A Novel Adaptive Fading Kalman Filter-Based Approach to Time-Varying Brain Spectral/Connectivity Analyses of Event-Related EEG Signals

Abstract

This paper proposes a novel adaptive fading Kalman filter (AF-KF)-based approach to time-varying brain spectral and functional connectivity analyses of event-related multi-channel electroencephalogram (EEG) signals. By modeling the EEG signals as a time-varying (TV) multivariate autoregressive (MVAR) process, a new AF-KF with variable number of measurements (AF-KF-VNM) is proposed for estimating the spectra of the EEG signals and identifying their functional connectivity. The proposed AF-KF-VNM algorithm uses a new adaptive fading method to adaptively update the model parameters of the KF for improved state estimation and utilizes multiple measurements for better adaptation to the nonstationary signal observations. Experimental results on a simulated data for modeling the TV directed interactions in multivariate neural data show that the proposed AF-KF-VNM method yields better tracking performance than other approaches tested. The proposed algorithm is then integrated into a novel methodology for combined functional Magnetic Resonance Imaging (fMRI) activation maps and EEG spectrum analyses for quantifying the differences in spectrum contents and information flows between the target and standard conditions in a visual oddball paradigm. The results and findings show that the proposed methodology agrees well with the literature and is capable of revealing significant frequency components and information flow involved as well as their time variations.