 This paper proposes an adaptive observer-based method for estimating the state of charge, SOC, of a lithium-ion battery pack used in an electric vehicle, EV. The RC equivalent circuit model was applied to simulate the battery pack, and its parameters were identified and optimized using a nonlinear least squares algorithm. An adaptive Lewenberger observer was then constructed to estimate SOC from the battery's output voltage and filtered terminal voltage measurements. The observer gain was adapted using a stochastic gradient approach to minimize the error between the estimated battery output voltage and the measured terminal voltage. The validated results showed that the proposed method could accurately estimate SOC with minimal computational overhead. This article was authored by Yuan Zou, Feng Chen Sun, and Xiaosong Hu.