This study introduces a new framework for estimating the state of charge (SOC). It blends optimization, deep learning, and adaptive filtering techniques. First, the Cuckoo Search Algorithm finds the best settings for a secondorder RC circuit model. This ensures accurate battery characterization. The parameters obtained is fed to the Adaptive Extended Kalman Filter (AEKF) to produce training data for a Bidirectional Long Short-Term Memory (BiLSTM) network. The BiLSTM model predicts SOC estimation errors. It integrates with a Squared Gain EKF (SGEKF) to adjust SOC estimates in real-time. We assess the BiLSTM-SGEKF method with real driving cycle data. We also compare it to traditional methods like AEKF and EKF. The results show that BiLSTMSGEKF has the lowest RMSE at 0.047%, MAE at 0.041%, and ME at 0.14%. It significantly outperforms AEKF and EKF. This hybrid approach adjusts easily to changing conditions. So, it’s a great option for real-time SOC estimation.