IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 1 Abstract—This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of non-stationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by conventional Kalman filtering. This study uses non-Gaussian state noise to model AR parameter variation with estimation by Monte Carlo particle filter (PF). Use of non-Gaussian noise such as heavy-tailed distribution is motivated by its ability to track abrupt and smooth AR parameter changes which are inadequately modeled by Gaussian models. Thus, more accurate spectral estimates and better ERD tracking can be obtained. This paper further proposes a non-Gaussian state space formulation of time-varying autoregressive moving average (TVARMA) models to improve the spectral estimation. Simulation on TVAR process with abrupt parameter variation shows superior tracking performance of non-Gaussian models. Evaluation on motor- imagery EEG data shows that the non-Gaussian models provide more accurate detection of abrupt changes in alpha rhythm ERD. Among the proposed non-Gaussian models, TVARMA shows better spectral representations while maintaining reasonable good ERD tracking performance. Index Terms—Time-varying autoregressive models, particle filters, event-related desynchronization I. INTRODUCTION VENT-RELATED de-synchronization (ERD) and synchronization (ERS) are used to represent frequency- specific changes of on-going EEG activity, induced by specific stimulus, which consist either of decrease or increase of power in specific frequency band. Left and right-hand motor imagery shows alpha rhythm ERD. Conventional Fourier transform based spectral analysis is limited by stationary assumptions and suffers tradeoff between time and Manuscript received June, 2010; revised September 2010. This work was supported by Minister of Higher Education and Universiti Teknologi Malaysia (UTM), under Fundamental Research Grant Scheme, Vot 78208. C.-M. Ting is with the Center for Biomedical Engineering, UTM, 81310 Skudai, Johor, Malaysia (e-mail: cmting1818@yahoo.com). Sh-Hussain Salleh is with the Center for Biomedical Engineering, UTM, 81310 Skudai, Johor, Malaysia (e-mail:shussain@utm.my). Z. M. Zainuddin is with the Department of Mathematics, Faculty of Science, UTM, 81310 Skudai, Johor, Malaysia (e-mail: zmz@fs.utm.my). A. Bahar is with the Department of Mathematics, Faculty of Science, UTM, 81310 Skudai, Johor, Malaysia (e-mail:arifah@utm.my). frequency resolution. The frequency resolution can be improved by using parametric spectral analysis. Common parametric models used are autoregressive (AR) and autoregressive moving average (ARMA) models which are able to represent appropriately many kinds of natural signals such as speech and EEG. To better model non-stationary signals, time varying AR (TVAR) and ARMA (TVARMA) models have been used, where the AR parameters vary instantaneously with time. The TVAR models were proposed for EEG modeling by [1] and applied for EEG analysis [2]. The TVAR models enable non-stationary spectral analysis by generating instantaneous estimates of power spectrum, thus provide high time-frequency resolution. This model is also adopted here. The TVAR model is formulated into state-space form to enable estimation of TVAR coefficients by using Kalman filter (KF), which is optimal in mean-square sense. TVAR models with KF have been used extensively in power spectrum estimation for biomedical signals in general [2], [3], [4], [5], and in EEG spectral estimation for ERD and ERS [6] [7], [8]. Tarvainen [7] proposed Kalman smoother for TVARMA for ERS and showed faster tracking of ERS and better time-frequency resolution compared with recursive least square (RLS) method and STFT. The work was extended in [6] using the expectation-maximization (EM) for parameter estimation. Results on ERD showed better performance. Most of the above mentioned studies for non-stationary biomedical signal analysis use TVAR models in linear and Gaussian state-space form where the state and observation noise are assumed to be Gaussian. However, there are processes for which linear Gaussian modeling is inappropriate, for instances time series with abrupt and smooth changes of means. The simple linear Gaussian models with small Gaussian noise variance cannot detect rapidly the abrupt changes while use of large variance produces noisy estimates. The poor AR parameter estimates will result in inaccurate spectrum. This Gaussian model problem was addressed by Kitagawa in an early study [9]. This problem is also inherent in the ERD/ERS problem, where the underlying AR coefficients of EEG process exhibit abrupt changes (perhaps event-related) [7], which cannot be tracked rapidly by Gaussian models and thus suffer tracking lag. To overcome the Gaussian model problem, Kitagawa [9] proposed the non- Gaussian state-space approach as alternative to model nonstationary time series when Gaussian modeling is inappropriate. Monte Carlo filtering and smoothing were used. The state and observation noise distributions are not Spectral Estimation of Non-Stationary EEG using Particle Filtering with Application to Event-Related Desynchronization (ERD) Chee-Ming Ting, Sh-Hussain Salleh, Z. M. Zainuddin, and Arifah Bahar E "Copyright (c) 2010 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending an email to pubs-permissions@ieee.org." Chee-Ming Ting, Sh-Hussain Salleh, Z. M. Zainuddin, and Arifah Bahar, “Spectral estimation of nonstationary EEG using particle filtering with application to event- related desynchronization (ERD),” IEEE Transaction on Biomedical Engineering, vol. 58. no. 3, pp. 321-331, 2011. DOI 10.1109/TBME.2010.2088396