Exact conditional and unconditional Cramér–Rao bounds for near field localization

Begriche, Youcef; Thameri, Messaoud; Abed-Meraim, Karim

doi:10.1016/j.dsp.2014.04.006

Cited by 17 publications

(26 citation statements)

References 26 publications

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“…In contrast, arrays that do not satisfy conditions (11) do not necessary satisfy (16) (see an example for linear arrays in [12]), an unexpected behavior due to a possible coupling (b 1;3 2 a0, b 2;3 2 a 0) between ðθ; ϕÞ and r in FðαÞ to the second-order in ϵ. Finally, for a source in the plane (x,y), (15) …”

Section: Arbitrary Planar Arraysmentioning

confidence: 83%

“…we easily prove that conditions (11) are satisfied if each circle include more than 5 (P i 4 5, for all i) sensors. By using the sensors polar coordinates ðr i ; θ p i ;i Þ, the following Taylor expansions of the terms of the matrix FðαÞ are proved in Appendix B.1 for P i Z 6: 2c…”

Section: Concentric Uniform Circular-based Arraysmentioning

confidence: 95%

“…For example the Vshaped antenna array highlighted in [7] satisfies (10) but no longer satisfies (11). Under the conditions (11), (6) simplifies to…”

Section: Arbitrary Planar Arraysmentioning

confidence: 98%

“…This approach, applied to uniform linear arrays (ULA) [11], arbitrary linear arrays [12] and uniform circular arrays (UCA) [13], is extended for the first time, here, to planar antenna arrays.…”

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confidence: 99%

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CRB analysis of planar antenna arrays for optimizing near-field source localization

et al. 2016

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International audienceThis paper focuses on the Cramér Rao bound (CRB) of the azimuth, elevation and range with planar arrays for narrowband near-field source localization, using the exact expression of the time delay parameter. Specifically, the aim of this paper is twofold. First, we derive explicit non-matrix closed-form expressions of approximations of these three CRBs. Second, we use these expressions to optimize near-field source localization. For deriving these expressions, we introduce conditions on the array geometry that allow us to decouple the azimuth, elevation and range parameters to a certain order in λ/r (in which λ and r denote the wavelength and the range, respectively). The proposed conditions complement those found for a far-field source that ensure the azimuth and elevation estimations are both exactly decoupled and isotropic. A particular attention is given to the popular array configurations which are the concentric uniform circular-based arrays, cross-based and squarebased centro-symmetric arrays which satisfy these conditions. In order to control directions of arrivals (DOA) ambiguity, we propose a new criterion, which allows us to design non-uniform square [resp., cross]-based centrosymmetric array configurations with improved near-field range estimation capabilities without deteriorating the DOA precisions w.r.t. uniform square [resp., cross]-based arrays. Finally, we specify the accuracy of our proposed approximated CRBs'expressions and isotropy's conditions w.r.t. the range and the number of sensor

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Section: Arbitrary Planar Arraysmentioning

confidence: 83%

Section: Concentric Uniform Circular-based Arraysmentioning

confidence: 95%

“…For example the Vshaped antenna array highlighted in [7] satisfies (10) but no longer satisfies (11). Under the conditions (11), (6) simplifies to…”

Section: Arbitrary Planar Arraysmentioning

confidence: 98%

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confidence: 99%

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CRB analysis of planar antenna arrays for optimizing near-field source localization

et al. 2016

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“…The near field (Fresnel) region of the transmitting ULA is a finite space around it bounded by the following lower and upper limits of ρ ep [3], [13]:…”

Section: Signal Modelmentioning

confidence: 99%

Near field targets localization using bistatic MIMO system with symmetric arrays

Singh¹,

Wang²,

Chargé³

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In this paper, we propose a subspace based method to localize multiple targets in the near field region of a bistatic MIMO system with symmetric uniform linear arrays (ULAs). The proposed method uses the symmetry in the transmitting and receiving arrays to estimate the angle of departure (AOD) and angle of arrival (AOA) of each target by using 1D rank reduction estimator (RARE) based method. For each estimated AOA, the range from the center of the transmitting array to the corresponding target is estimated by using 1D multiple signal classification (MUSIC). Finally, the receiver side range of each target is estimated by using the other three estimated location parameters in 2D MUSIC technique which also automatically pairs the location parameters.

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Cramér–Rao bound and statistical resolution limit investigation for near-field source localization

Bao

Korso²,

Ouslimani³

2016

Digital Signal Processing

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(M.N. El Korso). polarized far-field sources and in [27], the authors studied the angular resolution limit for far-field sources in the presence of modeling errors. Moreover, in [28], the authors provide a novel methodology to derive an approximation of the resolution limit. Nevertheless, to the best of our knowledge, no works have been done to quantify the resolvability of two closely spaced near-field sources in the non-uniform linear array (NULA) context for the general case 1 (general case, means that the time varying source signals, the noise variance, the range and the bearing are all unknown parameters). Consequently, the goal of this paper is to fill this lack by addressing the following question: "What is, in a nearfield source scenario, the minimum source separation required, under which two near-field sources can still be correctly resolved?" To this end, one common tool is the distance resolution limit (DRL) of two closely spaced sources, defined as the minimum distance with respect to the sources for which allows a correct resolvability. The DRL can be derived based on one of the following three fundamental approaches: i) the analysis of the mean null spectrum [30], ii) the detection theory [19,23] (using a binary hypothesis test and a proper generalized likelihood ratio test [27]), or iii) the estimation accuracy (namely, based on the Cramér-Rao

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Exact conditional and unconditional Cramér–Rao bounds for near field localization

Cited by 17 publications

References 26 publications

CRB analysis of planar antenna arrays for optimizing near-field source localization

CRB analysis of planar antenna arrays for optimizing near-field source localization

Near field targets localization using bistatic MIMO system with symmetric arrays

Cramér–Rao bound and statistical resolution limit investigation for near-field source localization

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