Traffic　state　estimation　is　the　acquisition　of　traffic　state　information　from　partially　observed　traffic　data,　which　is　crucial　to　the　effectiveness　of　traffic　management　and　control.　This　paper　investigates　the　estimation　problem　of　traffic　flow　state　with　shock　waves　in　the　congestion　regime　by　proposing　a　moving　boundary　observer.　The　macroscopic　traffic　flow　dynamics　in　the　congestion　regime　is　described　by　the　linearized　Aw-Rascle-Zhang　(ARZ)　traffic　flow　model　over　a　time-varying　moving　spatial　domain,　and　according　to　the　Rankine-Hugoniot　condition　and　the　characteristic　velocities　of　the　ARZ　model,　a　novel　propagation　model　of　the　shock　waves　is　proposed.　We　propose　a　moving　boundary　observer　that　can　estimate　the　aggregated　traffic　state　by　simply　measuring　the　average　vehicle　velocity　at　the　moving　interface　of　the　shock　wave.　The　observer　system　is　constructed　from　a　copy　of　the　plant　and　by　incorporating　injections　from　moving　boundary　output　measurement　errors,　in　which　the　observer　gains　are　obtained　based　on　the　PDE　backstepping　method.　The　exponential　stability　of　the　observer　error　system　in　the　L2　norm　is　proved　via　Lyapunov　analysis.　Finally,　the　validity　of　the　moving　boundary　observer　for　traffic　state　estimation　with　shock　waves　is　verified　by　numerical　simulations.　Copyright　(c)　2023　The　Authors.