Bayesian inference in non-Markovian state-space models with applications to fractional order systems

TL;DR

This paper introduces a Bayesian method using particle MCMC to estimate parameters in non-Markovian fractional order state-space models, specifically applied to battery impedance models, addressing challenges in parameter identifiability and sensitivity.

Contribution

It develops a novel Bayesian framework with particle MCMC tailored for non-Markovian fractional order systems, enabling effective parameter estimation in complex battery models.

Findings

Successful application to battery models demonstrating practical identifiability.

Analysis of sensitivity to priors, data quantity, input magnitude, and noise.

Extensive simulations validating the approach.

Abstract

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.