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ABSTRACT
An efficient time-varying autoregressive (TVAR) modelling scheme that expands the time-varying parameters onto the multi-scale wavelet basis functions is presented for modelling nonstationary signals and with applications to time–frequency analysis (TFA) of electroencephalogram (EEG) signals. In the new parametric modelling framework, the time-dependent parameters of the TVAR model are locally represented by using a novel multi-scale wavelet decomposition scheme, which can allow the capability to capture the smooth trends as well as track the abrupt changes of time-varying parameters simultaneously. A forward orthogonal least square (FOLS) algorithm aided by mutual information criteria are then applied for sparse model term selection and parameter estimation. Two simulation examples illustrate that the performance of the proposed multi-scale wavelet basis functions outperforms the only single-scale wavelet basis functions or Kalman filter algorithm for many nonstationary processes. Furthermore, an application of the proposed method to a real EEG signal demonstrates the new approach can provide highly time-dependent spectral resolution capability.
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Notes on contributors
Yang Li
Yang Li obtained his Ph.D. degree in Automatic Control and Systems Engineering at Sheffield University in September 2011. After one year of postdoctoral research in the Department of Computer and Biomedical Engineering at the University of North Carolina at Chapel Hill, Dr. Li joined Beihang University as an Associate Professor in the Department of Automation Sciences and Electrical Engineering starting in February, 2013. His main research area is involved system identification and modeling for complex nonlinear processes: NARMAX methodology and applications; nonlinear and nonstationary signal processing; intelligent computation and data mining, parameter estimation and model optimization, sparse representation etc.
Wei-Gang Cui
Wei-Gang Cui was born in Shaanxi province, China, in March 1994. He received his bachelor's degree in mathematics from Beihang University, Beijing, China, in 2016. He is currently a Ph.D. candidate in Department of Automation Science and Electrical Engineering at Beihang University. His research interests include signal processing, system identification and time-frequency domain analysis.
Mei-Lin Luo
Mei-Lin Luo received his bachelor degree from Beihang University in 2014. Now he is a graduate student in Department of Automation Science and Electrical Engineering at Beihang University, Beijing, China. His main research interests include time series analysis, machine learning and pattern recognition.
Ke Li
Ke Li received his Ph.D. degree from Beihang University, Beijing, China, in 2008. After two year of postdoctoral research in the School of Aeronautic Science and Engineering at the Beihang University, Dr. Li joined Beihang University as an Assistant Professor in the School of Aeronautic Sciences and Engineering starting in April, 2010. His current research interests include control methods of thermal engineering, intelligent control algorithms, process control, and machine learning methods.
Lina Wang
Lina Wang received the B.E. degree in computer science and Engineering from Xi'an Institute of Technology, in July 2002, the M.E. degree in computer science from China Academy of Launch Vehicle Technology, in December 2004, and Ph.D. degree in computer science and Engineering from Beihang University, in June 2016. Currently, she works for National Laboratory of Aerospace Intelligent Control Technology. Her research interests include Intelligent Control and information fusion.