An integrated bidirectional LSTM and adaptive cubature Kalman filter estimation method for accurate state-of-charge estimation of lithium-ion battery

Abstract Model-based observers for lithium-ion battery state-of-charge (SOC) estimation lose accuracy under strong nonlinearities and sensor noise, while purely data-driven estimators lack physical consistency and generalise poorly outside their training distribution. Existing hybrid designs address this gap only partially: neural-network outputs are typically fused with an Extended Kalman Filter (EKF) as a loosely coupled correction term, so first-order linearisation error and static noise statistics still limit performance under aggressive drive cycles. This paper proposes a tightly coupled Bidirectional Long Short-Term Memory-Adaptive Cubature Kalman Filter (BiLSTM-ACKF) framework that resolves these limitations through three distinct mechanisms. First, the BiLSTM output is reformulated as a scalar pseudo-measurement of SOC, rather than a terminal-voltage correction, so the innovation is expressed directly in SOC units and is independent of the open-circuit-voltage-SOC slope. Second, an innovation-driven adaptive covariance law continuously re-weights the measurement noise covariance according to the real-time agreement between the BiLSTM output and the model-predicted SOC, self-regulating the filter’s trust in the data-driven channel. Third, cubature-point propagation replaces Jacobian linearisation in a single-RC Thevenin equivalent-circuit model, eliminating first-order truncation bias under strongly nonlinear transients. A sliding window sequence of voltage and current measurements were used to train the BiLSTM. Validation was conducted with four different driving cycles (DST, FUDS, UDDS and US06), at three temperatures (5° C, 25° C and 45° C), and six levels of Gaussian white voltage noise (0 mV, 30 mV, 80 mV) using two datasets provided by the TU-Berlin repository (LA92 and US06). Comparison results show that BiLSTM-ACKF significantly outperformed both the stand-alone BiLSTM (with a range of 40–60% lower RMSE values than BiLSTM) and BiLSTM-AEKF (with a range of 30–52% lower RMSE values than BiLSTM-AEKF) across all four driving cycles and all six levels of noise. With respect to error magnitude, BiLSTM-ACKF also demonstrated a consistent upper bound of less than 1.5% over all test cases.