The performance of electric and hybrid vehicles relies on an effective battery management strategy to ensure safety, driving range, and durability. Among all monitored parameters, the state of charge (SOC) plays an essential role in optimally implementing the control logic strategies. However, since SOC cannot be directly measured, its estimation relies on algorithms capable of guaranteeing a balance between accuracy and computational efficiency. This thesis proposes the design and implementation of an extended Kalman filter (EKF) for SOC estimation of a lithium-ion cell - LG INR18650 MJ1 - within Matlab and Simulink environments. The cell was first modelled adopting a Dual Polarisation Model (DPM) and characterised through experimental data, with model parameters optimised via Simulink Design Optimisation (SDO) toolbox.