A Hybrid Transformer Network Optimized by Kalman Filter for State of Health Prediction on Lithium-Ion Battery

State of Health (SOH) is a critical metric for assessing the efficient and reliable operation of lithium-ion Battery (LIB), despite its indirect measurability. Accurate SOH prediction poses significant challenges through the LIB lifecycle, due to severe signal oscillations and complex degradation mechanisms. In this paper, a novel hybrid Transformer-based architecture for SOH prediction is introduced, termed KF-SAMformer-GRU, which integrates a Kalman filter (KF) optimizer, a Sharpness-Aware Minimization Transformer (SAMformer) model, and a multi-layer gated recurrent unit (GRU). Given the SOH prediction involves multivariate long-term forecasting, the SAMformer enhances prediction capabilities, optimizing with Sharpness-Aware Minimization (SAM). The SAMformer extracts feature indicators from battery sequence data, effectively addressing data distribution shifts. Additionally, the KF facilitates multiple features fusion, thereby reducing computational costs and improving training efficiency. Finally, the multi-layer GRU refines the mapping between SOH metrics and predicted values. To validate the method effectiveness, we conducted experiments on the NASA and CALCE datasets. Compared with mainstream methods, our approach achieved superior performance, with MAPE of 0.01, RMSE of 0.91%, and R² of 0.99. Moreover, our method can accurately capture phenomena such as battery capacity regeneration and predict battery capacity recovery, demonstrating better performance at peaks and valleys while maintaining higher computational efficiency.