In　order　to　accurately　and　timely　estimate　traffic　densities　in　a　large-scale　urban　freeway　network　when　traffic　sensors　do　not　completely　cover　the　whole　freeway　network　and　thus　only　local　measurement　data　can　be　utilized,　this　paper　proposes　a　distributed　state　observer　approach　based　on　a　macroscopic　traffic　flow　model.　Firstly,　the　urban　freeway　network　is　modeled　in　the　way　of　distributed　systems　by　combining　the　cell　transmission　model　(CTM)　with　the　dynamic　graph　hybrid　automata　(DGHA),　and　a　Piece　Affine　Linear　System　(PWALS)　is　deduced.　Furthermore,　based　on　the　PWALS　model,　a　switched　and　distributed　state　observer　is　designed　to　estimate　traffic　densities　of　the　freeway　network,　where　a　set　of　gain　matrices　for　the　observer　are　computed　by　using　LMI　technique　with　the　help　of　the　S-procedure　theory.　Finally,　the　PWALS　model　and　the　corresponding　distributed　observer　are　utilized　to　Beijing　second　ring　freeway,　and　the　experimental　results　demonstrate　the　effectiveness　and　applicability　of　the　proposed　approach.