Title

OBSERVATIONS OF LINEAR ESTIMATION.

Document Type

Article

Date of Original Version

1-1-1978

Abstract

Heisey and Griffiths proposed a generalization of linear prediction, called ″linear estimation″ , in which both past and future data samples are used to predict (estimate) the present sample. They report that although the mean-square error from this formulation is usually smaller than from standard linear prediction, the corresponding spectral estimate is a poorer fit to the true spectrum. A general explanation is given for this apparent paradox in terms of the zeros of the estimated inverse filter and the authors examine specifically the case of frequency estimation for a single complex sinusoid in noise. The intuitively appealing idea that future as well as past data should be included in the estimates is best implemented by a combined forward-backward prediction method.

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