Performance of high resolution frequencies estimation methods compared to the Cramer-Rao bounds

Clergeot, H.; Tressens, S.; Ouamri, Abdelaziz

doi:10.1109/29.46553

Cited by 101 publications

(48 citation statements)

References 16 publications

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“…Similar conclusions can be reached for the two-source case [4], [7], while for the general results, we refer to [7] and [21].…”

Section: A Analysis Of Noise Sensitivitysupporting

confidence: 65%

“…If we denote by and , then (3) is equivalent to (4) where . Note that the samples are given by a linear combination of exponentials ; thus, we can reduce the problem of estimating the unknown parameters and , into the classical spectral estimation problem, that is, the problem of estimating frequencies and weighting coefficients of superimposed exponentials [8], [16], [19].…”

Section: Problem Statementmentioning

confidence: 99%

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Sampling and reconstruction of signals with finite rate of innovation in the presence of noise

Maravic

Vetterli

2005

IEEE Trans. Signal Process.

215

214

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Abstract-Recently, it was shown that it is possible to develop exact sampling schemes for a large class of parametric nonbandlimited signals, namely certain signals of finite rate of innovation. A common feature of such signals is that they have a finite number of degrees of freedom per unit of time and can be reconstructed from a finite number of uniform samples. In order to prove sampling theorems, Vetterli et al. considered the case of deterministic, noiseless signals and developed algebraic methods that lead to perfect reconstruction. However, when noise is present, many of those schemes can become ill-conditioned. In this paper, we revisit the problem of sampling and reconstruction of signals with finite rate of innovation and propose improved, more robust methods that have better numerical conditioning in the presence of noise and yield more accurate reconstruction. We analyze, in detail, a signal made up of a stream of Diracs and develop algorithmic tools that will be used as a basis in all constructions. While some of the techniques have been already encountered in the spectral estimation framework, we further explore preconditioning methods that lead to improved resolution performance in the case when the signal contains closely spaced components. For classes of periodic signals, such as piecewise polynomials and nonuniform splines, we propose novel algebraic approaches that solve the sampling problem in the Laplace domain, after appropriate windowing. Building on the results for periodic signals, we extend our analysis to finite-length signals and develop schemes based on a Gaussian kernel, which avoid the problem of ill-conditioning by proper weighting of the data matrix. Our methods use structured linear systems and robust algorithmic solutions, which we show through simulation results.

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“…Similar conclusions can be reached for the two-source case [4], [7], while for the general results, we refer to [7] and [21].…”

Section: A Analysis Of Noise Sensitivitysupporting

confidence: 65%

Section: Problem Statementmentioning

confidence: 99%

Sampling and reconstruction of signals with finite rate of innovation in the presence of noise

Maravic

Vetterli

2005

IEEE Trans. Signal Process.

215

214

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“…The theorem generalizes the approximation result in [41] to allow an arbitrary combination of scattering types, rather than only one type of nonpoint scattering. For statistical accuracy of parameter estimates using damped exponential modeling, is often suggested [42], [39], [30]. Theorem 1 shows that the Hankel data matrix formed from GTD scattering model (8) is close to a Hankel data matrix formed from a damped exponential model whose mode angles are exactly specified by the scattering center range parameters.…”

Section: A Damped Exponential Model 1) Scattering Modelmentioning

confidence: 99%

Attributed scattering centers for SAR ATR

Potter

Moses

1997

IEEE Trans. on Image Process.

451

210

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Abstract-High-frequency radar measurements of man-made targets are dominated by returns from isolated scattering centers, such as corners and flat plates. Characterizing the features of these scattering centers provides a parsimonious, physically relevant signal representation for use in automatic target recognition (ATR). In this paper, we present a framework for feature extraction predicated on parametric models for the radar returns. The models are motivated by the scattering behavior predicted by the geometrical theory of diffraction. For each scattering center, statistically robust estimation of model parameters provides highresolution attributes including location, geometry, and polarization response. We present statistical analysis of the scattering model to describe feature uncertainty, and we provide a leastsquares algorithm for feature estimation. We survey existing algorithms for simplified models, and derive bounds for the error incurred in adopting the simplified models. A model order selection algorithm is given, and an M-ary generalized likelihood ratio test is given for classifying polarimetric responses in spherically invariant random clutter.

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“…Thus we will not try to propose new approaches regarding the algorithms. One of the difficulties is that there is as yet no unanimously agreed optimal algorithm for retrieving sinusoids in noise, although there has been numerous evaluations of the different methods (see, e.g., [10]). For this reason, our choice falls on the the simplest approach, the total least-squares approximation (implemented using a singular value decomposition (SVD), an approach initiated by Pisarenko in [11]), possibly enhanced by an initial "denoising" (more exactly, model matching) step provided by what we call Cadzow's iterated algorithm [12].…”

Section: A =mentioning

confidence: 99%