In this work, the problem of battery state of charge estimation is investigated using a model based approach. An experimentally validated model of a battery developed by AllCell Technologies, specific for light electric vehicles (electric scooter or bicycles) is used. Two state of charge estimation algorithms are developed: an extended Kalman filter and an adaptive extended Kalman filter. The adaptive version of Kalman filter is designed in order to adaptively set a proper value of the model noise covariance, using the information coming from the on-line innovation analysis. A comparison between the two approaches is conducted that shows that the adaptive Kalman filter can deal with the problem of incorrect value of the model noise covariance matrix producing lower estimation error.