors. The existing studies for traffic estimation mainly focus on the traffic parameters (density, velocity, etc.) of mainline traffic and ignore flux fluctuations at boundary sections of the freeway. We propose a stochastic hybrid traffic flow model by extending the cell transmission model (CTM) with Markovian multi-mode switching. A novel interacting multiple model (IMM) filtering for simultaneous input and state estimation is developed for discrete-time Markovian switching systems with unknown input. A freeway segment of Interstate 80 East (I-80E) in Berkeley, Northern California, is chosen to investigate the performance of the developed approach. Traffic data is obtained from the Performance Measurement System (PeMS).
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