A Multi-Stage AdSS-NARX-LSTM Approach for Enhanced State-of-Charge Estimation in Lithium-Ion Batteries

Accurate state of charge (SoC) estimation is essential for the reliable operation, energy management, and safety of lithium-ion batteries in electric vehicles and energy storage systems. However, accurate estimation remains challenging due to battery nonlinearities, measurement uncertainties, and changing operating conditions. This study proposes a hybrid AdSS-NARX-LSTM framework integrating Adaptive State Smoothing (AdSS), Nonlinear Autoregressive with Exogenous Inputs (NARX), and Long Short-Term Memory (LSTM) networks for SoC estimation. Battery voltage and current are used as primary inputs. The AdSS stage generates a temporally consistent SoC trajectory through an adaptive smoothing process, reducing the influence of measurement noise and short-term signal fluctuations while preserving the overall state evolution trend. In parallel, the NARX model exploits historical input-output relationships to capture nonlinear temporal dynamics associated with battery behavior. The AdSS and NARX outputs are fused with measured variables as auxiliary features before being fed into the LSTM network. This integration enables the LSTM to exploit complementary information while learning long-term temporal dependencies from sequential data. The framework improves estimation stability and robustness without requiring complex electrochemical or equivalent-circuit models. The effectiveness of the proposed method is evaluated using five dynamic driving cycles, including US06, UDDS, LA92, HWFTa, and HWFTb. Estimation performance is assessed using mean absolute error (MAE), mean squared error (MSE), and coefficient of determination (R²) metrics and compared with AdSS, NARX, LSTM, AdSS+LSTM, and NARX+LSTM approaches. Results demonstrate that the proposed framework achieves high estimation accuracy and stable performance across different driving profiles, indicating its potential for battery management applications. Further validation, including computational complexity and embedded-system implementation, is required to assess its suitability for real-time operation.