title: Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing.
abstract: Linear Time Invariant (LTI) processes can be modelled by means of Auto-Regressive Moving Average (ARMA) model systems. In this paper, we examine whether an ARMA model can be fitted to a process characterised by switched nonlinearities. In particular, we conduct the following test: we generate data from known LTI and nonlinear (threshold/dead-zone) models of human balance and analyse the output using ARMA. We show that both these known systems can be fitted, according to standard criteria, with low order ARMA models. To check if there are some obvious effects of the dead-zone, we compare the power spectra of both systems with the power spectra of their ARMA models. We then examine spectral properties of three posturographic data sets and their ARMA models and compare them with the power spectra of our model systems. Finally, we examine the dynamics of our model systems in the absence of noise to determine what is the effect of the switching threshold (dead-zone) on the asymptotic dynamics.
authors.affiliation: School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, United Kingdom.
authors.forename: Piotr
authors.initials: P
authors.lastname: Kowalczyk
authors.affiliation: School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, United Kingdom.
authors.forename: Salam
authors.initials: S
authors.lastname: Nema
authors.affiliation: School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA), University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Paul
authors.initials: P
authors.lastname: Glendinning
authors.affiliation: Institute for Biomedical Research into Human Movement and Health (IRM), Manchester Metropolitan University, Chester Street, Manchester M1 5GD, United Kingdom.
authors.forename: Ian
authors.initials: I
authors.lastname: Loram
authors.affiliation: School of Electrical and Electronic Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Martin
authors.initials: M
authors.lastname: Brown
mesh_terms: D000465:Algorithms; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D004856:Postural Balance / Q000502:physiology*; D011187:Posture / Q000502:physiology*; D013997:Time Factors