Bounds for Estimation of Complex Exponentials in Unknown Colored Noise

Joseph M. Francos

doi:10.1109/78.414780

Bounds for Estimation of Complex Exponentials in Unknown Colored Noise

Joseph M. Francos

School of Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We consider the problem of estimating the parameters of complex exponentials in the presence of complex additive Gaussian noise with unknown covariance. Bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise. We first present an exact Cramér-Rao bound (CRB) for this problem and specialize it for the cases of circular Gaussian processes and autoregressive processes. We also derive an approximate expression for the CRB, which is related to the conditional likelihood function. Numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy.

Original language	English
Pages (from-to)	2176-2185
Number of pages	10
Journal	IEEE Transactions on Signal Processing
Volume	43
Issue number	9
DOIs	https://doi.org/10.1109/78.414780
State	Published - 1 Jan 1995

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/78.414780

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title = "Bounds for Estimation of Complex Exponentials in Unknown Colored Noise",

abstract = "We consider the problem of estimating the parameters of complex exponentials in the presence of complex additive Gaussian noise with unknown covariance. Bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise. We first present an exact Cram{\'e}r-Rao bound (CRB) for this problem and specialize it for the cases of circular Gaussian processes and autoregressive processes. We also derive an approximate expression for the CRB, which is related to the conditional likelihood function. Numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy.",

author = "Francos, {Joseph M.}",

note = "Funding Information: Manuscript received November 6, 1993; revised February 10, 1995. This work was supported by the Army Research Oflice under Contract No. DAAL03-91-C-0022, sponsored by U.S. Army Communications Electronics Command, Center for Signals Warfare. The associate editor coordinating the review of this paper and approving it for publication was Prof. Fu Li. J. M. Francos is with the Department of Electrical and Computer Engineering, Ben-Gurion University, Beer-Sheva, Israel. B. Friedlander is with the Department of Electrical and Computer Engineering, University of Califomia, Davis, CA 95616 USA. IEEE Log Number 9413326.",

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N2 - We consider the problem of estimating the parameters of complex exponentials in the presence of complex additive Gaussian noise with unknown covariance. Bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise. We first present an exact Cramér-Rao bound (CRB) for this problem and specialize it for the cases of circular Gaussian processes and autoregressive processes. We also derive an approximate expression for the CRB, which is related to the conditional likelihood function. Numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy.

AB - We consider the problem of estimating the parameters of complex exponentials in the presence of complex additive Gaussian noise with unknown covariance. Bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise. We first present an exact Cramér-Rao bound (CRB) for this problem and specialize it for the cases of circular Gaussian processes and autoregressive processes. We also derive an approximate expression for the CRB, which is related to the conditional likelihood function. Numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy.

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Bounds for Estimation of Complex Exponentials in Unknown Colored Noise

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