Battery State-of-Charge Estimation Using Factor Graph Optimization with Linear and Nonlinear Voltage Observation Models

Accurate battery state-of-charge (SOC) estimation is essential for battery management systems in electric vehicles and energy storage applications. Traditional estimation methods often rely on recursive filtering techniques and may experience performance degradation under nonlinear operating conditions and measurement uncertainty. This study proposes a factor graph optimization (FGO)-based SOC estimation framework incorporating voltage observation constraints. Three estimation configurations are investigated, including Current-Only FGO, Linear Voltage FGO, and Nonlinear Voltage FGO. A custom 3 Ah lithium-ion battery simulation model implemented in C++ was developed to generate benchmark datasets under both constant-current and random-current operating conditions. The results indicate that incorporating voltage information can improve SOC estimation accuracy within the investigated simulation benchmark. Under constant-current conditions, the Current-Only FGO achieved an RMSE of 0.128303, while the Linear Voltage FGO reduced the RMSE to 0.067395. The Nonlinear Voltage FGO further reduced the RMSE to 0.013604. Under random-current conditions, the nonlinear voltage formulation achieved an RMSE of 0.009022. Noise sensitivity analysis was conducted by injecting zero-mean Gaussian voltage measurement noise ranging from 0.01 V to 0.10 V. Additional validation experiments were conducted by including an EKF baseline, practical uncertainty cases, OCV–SOC model mismatch, and covariance sensitivity analysis. The results suggest that the nonlinear voltage formulation maintained relatively low estimation errors under the investigated voltage noise levels, while model mismatch and covariance settings can influence estimation accuracy. Since the present study is based on a simplified simulation model, the proposed framework should be regarded as a simulation-based proof-of-concept for voltage-constrained FGO-based SOC estimation. Future work will focus on validation using real battery datasets and comparison with conventional battery state estimation methods.