State　estimate　of　traffic　flow　of　a　freeway　segment　is　considered　by　using　the　method　of　boundary　observer　design.　The　observer　control　and　measurements　are　all　located　at　the　boundaries.　The　nonequilibrium　traffic　flow　dynamics　are　modeled　as　a　Markov　jump　linear　hyperbolic　system　with　phase　transitions.　Based　on　the　Lyapunov　techniques,　the　sufficient　conditions　of　matrix　inequalities　are　derived　for　the　exponentially　mean-square　static　as　well　as　the　dynamic　boundary　observer　design.　Using　real　traffic　data　of　vehicle　trajectories　from　the　Next　Generation　Simulation　(NGSIM)　project,　the　developed　stochastic　phase　transition　model　of　the　nonequilibrium　traffic　flow　is　calibrated.　Moreover,　the　simulation　results　illustrate　the　effectiveness　of　the　boundary　observer　design　for　traffic　estimation.