The accurate online state estimation for some types of nonlinear singularly perturbed systems is challenging due to extensive computational requirements, ill-conditioned gains and/or convergence issues. This paper proposes a multi-time-scale estimation algorithm for a class of nonlinear systems with coupled fast and slow dynamics. Based on a boundary-layer model and a reduced model, a multi-time-scale estimator is proposed in which the design parameter sets can be tuned in different time-scales. Stability property of the estimation errors is analytically characterized by adopting a deterministic version of extended Kalman filter (EKF). This proposed algorithm is applied to estimator design for the state-of-charge (SOC) and state-of-health (SOH) in a lithium-ion battery using the developed reduced order battery models. Simulation results on a high fidelity lithium-ion battery model demonstrate that the observer is effective in estimating SOC and SOH despite a range of common errors due to model order reductions, linearisation, initialisation and noisy measurement.