Precise　state　of　charge　(SOC)　estimation　is　crucial　to　assure　safe　and　reliable　operation　of　lithium-ion　battery　in　electric　vehicles.　Adaptive　unscented　Kalman　filter　(AUKF)　has　been　intensively　applied　to　estimate　SOC　due　to　its　features　of　self-correction　and　high　accuracy.　Nevertheless,　the　estimation　by　traditional　AUKF　cannot　proceed　when　error　covariance　matrix　is　non-positive　definite,　greatly　influencing　the　stability　of　SOC　estimation.　To　address　this　issue,　an　improved　AUKF　is　proposed　in　this　paper.　Firstly,　the　forgetting　factor　recursive　least　square　is　employed　to　online　identify　parameters　of　electrical　equivalent　circuit　model.　With　these　identified　parameters,　an　improved　AUKF,　whose　Cholesky　decomposition　for　error　covariance　matrix　of　tradition　AUKF　is　replaced　by　singular　value　decomposition,　is　applied　here　to　provide　online　accurate　SOC　estimation.　The　feasibility　of　the　proposed　method　is　verified　by　experimental　data　under　Federal　Urban　Driving　Schedule　test.　The　validation　results　of　robustness　present　that　the　algorithm　has　satisfactory　robustness　against　inaccurate　initial　SOC.　Moreover,　through　the　comparison　with　traditional　AUKF,　it　can　be　easily　concluded　that　the　proposed　method　can　achieve　precise　and　stable　SOC　estimation　even　though　error　covariance　matrix　is　non-positive　definite.　©　2020