This　paper　studies　the　state　observer　design　of　a　spatial　two-dimensional　(2-D)　linear　diffusion　process　described　by　a　linear　parabolic　partial　differential　equation　(PDE)　under　mobile　sensors.　Firstly,　we　analyze　the　well-posedness　of　the　PDE　system　and　give　the　structure　form　of　the　state　observer　with　mobile　sensors.　Subsequently,　according　to　the　number　of　mobile　sensors,　the　2-D　space　domain　is　divided　into　multiple　sub-domains,　and　the　mobile　sensors　are　guided　by　the　projection　operator　method,　which　can　guarantee　that　the　mobile　sensors　can　only　move　in　their　respective　2-D　sub-domains.　Then,　in　the　light　of　Lyapunov　theory,　Poincaré-Wirtinger　inequality　and　Barbalat　lemma,　we　propose　an　observation-plus-guidance　design　method　to　ensure　the　asymptotic　stability　of　the　state　estimation　error　system.　In　the　designed　mobile　strategy,　the　actual　guidance　of　mobile　sensors　is　essentially　a　physical　synthesis　of　two　direction　guidance　laws,　where　two　dimensional　guidance　laws　are　designed　separately.　Moreover,　the　existence　condition　of　the　observer　is　given　by　linear　matrix　inequalities.　At　last,　a　numerical　example　is　provided　to　demonstrate　the　efficacy　of　the　proposed　design　scheme.　　©　2004-2012　IEEE.