Fast Convergent On-Board Li-Ion Battery State-of-Charge Estimation via Back-Forth Moving Horizon Estimation

Accurate state of charge (SOC) estimation is crucial for the safe operation of lithium-ion batteries (LIBs), yet existing methods are limited by sensitivity to initial SOC guess or high computational complexity. To address these challenges, this study proposes an onboard back-forth moving horizon estimation (BFMHE) framework for SOC estimation, achieving high precision, robustness, and computational efficiency compatible with microcontroller implementation. An efficient linear equivalent circuit model (ECM) is established, where the open-circuit voltage-SOC relationship is approximated by piecewise linear functions. The proposed framework employs two MHE estimators that iteratively operate in opposite directions over a finite time horizon, which enables rapid convergence. Moreover, this study provides a rigorous proof of the stability of the BFMHE method for the battery system with current input. The proposed approach is validated experimentally under various operating conditions and with different initial SOC guesses. Experimental results show that the proposed onboard BFMHE method achieves a maximum estimation error of less than 1% and quickly converges to the true SOC value, demonstrating strong robustness to initial estimation errors.