Electrode-Level State Estimation in Lithium-Ion Batteries via Kalman Decomposition

Lithium-ion battery electrode-level online state estimation using high-fidelity nonlinear electrochemical models remains a key challenge. This is particularly due to weak observability inherited from the complex model structure, even for reduced-order electrochemical models. This letter presents a systematic and rigorous strategy to analyze the local observability of a single particle model (SPM) with both electrodes, which is commonly known to be locally unobservable from current-voltage measurements. Estimating the essential states, e.g., state of charge (SOC) and solid-phase lithium surface concentration, is crucial for battery charge and health monitoring since different degradation mechanisms affect each electrode individually. In this letter, the proposed observability analysis approach based on the Kalman decomposition enables provably convergent estimates. Ultimately, using the observability analysis, we propose a state estimator based on the nonlinear SPM dynamics and prove estimation error system stability. The observability analysis and state estimation scheme exploits the conservation of lithium property. Simulations demonstrate the effectiveness of the electrode-level state estimator as opposed to the cell-level estimator.