This paper proposes a battery state estimation on a battery management system (BMS) for hybrid electric vehicles (HEVs) and electric vehicles (EVs). It is important to estimate a state of charge (SOC) and parameters of the battery such as a state of health (SOH), internal resistances and dynamics of electrochemical reactions. The BMS can provide information on the driving range of the EVs to the drivers by accurately estimating SOC and SOH. It can also calculate a state of power (SOP) to use the battery safely by accurately estimated SOC, internal resistances and others. For that purpose, this paper proposes the BMS adopted a simultaneous state of charge (SOC) and parameter estimation method using log-normalized unscented Kalman filter (LnUKF). The key idea is a lognormalization of the parameters to improve numerical stability and robustness of the algorithm. The proposed system is verified by a series of simulations using experimental data with EVs. One of the SOC and parameter estimation results is for low temperature data on the chassis dynamometer. The proposed system can accurately estimate SOC and parameters of the battery without relying on the experimentally obtained data even if it is under the harsh conditions such as low temperature environment. As a result, it can accurately estimate SOH and SOP of the battery since they are estimated by using estimates of SOC and parameters of the battery.