A method of the present invention using a prediction process including a battery equivalent circuit model used to predict a voltage and a state of charge of a battery. The equivalent circuit battery model includes different equivalent circuit models consisting of at least an ideal DC power source, internal resistance, and an arbitrary number of representative parallel resistors and capacitors. These parameters are obtained a priori by fitting the equivalent circuit model to battery testing data. The present invention further uses a correction process includes determining a corrected predicted state of charge of the battery; and storing the corrected state of charge of the battery in a storage medium. In the present invention, an expectation of the predicted voltage of the battery and an expectation of the predicted state of charge of the battery are obtained by an unscented transform with sigma points selected by a Gaussian process optimization.