A two-step approach for state-of-health (SOH) estimation of a lithium-ion (Li-ion) battery is developed. In the first step, state-of-charge (SOC) estimation is performed by a constrained extended Kalman filter (EKF) based on the so-called equivalent-hydraulic model. The latter model allows to characterize the internal battery state and main physical parameters while being suitable for on-line computation. The internal battery states are further exploited in the second step of the approach to obtain parameter-based SOH indicators that characterize the long term evolution of the diffusion and charge transfer processes associated to aging. Capacity and power fade indicators are determined by using notably an instrumental variable method in order to obtain unbiased parameter estimates in the presence of heteroscedastic colored noise. The methodology is validated on both simulation and experimental data for a lithium iron phosphate (LFP) half battery cell. This also provides insight on the properties of the LFP electrodes.