Adaptive AR modeling of nonstationary time series by means of Kalman filtering

Abstract

An adaptive on-line procedure is presented for autoregressive (AR) modeling of nonstationary multivariate time series by means of Kalman filtering. The parameters of the estimated time-varying model can be used to calculate instantaneous measures of linear dependence. The usefulness of the procedures in the analysis of physiological signals is discussed in two examples: First, in the analysis of respiratory movement, heart rate fluctuation, and blood pressure, and second, in the analysis of multichannel electroencephalogram (EEG) signals. It was shown for the first time that in intact animals the transition from a normoxic to a hypoxic state requires tremendous short-term readjustment of the autonomic cardiac-respiratory control. An application with experimental EEG data supported observations that the development of coherences among cell assemblies of the brain is a basic element of associative learning or conditioning.

Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics

“…Moreover, since vector AR identification may yield unreliable parameter estimates in the presence of noisy data and non-stationary dynamics, variants of the traditional least squares estimators (e.g., exploiting Kalman filters to increase robustness [58] or to track time-varying behaviors [59]) should be considered when these aspects are deemed significant. In the cardiorespiratory data analyzed in this study, good signal-to-noise ratios and stationarity within the observed windows were guaranteed by careful experimental settings and time series measurements and editing, and the linear Gaussian approximation was supported by the knowledge that a conspicuous amount of cardiorespiratory variability can be explained by linear interaction models [6,60].…”

Removal of CPR Artifacts From the Ventricular Fibrillation ECG by Adaptive Regression on Lagged Reference Signals

“…In this article, we propose Kalman state-space methods [19]- [21] which extend ordinary least-squares (OLS) regression. We consider Kalman methods to be appropriate for CPR artifact removal because:…”

“…We propose a state-space regression model-called adaptive least squares (ALS)-whose states are time-varying regression coefficients and whose observations are the CPR-corrupted ECG signal, cf. [21]. This is a generalization of the aformentioned OLS model having constant coefficients.…”

Parametric Modelling of EEG Data for the Identification of Mental Tasks

“…The results showed that the MVAR features have a slightly better classification performance and better consistency. Adaptive on-line MVAR was explored in (Arnold et al, 1998), adapting the use of the Kalman filter from the univariate case to the multivariate model. A trivariate AR model of order 22 was used, from which spectral parameters were extracted yielding relevant information regarding neural communication processes.…”