This paper studies the state estimation of a solid-state battery modeled as a partial differential equation system. Three assumptions simplifying the battery model underlie the study of state estimation: (1) neglecting the generation/recombination of Li-ions in the solid electrolyte; (2) assuming the charge transfer number of 0.5; and (3) the uniform electrolyte concentration. Results of a sensitivity study show the validity of the approaches to model simplification for the voltage prediction. Especially, two simplified models focused on the diffusion dynamics at cathode only and at both cathode and electrolyte are used for state estimation by applying an extended Kalman filter (EKF). Simulation results show that the state-of-charge of the battery can be reasonably well estimated by the EKFs. However, the inaccuracy of the state estimation in low SOC range ( 0.1 < SOC < 0.4 ) due to weak observability cannot be addressed without including the diffusion dynamics in the electrolyte. This inclusion leads in a 40% reduction in state-of-charge estimation error, from 9% to 5% error for the considered case.