Currently, the estimation of the State of Charge (SoC) of electrochemical energy storage systems represents one of the most challenging task in application fields that require high performance and reliability. It is usually performed by the Battery Management System (BMS) according to cell voltage and current measurements. The Coulomb Counting method is widely used in real-world applications due to its simplicity and low computational cost. However, the disadvantages include uncertainty in defining the initial SoC and undesired estimation errors due to the accuracy of current sensors. To overcome these issues, different SoC estimation methods have been proposed in literature, which consider model-based approach. In this paper, Kalman filter methods are investigated since they represent robust state estimators unaffected by measurement noise and capable of correcting the initial state estimation error. In particular, the Unscented Kalman Filter and the Square-Root Unscented Kalman Filter (SR-UKF) are considered and their performances are compared. Moreover, a novel adaptive algorithm based on SR-UKF is proposed, which allows for reducing the SoC estimation errors when parameters variations of the battery model are considered. Numerical and experimental results are carried out for validating the performance of the proposed adaptive SR-UKF.