A bayesian approach to array geometry design

Oktel, U.; Moses, Randolph L.

doi:10.1109/tsp.2005.845487

Cited by 34 publications

(42 citation statements)

References 23 publications

(45 reference statements)

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“…We adopt a Bayesian approach by using [13, May 28, 2012 DRAFT p. 6] the expectation of the conditional CRBs (ECRB)C ΦΦ= E Φ,Θ (C ΦΦ ) andC Θ,Θ= E Φ,Θ (C ΘΘ ) as criteria to minimize. The ECRB was also used in [4] as a cost function, but only the azimuth DOA angle was considered therein. Advantageously, these cost functions inherit the convenient structure of the CRB.…”

Section: Data Model and Performance Criteriamentioning

confidence: 99%

“…Estimation accuracy depends on the sensor positions, in a way that has remained largely unquantified [1], [2], mainly because of the complexity of the Cramer Rao Bound (CRB), even in the single source case [3]. Because of the intricate original expression of the CRB [3], early attempts to achieve array optimization were conducted mostly using heuristic techniques [4], [5]. A recent simplification of the CRB of the planar antenna array shows a convenient sinusoidal dependency on the source azimuth [6], as long as the array geometry is concerned.…”

Section: Introductionmentioning

confidence: 99%

“…A recent simplification of the CRB of the planar antenna array shows a convenient sinusoidal dependency on the source azimuth [6], as long as the array geometry is concerned. Estimation accuracy increases if sensors are allowed to occupy a larger region [4], at the expense of increased array ambiguities [7]. They occur when two (first-order ambiguity) or more (higher-order ambiguity) steering vectors at different look directions are linearly dependent [8].…”

Section: Introductionmentioning

confidence: 99%

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Direction Finding Antenna Arrays for the Randomly Located Source

Gazzah¹,

Delmas²

2012

IEEE Trans. Signal Process.

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We consider the problem of sensor placement for estimating the direction of arrival of a narrow-band source randomly located in the far-field of a planar antenna array. Performance is evaluated by means of the expectation of the conditional Cramer Rao bound, normalized to that of the uniform circular array.Two cost functions are obtained, relative to azimuth and elevation, respectively. They depend on the array geometry as well as the distribution of the source azimuth. A class of uniform antenna arrays is investigated. It is adapted to the particular probabilistic distribution of the azimuth, while ensuring protection against array ambiguities. Using an exhaustive search procedure, we either seek the same reduction of both cost functions, or rather focus on one in particular. In the first approach, we achieve a reduction of almost 36% of both, regardless of the source azimuth distribution. In the second approach, we can obtain larger reductions for the targeted parameter. In both cases, optimal arrays are close to the V shape, for which performance analysis is conducted and closed-form expressions are obtained.

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Section: Data Model and Performance Criteriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Direction Finding Antenna Arrays for the Randomly Located Source

Gazzah¹,

Delmas²

2012

IEEE Trans. Signal Process.

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“…Let a i (θ) be the gain pattern of the i-th sensor located at position p i (a one-dimensional linear array is used). For a linear array with M sensors, the received signal can be collected in an M × 1 vector r(t) which leads to the wellknown data model [1], [5], [8] r(t) = a(θ)s(t) + n(t), t = 1, . .…”

Section: A Data Modelmentioning

confidence: 99%

“…In [4], the Weiss-Weinstein bound (WWB) has been used to optimize the array geometry. In [5], the array geometry is optimized by minimizing the Bayesian CRB (BCRB), where a prior probability density function (PDF) of the source DOA is available. A method for optimizing the array geometry by minimizing a modified beampattern has been proposed in [7].…”

Section: Introductionmentioning

confidence: 99%

Sparsity-enforcing sensor selection for DOA estimation

Roy

Chepuri

Leus

2013

2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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Abstract-The sensitivity of direction-of-arrival (DOA) estimation to different array geometries motivates the design of optimal sensor constellations. We propose a framework for array geometry design for a linear array with fixed aperture and fixed inter-element spacing, where the array geometry design is formulated as a sensor selection problem. The sensor selection is performed such that it achieves a desired Cramér-Rao bound (CRB) for estimating the DOA of a single source. The nonuniformity of the sensor selection typically results in sidelobes. These sidelobes are suppressed in a specified angular sector again via sensor selection. The aforementioned problems are jointly casted as a semidefinite programming (SDP) problem which can be efficiently solved in polynomial time. Simulations exhibit the trade-offs among the number of selected sensors, sidelobe minimization, and CRB of the DOA estimates.

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A Cramér Rao bounds based analysis of 3D antenna array geometries made from ULA branches

Renaux

Boyer

et al. 2011

Multidim Syst Sign Process

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In the context of passive sources localization using antenna array, the estimation accuracy of elevation, and azimuth are related not only to the kind of estimator which is used, but also to the geometry of the considered antenna array. Although there are several available results on the linear array, and also for planar arrays, other geometries existing in the literature, such as 3D arrays, have been less studied. In this paper, we study the impact of the geometry of a family of 3D models of antenna array on the estimation performance of elevation, and azimuth. The Cramér-Rao Bound (CRB), which is widely spread in signal processing to characterize the estimation performance will be used here as a useful tool to find the optimal configuration. In particular, we give closed-form expressions of CRB for a 3D antenna array under both conditional, and unconditional observation models. Thanks to these explicit expressions, the impact of the third dimension to the estimation performance is analyzed. Particularly, we give criterions to design an isotropic 3D array depending on the considered observation model. Several 3D particular geometry antennas made from uniform linear array (ULA) are analyzed, and compared with 2D antenna arrays. The isotropy condition of such arrays is analyzed. The presented framework can be used for further studies of other types of arrays.

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A bayesian approach to array geometry design

Cited by 34 publications

References 23 publications

Direction Finding Antenna Arrays for the Randomly Located Source

Direction Finding Antenna Arrays for the Randomly Located Source

Sparsity-enforcing sensor selection for DOA estimation

A Cramér Rao bounds based analysis of 3D antenna array geometries made from ULA branches

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