Accurate State of Energy (SOE) estimation is a critical prerequisite for ensuring the safety, reliability, and optimal performance of lithium-ion batteries (LIBs) in modern Battery Management Systems (BMSs). While model-based approaches, such as the standard Extended Kalman Filter (EKF), are widely utilized in industrial applications, their precision is fundamentally compromised by a reliance on static, pre-defined noise covariance matrices (Q and R). These static parameters often fail to account for the highly non-linear, time-variant electrochemical behavior of LIBs under dynamic operating conditions, frequently leading to filter divergence and estimation lag. This research presents an enhanced state estimation framework utilizing an Improved Sage–Husa Extended Kalman Filter (SHEKF) to address these limitations. A second-order (2RC) equivalent circuit model (ECM) is chosen in this research for its optimal balance between computational efficiency and high-fidelity representation of battery dynamics. To ensure a precise model foundation, internal parameters including ohmic resistance, charge transfer, and mass transfer effects, were identified through offline analysis of Hybrid Pulse Power Characterization (HPPC) test data. The non-linear relationship between Open-Circuit Voltage (OCV) and SOE was further refined using a sixth-order polynomial fit to minimize model-induced errors. The proposed SHEKF algorithm incorporates a recursive adaptive mechanism that utilizes filter innovation to estimate and update process and measurement noise statistics in real time. This eliminates the need for manual parameter tuning and allows the estimator to maintain stability across varying current rates and drive cycles. The robustness of the SHEKF was rigorously validated through a comparative analysis against baseline EKF and Strong Tracking EKF (STEKF) algorithms. Evaluations were conducted using standardized dynamic datasets, specifically the Federal Urban Driving Schedule (FUDS) and the Urban Dynamometer Driving Schedule (UDDS). Results obtained demonstrate that the SHEKF significantly outperforms traditional estimators, achieving a 75% reduction in Root Mean Square Error (RMSE) for both SOE and terminal voltage estimation compared to the baseline EKF. Specifically, the SHEKF maintained an exceptionally low SOE RMSE of 0.58% and a Maximum Absolute Error (MAE) below 0.84%, even under the volatile current profiles of the UDDS cycle. These findings confirm that the adaptive Sage–Husa mechanism provides a superior, self-correcting solution for high-precision battery state monitoring in real-world electric vehicle applications.