Robust Autoregression with Exogenous Input Model for System Identification and Predicting

Abstract

Autoregression with exogenous input (ARX) is a widely used model to estimate the dynamic relationships between neurophysiological signals and other physiological parameters. Nevertheless, biological signals, such as electroencephalogram (EEG), arterial blood pressure (ABP), and intracranial pressure (ICP), are inevitably contaminated by unexpected artifacts, which may distort the parameter estimation due to the use of the L2 norm structure. In this paper, we defined the ARX in the Lp (p ≤ 1) norm space with the aim of resisting outlier influence and designed a feasible iteration procedure to estimate model parameters. A quantitative evaluation with various outlier conditions demonstrated that the proposed method could estimate ARX parameters more robustly than conventional methods. Testing with the resting-state EEG with ocular artifacts demonstrated that the proposed method could predict missing data with less influence from the artifacts. In addition, the results on ICP and ABP data further verified its efficiency for model fitting and system identification. The proposed Lp-ARX may help capture system parameters reliably with various input and output signals that are contaminated with artifacts.