With　the　development　of　traffic　detection　technology,　spatially　discrete　traffic　data　(eg,　cross-sectional　data)　have　been　transformed　to　spatially　continuous　data　(eg,　trajectory　data,　images,　etc.).　In　this　paper,　a　continuous　multi-mode　boundary　observer　based　on　Aw-Rascle-Zhang　(ARZ)　model　is　designed　for　continuous　measured　data　and　applied　to　actual　road　traffic　state　estimation.　We　consider　both　static　and　dynamic　boundary　controls　for　the　observer　design.　By　means　of　Lyapunov　based　techniques,　we　derive　some　sufficient　conditions　for　the　observer　using　only　the　information　from　the　boundary　conditions.　With　the　multi-mode　filter　method,　we　employ　the　linear　free-flow　observers　and　congested　observers　to　approach　the　quasi-linear　ARZ　model.　After　that,　the　state　estimates　obtained　from　the　different　models　are　fused　according　to　weights,　and　the　fused　state　is　then　used　as　the　initial　value　of　PDEs　for　the　next　period.　A　freeway　link　of　Interstate　80　in　Emeryville,　California　is　chosen　to　investigate　the　performance　of　the　developed　observer　and　multi-mode　filter　approach.