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This paper develops boundary observer for estimation of congested freewaytraffic states based on Aw-Rascle-Zhang(ARZ) partial differential equations(PDE) model. Traffic state estimation refers to acquisition of traffic stateinformation from partially observed traffic data. This problem is relevant forfreeway due to its limited accessibility to real-time traffic information. Wepropose a boundary observer design so that estimates of aggregated trafficstates in a freeway segment are obtained simply from boundary measurement offlow and velocity. The macroscopic traffic dynamics is represented by the ARZmodel, consisting of $2 \times 2$ coupled nonlinear hyperbolic PDEs for trafficdensity and velocity. Analysis of the linearized ARZ model leads to the studyof a hetero-directional hyperbolic PDE model for congested traffic regime.Using spatial transformation and PDE backstepping method, we construct aboundary observer with a copy of the nonlinear plant and output injection ofboundary measurement errors. The output injection gains are designed for theerror system of the linearized ARZ model so that the exponential stability oferror system in the $L^2$ norm and finite-time convergence to zero areguaranteed. Simulations are conducted to validate the boundary observer designfor nonlinear ARZ model without knowledge of initial conditions.

Boundary Observer for Congested Freeway Traffic State Estimation via Aw-Rascle-Zhang model