Sensors　play　a　key　role　in　monitoring　distributed　parameter　systems　(DPSs),　such　as　thermal　and　chemical　diffusion-reaction　processes.　However,　sensor　faults　can　result　in　data　distortion,　degraded　system　performance,　and　even　catastrophic　consequences.　This　article　proposes　a　model-based　sensor　fault　diagnosis　framework　for　DPSs,　which　can　effectively　detect　the　fault　time　and　estimate　the　fault　intensity.　The　proposed　method　only　requires　the　limited　measured　output　without　any　state　information.　Besides,　noise　will　cause　perturbations　in　the　sampling　data.　Correspondingly,　a　linear　matrix　inequality　(LMI)　considering　disturbance　is　designed.　Through　theoretical　analysis,　the　convergence　of　fault　estimation　error　is　ensured.　The　effectiveness　of　the　proposed　method　is　verified　on　a　heat　transfer　rod　and　a　chemical　diffusion-reaction　system　with　static　and　time-varying　sensor　faults　under　disturbances.　The　root　mean　square　errors　of　all　sensor　fault　estimates　are　within　0.1078.