Estimation of Frequencies of Multiple Sinusoids: Making Linear Prediction Perform Like Maximum Likelihood

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The frequency-estimation performance of the forward-backward linear prediction (FBLP) method of Nuttall/Ulrych and Clayton, is significantly improved for short data records and low signal-to-noise ratio (SNR) by using information about die 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 die lower rank M. A second, related cause for the improvement is an increase in the order of die 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 man attempting to explain all of the observed data by linear prediction. Copyright © 1982 by The Institute of Electrical and Electronics Engineers, Inc.

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Proceedings of the IEEE