The state of charge (SoC) of a battery is a crucial monitoring indicator for battery management systems and it helps to assess how much further an electric vehicle can travel. This work proposes a novel approach for predicting battery SoC by developing a closed-loop system that integrates a bidirectional long short-term memory neural network with an innovative algorithm-extended Kalman filter. A second-order equivalent circuit model is selected, and its parameters are computed using the variational and logistic map cuckoo search approach. Further, an Extended Kalman filter is combined with an innovation algorithm to update process noise in real-time, and a bidirectional long short-term memory neural network takes the input from the Extended Kalman filter and gives the compensated error value for the final SoC estimation. 75% of dynamic stress test data from the Extended Kalman filter is used for training purposes, remaining data sets are used for testing purposes. The addressed algorithm is validated by evaluating its performance in comparison to individual algorithms and various combined approaches. Empirical analysis demonstrates that the proposed model achieves a root mean square error of 0.11 % and mean absolute error of 0.1 % positioning it as a valuable tool for battery management systems.