An adaptive nonlinear autoregressive approach for modeling biological signals

The noisy and complex nature of many biological signals such as the electroencephalogram (EEG) has long constituted a major challenge in terms of analysis and prediction for single and multivariate problems. Nonlinear signal modeling, despite its widespread applicability, often shows limited success whenever the signal is contaminated with noise or is time varying in nature. We herein introduce a novel approach for joint modeling and de-noising of time series data such as EEG recordings. The approach extends a recently introduced hybrid autoregressive kernel model to noisy time-invariant signals by employing Square-Root Cubature Kalman Filtering for adaptively tracking the (nonlinear) model regression parameters and predicting the time series. The approach is demonstrated to outperform the Yule-Walker method previously used in terms of mean square error, and to account for the presence of additive white Gaussian noise. Simulations include a nonlinear benchmark example, the chaotic Mackey Glass time series, and real EEG recordings.