Conference Paper

Performance comparisons of the minimum free energy algorithms with the reduced rank modified covariance eigenanalysis algorithm

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Abstract

Low SNR simulations comparing the minimum-free-energy (MFE) spectral estimation algorithms of Silverstein and Pimbley (1988) with the reduced rank modified covariance eigenanalysis algorithm of Tufts and Kumaresan (1982) have been performed. Two different MFE algorithms are discussed and simulated. The results of the statistical analyses demonstrate that both MFE algorithms are robust, low-variance spectral estimators capable of making reliable frequency estimations of closely spaced sources at very low SNRs, from single snapshot data. They are applicable to the general domain of spectral estimation, while the eigenanalysis algorithms are primarily restricted to line spectra frequency estimation. Nonetheless, for simulations of closely spaced line spectra at low SNRs, the MFE estimations are considerably more robust than the Tufts-Kumaresan estimations

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The frequency-estimation performance of the forward-backward linear prediction (FBLP) method of Nuttall/Uhych and Clayton, is significantly improved for short data records and low signal-to-noise ratio (SNR) by using information about the rank M of the signal correlation matrix. A source for the improvement is an implied replacement of the usual estimated correlation matrix by a least squares approximation matrix having the lower rank M. A second, related cause for the improvement is an increase in the order of the prediction filter beyond conventional limits. Computationally, the recommended signal processing is the same as for the FBLP method, except that the vector of prediction coefficients is formed from a linear combination of the M principal eigenvectors of the estimated correlation matrix. Alternatively, singular value decomposition can be used in the implementation. In one special case, which we call the Kumaresan-Prony (KP) case, the new prediction coefficients can be calculated in a very simple way. Philosophically, the improvement can be considered to result from a preliminary estimation of the explainable, predictable components of the data, rather than attempting to explain all of the observed data by linear prediction.
Estimation of Frequencies of Multiple Sinusoids: Making Linear Prediction Perform Like Max-imum Likelihood A New Analysis technique for Time series dah Modern Specfral Esrimiion: lheory & Applica-lion
  • D W Tufts
  • R Kumaresan
  • J P Burg
Tufts, D.W.. and R. Kumaresan. "Estimation of Frequencies of Multiple Sinusoids: Making Linear Prediction Perform Like Max-imum Likelihood", Proc. IEEE. vol. 70, pp. 975-989, Sept. 1982 Burg, J.P., " A New Analysis technique for Time series dah," Proc. NAlO Advanced Sfdies Inairuie on Signal Proc., Enschede, Thc Nctherlands, 1968. Cf. Kay, S.M. Modern Specfral Esrimiion: lheory & Applica-lion. Prentice Hall. New Jersey, 1987; Marple, S.L,,Jr., Digiral Specfral Analysis, Prentice Hall. New Jersey. 1987. I41 [51