A data-driven framework for joint estimation of state of charge and state of health in lithium-ion batteries using Gaussian process Kalman filtering and patch-based time series transformers

The State of Charge (SOC) and State of Health (SOH) are key parameters for evaluating and managing battery status in Battery Management Systems. This paper proposes a joint estimation method for lithium-ion battery SOC and SOH based on GP Kalman filtering (GPKalman), an Online Sequential Extreme Learning Machine (OSELM), Patch-based Time Series Transformer (PatchTST), and the Arithmetic Optimization Algorithm (AOA). Firstly, a SOC estimation method based on GPKalman is proposed, and Online Sequential Extreme (Learning Machine OSELM) is introduced to correct its estimation errors. Secondly, for joint SOC and SOH estimation, a PatchTST-based neural network is employed, with hyperparameters optimized via AOA enhanced by Singer chaotic mapping. In SOC estimation experiments, Kalman Filter (KF), Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Adaptive Kalman Filter (AKF) are used as baselines to verify the superior performance of GPKalman. The error correction method further reduces estimation error by 8.06% compared to direct GPKalman output. For joint SOC and SOH estimation, Transformer, Autoformer, and TimesNet serve as comparison models. PatchTST achieves better performance, while the improved AOA effectively finds the model's optimal parameter set. Experimental results demonstrate that the proposed data-driven method provides accurate and stable SOC and SOH estimation, with strong practical value and applicability.