Physics-based models of electrochemical cells are of great interest for the future battery management systems (BMSs), due to their accuracy and capability to predict cell physical states. One of their main disadvantages, when compared to equivalent circuit models, is the fact that they rely on numerous parameters. The identification of these parameters is difficult and usually needs the tear-down of the cell and detailed electrochemical analyses. In this work, we address this issue by developing a novel non-invasive procedure for the parameter identification of a single-particle model (SPM) of a Li-ion cell. The main contributions are: (i) the reformulation of the SPM in order to achieve a minimum number of grouped parameters to be identified; (ii) the formulation of a series of experimental tests capable to identify individually and non-invasively given subsets of these parameters. Notably, we craft specific tests to identify separately the parameters related to equilibrium, intercalation and diffusive phenomena that occur within the cell; (iii) the validation of the reformulated SPM and the associated parameter identification procedure through comparison of simulation results with both synthetic and experimental data. The former are obtained from a detailed pseudo-2-dimensional (P2D) model of a MCMB-LiCoO2 cell. The latter are obtained through experimental tests performed on a Lithium-titanate cell. Both are cycled with current profiles representative of power-grid and electric-vehicles (EVs) operating conditions. For these profiles, the model identified versus synthetic data achieves a root-mean-square error lower than 0.3% on the cell states and lower than 0.75% on the cell voltage. The model identified versus experimental data achieves a root-mean-square error on cell voltage lower than 1%.