Asymptotic analysis of the least squares estimate of 2-D exponentials in colored noise

Research output: Contribution to conferencePaperpeer-review

Abstract

This paper considers the problem of estimating the parameters of complex-valued sinusoidal signals observed in colored noise. This problem is a special case of the general problem of estimating the parameters of a complex-valued homogeneous random field with mixed spectral distribution from a single observed realization of it. The large sample properties of the least squares estimator of the exponentials' parameters are derived, making no assumptions as to the probability distribution of the observed field. It is shown that the least squares estimator is asymptotically unbiased. A simple expression for the estimator asymptotic covariance matrix is derived. The derivation shows that, asymptotically, the least squares estimation of the parameters of each exponential is decoupled from the estimation of the parameters of the other exponentials. Assuming the observed field is a realization of a Gaussian random field, it is further demonstrated that the asymptotic error covariance matrix of the least squares estimate attains the Cramer-Rao bound, even for modest dimensions of the observed field and low signal to noise ratios.

Original languageEnglish
Pages396-399
Number of pages4
StatePublished - 1 Jan 2000
EventProceedings of the 10th IEEE Workshop on Statiscal and Array Processing - Pennsylvania, PA, USA
Duration: 14 Aug 200016 Aug 2000

Conference

ConferenceProceedings of the 10th IEEE Workshop on Statiscal and Array Processing
CityPennsylvania, PA, USA
Period14/08/0016/08/00

ASJC Scopus subject areas

  • General Engineering

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