The　proton　exchange　membrane　fuel　cell　has　been　introduced　into　the　fields　of　transportation,　power　production,　and　mobile　devices.　Especially,　priority　is　given　to　promoting　the　application　in　commercial　vehicles.　However,　more　severe　fluctuations　in　power　demands　give　new　challenges　to　the　lifespan　of　fuel　cells.　The　accurate　state　estimation　and　reasonable　degradation　prediction　can　assist　in　improving　the　lifetime　of　fuel　cell　devices.　To　realize　the　on-road　prediction,　herein,　a　novel　generalized　prognostic　method　called　the　Multi-point　Square-root　central　difference　Kalman　filter　(MP-SRCDKF)　is　proposed.　First　of　all,　an　extended　mathematical　model　is　introduced.　Later,　the　sensitivity　analysis　and　parameter　recognition　are　conducted　based　on　the　Sobol＇　method　and　the　jellyfish　searching　algorithm.　The　performance　of　the　SRCDKF　method　is　compared　under　static　and　quasi-dynamic　conditions,　which　is　further　extended　into　the　road　condition　and　verified　under　the　dynamic　cycle　condition　temporarily.　In　the　end,　the　remaining　useful　life　prediction　under　various　operating　conditions　is　discussed.　Furthermore,　the　generalized　method　can　provide　an　approach　for　prognostic　decision-making　and　the　updating　of　the　dynamic　polarization　curve　to　expand　the　lifetime　and　optimize　the　control　system.