  In this work we analyse the local nonlinear electrochemical impedance
spectroscopy (NLEIS) response of a lithium-ion battery and estimate model
parameters from measured NLEIS data. The analysis assumes a single-particle
model including nonlinear diffusion of lithium within the electrode particles
and asymmetric charge transfer kinetics at their surface. Based on this model
and assuming a moderately-small excitation amplitude, we systematically derive
analytical formulae for the impedances up to the second harmonic response,
allowing the meaningful interpretation of each contribution in terms of
physical processes and nonlinearities in the model. The implications of this
for parameterization are explored, including structural identifiability
analysis and parameter estimation using maximum likelihood, with both synthetic
and experimentally measured impedance data. Accurate fits to impedance data are
possible, however inconsistencies in the fitted diffusion timescales suggest
that a nonlinear diffusion model may not be appropriate for the cells
considered. Model validation is also demonstrated by predicting time-domain
voltage response using the parameterized model and this is shown to have
excellent agreement with measured voltage time-series data (11.1 mV RMSE).
