This paper aims at developing a management system for a lithium-ion battery in order to monitor its state-of-health. Based on the electrochemical processes within the battery, state-of-health indicators are deduced from the solid phase diffusion coefficients that describe the propagation of lithium in each electrode. Hence the estimation of these diffusion coefficients is the focus of the paper. The proposed method properly accounts for measurement noise and provides a confidence interval for the estimates. It relies on a three step procedure. A temporal transfer function is first highlighted from the partial differential equation describing the evolution of the lithium concentration inside the particles. Next a nonlinear parameter estimation problem for the transfer function identification is solved by resorting to the so-called simplified refined instrumental variable method. From this first estimation, the diffusion coefficients are then computed. A resampling scheme is used to estimate a confidence interval for the estimated parameters.