Asymptotic behavior of maximum likelihood estimates of superimposedexponential signals

  • Authors:
  • C.R. Rao;L.C. Zhao

  • Affiliations:
  • Dept. of Stat., Pennsylvania State Univ., University Park, PA;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1993

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Abstract

Strong consistency and asymptotic normality are derived for the maximum-likelihood estimates (MLEs) of the unknown parameters (ω 1,. . .,ωp), (α1,. . ., αp), and σ2 in the superimposed exponential model for signals, Yt=Σ α exp (itωk)+et, where the summation is from k=1 to p, t=0, 1, . . ., n-1, and σ2 is the variance of the complex normal distribution of et. As a by-product, it is found that the MLEs of the parameters attain the Cramer-Rao lower bound for the asymptotic covariance matrix