This　study　simulates　the　polarization　effect　during　the　process　of　battery　charging　and　discharging,　and　investigates　the　characteristics　of　the　process.　A　fractional-order　model　(FOM)　is　established　and　the　parameters　of　the　FOM　are　identified　with　the　adaptive　genetic　algorithm.　As　Kalman　filter　estimation　causes　error　accumulation　over　time,　using　the　fractional-order　multi-innovation　unscented　Kalman　filter　(FOMIUKF)　is　a　better　choice　for　state　of　charge　(SOC)　estimation.　A　comparative　study　shows　that　the　FOMIUKF　has　higher　accuracy.　A　multiple　timescales-based　joint　estimation　algorithm　of　SOC　and　state　of　health　is　established　to　improve　SOC　estimation　precision　and　reduce　the　amount　of　computation.　The　FOMIUKF　algorithm　is　used　for　SOC　estimation,　while　the　UKF　algorithm　is　used　for　SOH　estimation.　The　joint　estimation　algorithm　is　then　compared　and　analyzed　alongside　other　Kalman　filter　algorithms　under　different　dynamic　operating　conditions.　Experimental　results　show　that　the　joint　estimation　algorithm　possesses　high　estimation　accuracy　with　a　mean　absolute　error　of　under　1%　and　a　root　mean　square　error　of　1.35%.