Statistical resolution limits and the complexified Crame/spl acute/r-Rao bound

Smith, Steven T.

doi:10.1109/tsp.2005.845426

Cited by 159 publications

(156 citation statements)

References 44 publications

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“…The Cramé r-Rao bound has provided more accuracy achievable by any unbiased estimator of signal parameters and fundamental physical limit on system accuracy [21]- [22]. For Gaussian process, M snapshots, and response corresponding sensors I×L, it has…”

Section: Cramér-rao Bounds (Crb) For the 2d Casementioning

confidence: 99%

A Modified T-ESPRIT for 2-D Direction of Arrival Estimation Performance Enhancement

Fayad¹,

Cao²

2015

IJMO

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Abstract-A new algorithm for improving 2D-Direction of Arrival Estimation (2D-DOAE) accuracy and estimator performance has been carried out. Subspace concept has been employed into ESPRIT method to reduce the computational complexity and the model's non-linearity effect into 2D-DOAE problem. The algorithm accuracy is verified by closed-form Cramé r-Rao bound (CRB). The simulation results show that the proposed algorithm realizes estimation process better than those of the previous estimation techniques leading to the estimator performance enhancement.Index Terms-DOAE, Subspace, ESPRIT, angle glint.

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Section: Cramér-rao Bounds (Crb) For the 2d Casementioning

confidence: 99%

A Modified T-ESPRIT for 2-D Direction of Arrival Estimation Performance Enhancement

Fayad¹,

Cao²

2015

IJMO

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“…The resolvability of closely spaced signals, in terms of parameter of interest, for a given scenario (e.g., for a given signal-to-noise ratio (SNR), for a given number of snapshots and/or for a given number of sensors) is a former and challenging problem which was recently updated by Smith [11], Shahram and Milanfar [12], Liu and Nehorai [13], and Amar and Weiss [14]. More precisely, the concept of statistical resolution limit (SRL), i. e., the minimum distance between two closely spaced signals a embedded in an additive noise that allows a correct resolvability/parameter estimation, is rising in several applications (especially in problems such as radar, sonar, and spectral analysis [15].…”

Section: Introductionmentioning

confidence: 99%

“…The concept of the SRL was defined/used in several manners [11][12][13][14][16][17][18][19][20][21][22][23][24], which could turn in it to a confusing concept. There exist essentially three approaches to define/obtain the SRL.…”

Section: Introductionmentioning

confidence: 99%

“…However, one can note that the coupling between the parameters, CRB(f 1 , f 2 ) (i.e., the CRB for the cross parameters f 1 and f 2 ), is ignored by this latter criterion. (2) To extend this, Smith [11] has proposed the following criterion: two signals are resolvable w.r.t. the frequencies if the difference between the frequencies, δ f , is greater than the standard deviation of the DOA difference estimation.…”

Section: Introductionmentioning

confidence: 99%

“…In [11,23], Smith has derived the SRL for two closely spaced sources in terms of DOA, each one modeled by one complex pole. In [24], Delmas and Abeida have derived the SRL based on the Smith criterion for DOA of discrete sources under QPSK, BPSK, and MSK model assumptions.…”

Section: Introductionmentioning

confidence: 99%

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Statistical resolution limit for the multidimensional harmonic retrieval model: hypothesis test and Cramér-Rao Bound approaches

Korso

Boyer

Renaux

et al. 2011

EURASIP J. Adv. Signal Process.

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The statistical resolution limit (SRL), which is defined as the minimal separation between parameters to allow a correct resolvability, is an important statistical tool to quantify the ultimate performance for parametric estimation problems. In this article, we generalize the concept of the SRL to the multidimensional SRL (MSRL) applied to the multidimensional harmonic retrieval model. In this article, we derive the SRL for the so-called multidimensional harmonic retrieval model using a generalization of the previously introduced SRL concepts that we call multidimensional SRL (MSRL). We first derive the MSRL using an hypothesis test approach. This statistical test is shown to be asymptotically an uniformly most powerful test which is the strongest optimality statement that one could expect to obtain. Second, we link the proposed asymptotic MSRL based on the hypothesis test approach to a new extension of the SRL based on the Cramér-Rao Bound approach. Thus, a closed-form expression of the asymptotic MSRL is given and analyzed in the framework of the multidimensional harmonic retrieval model. Particularly, it is proved that the optimal MSRL is obtained for equi-powered sources and/or an equi-distributed number of sensors on each multi-way array.

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Adaptive Radar

Smith¹

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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The sections in this article are Adaptive Radar Fundamentals Statistical Model for Adaptive Radar Optimum Adaptive Processing Space–Time Adaptive Processing Adaptive Detection Adaptive Weight Computation Adaptive Radar Estimation Conclusions

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Statistical resolution limits and the complexified Crame/spl acute/r-Rao bound

Cited by 159 publications

References 44 publications

A Modified T-ESPRIT for 2-D Direction of Arrival Estimation Performance Enhancement

A Modified T-ESPRIT for 2-D Direction of Arrival Estimation Performance Enhancement

Statistical resolution limit for the multidimensional harmonic retrieval model: hypothesis test and Cramér-Rao Bound approaches

Adaptive Radar

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