Supercapacitors　are　characterized　by　a　long　service　lifetime　and　high　power　density,　which　can　meet　the　instantaneous　high-power　demand　during　the　acceleration　of　electric　vehicles.　In　this　study,　a　fractional-order　model　is　developed　to　simulate　the　polarization　effect　and　charging/discharging　characteristics　of　supercapacitors,　considering　the　precision　of　the　electrochemical　model　and　the　amount　of　calculation　of　the　equivalent　circuit　model　and　using　the　adaptive　genetic　algorithm　to　identify　the　parameters.　The　accurate　prediction　of　the　state　of　charge　(SOC)　can　improve　efficiency,　prolong　the　service　lifetime,　and　ensure　the　safety　of　supercapacitors.　This　study　proposes　a　multi-innovation　unscented　Kalman　filter　algorithm　based　on　the　fractional-order　model　to　improve　the　SOC　estimation　accuracy.　The　proposed　algorithm　is　compared　with　other　algorithms　and　analyzed　under　different　temperatures　and　operating　conditions　to　verify　the　accuracy　and　effectiveness　of　the　proposed　algorithm　in　estimating　the　SOC　and　tracking　the　terminal　voltage.　Experimental　results　show　that　the　root　mean　squared　error　and　mean　absolute　error　of　the　proposed　algorithm　are　less　than　those　of　the　other　algorithms.　The　proposed　algorithm　accurately　estimates　the　SOC　and　tracks　the　terminal　voltage.　The　maximum　root　mean　squared　error　and　mean　absolute　error　of　SOC　estimation　error　are　1.8%　and　1.78%,　respectively.