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

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-commensurat...

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Bibliographic Details
Published in:arXiv.org 2016-01
Main Authors: Jacob, Pierre E, Mahdi Alavi, S M, Mahdi, Adam, Payne, Stephen J, Howey, David A
Format: Article
Language:English
Subjects:
Bayesian analysis
Computer simulation
Differential equations
Equivalent circuits
Markov analysis
Markov chains
Monte Carlo simulation
Noise measurement
Parameter estimation
Parameter identification
Parameter sensitivity
Process parameters
State space models
Statistical inference
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Summary: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.
ISSN:2331-8422