arXiv:2508.21610v3 Announce Type: replace Abstract: Accurate state-of-charge (SOC) estimation is essential for safe and efficient lithium-ion battery operation. Electrochemical models provide physically grounded SOC estimates, but nonlinear voltage dynamics and coupled state-parameter errors can destabilize online adaptation. This paper proposes an adaptive dead-zone dual sliding-mode observer (ADZ-DSMO) based on an improved extended single-particle (IESP) model. A state SMO estimates SOC-related states, while a parameter SMO updates dominant model parameters. An online-computable, Lyapunov-guided adaptive boundary selectively gates parameter updates while the state observer remains active at every sampling step. Validation on a Panasonic NCR18650PF cell under 1C and 3C constant-current discharge and the Urban Dynamometer Driving Schedule (UDDS) and New European Driving Cycle (NEDC) profiles shows lower SOC estimation errors than conventional dual SMO and the IESP-based dual extended Kalman filter (DEKF). Compared with DEKF, the proposed observer provides faster recovery from a 30% initial SOC bias. Selective parameter updating reduces the average per-step computation time compared with the always-updating dual SMO. Temperature tests and capacity-based, model-generated aging cases further assess robustness. These results support adaptive gating as a means of reducing error propagation and computational overhead in electrochemical-model-based joint state-parameter estimation.