  Battery impedance spectroscopy models are given by fractional order (FO)
differential equations. In the discrete-time domain, they give rise to
state-space models where the latent process is not Markovian. Parameter
estimation for these models is therefore challenging, especially for
non-commensurate FO models. In this paper, we propose a Bayesian approach to
identify the parameters of generic FO systems. The computational challenge is
tackled with particle Markov chain Monte Carlo methods, with an implementation
specifically designed for the non-Markovian setting. The approach is then
applied to estimate the parameters of a battery non-commensurate FO equivalent
circuit model. Extensive simulations are provided to study the practical
identifiability of model parameters and their sensitivity to the choice of
prior distributions, the number of observations, the magnitude of the input
signal and the measurement noise.
