1. A method for estimating battery state of charge of an electric vehicle including an internal combustion engine, a battery having a state of charge (SOC) and an open circuit voltage (OCV), the method comprising: establishing a system operable in open and closed loop modes for estimating battery SOC based on a current-time integration in the open loop mode, including (i) a parameter estimation subsystem including a recursive parameter estimator for estimating battery parameters based on a previous estimate of battery OCV in the closed loop mode and (ii) an OCV estimation subsystem including a nonlinear adaptive observer for estimating battery OCV based on the battery parameters and a previous estimate of battery OCV, wherein estimated battery OCV is related to estimated battery SOC by a mapping and wherein the system operates in the open loop mode at startup and switches to the closed loop mode based on a predetermined condition; and generate an output based on the estimated battery SOC.