Adaptive modeling and spectral estimation of nonstationary biomedical signals based on Kalman filtering

We describe an algorithm to estimate the instantaneous power spectral density (PSD) of nonstationary signals. The algorithm is based on a dual Kalman filter that adaptively generates an estimate of the autoregressive model parameters at each time instant. The algorithm exhibits superior PSD tracking performance in nonstationary signals than classical nonparametric methodologies, and does not assume local stationarity of the data. Furthermore, it provides better time-frequency resolution, and is robust to model mismatches. We demonstrate its usefulness by a sample application involving PSD estimation of intracranial pressure signals (ICP) from patients with traumatic brain injury (TBI).

[1]  Eric A. Wan,et al.  Neural dual extended Kalman filtering: applications in speech enhancement and monaural blind signal separation , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

[2]  Dimitris G. Manolakis,et al.  Statistical and Adaptive Signal Processing , 2000 .

[3]  Eric A. Wan,et al.  A two-observation Kalman framework for maximum-likelihood modeling of noisy time series , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[4]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[5]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .

[6]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[7]  J. W. Tukey,et al.  The Measurement of Power Spectra from the Point of View of Communications Engineering , 1958 .

[8]  M. S. Babtlett.  Smoothing Periodograms from Time-Series with Continuous Spectra , 1948, Nature.

[9]  J. Cadzow.  Maximum Entropy Spectral Analysis , 2006 .

[10]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[11]  Eric A. Wan,et al.  Removal of noise from speech using the dual EKF algorithm , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[12]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[13]  M. Bartlett.  Smoothing Periodograms from Time-Series with Continuous Spectra , 1948 .

[14]  Ali H. Sayed,et al.  Linear Estimation (Information and System Sciences Series) , 2000 .

[15]  Dimitris G. Manolakis,et al.  Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing , 1999 .