Three necessary conditions for the validity of the Fresnel phase approximation for the near-field beam pattern of an aperture

Ziomek, Lawrence J.

doi:10.1109/48.211494

Cited by 38 publications

(17 citation statements)

References 3 publications

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“…This concurs with the specification in[4] (on page 74) of "the region of validity for the Fresnel approximation" as .…”

supporting

confidence: 80%

“…These approximations use some finite-order Taylor-series, to "expand" the phase-delay with respect to the emitter-sensor range. For example, the "Fresnel approximation" [4] represents a second-order Taylor-series expansion of the phase-delay among identical isotropic sensors in a uniformly spaced linear array (ULA), to produce a second-order polynomial with respect to the sensor-index [3], [5], [7]- [13], [15]- [23], [25]- [40]. Similarly, [6], [24] discard the exact ULA array-manifold for an approximation consisting of a sum of approximate array-manifolds, each corresponding to a different order of a Taylor-series expansion of the exact array-manifold.…”

Section: Mismatch Of Near-field Bearing-range Spatial Geometry In Soumentioning

confidence: 99%

“…Please see[14], especially chapter 7 therein 4. The spherical spread factor has also been overlooked in the measurementmodels of[3],[8]-[13],[16]-[18],[20],[22],[23],[25]-[36],[38]-[40] for near-field direction-finding 5.…”

mentioning

confidence: 99%

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Mismatch of Near-Field Bearing-Range Spatial Geometry in Source-Localization by a Uniform Linear Array

Hsu

Wong

Yeh

2011

IEEE Trans. Antennas Propagat.

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Many near-field source-localization algorithms intentionally simplifies the exact spatial geometry among the emitter and the sensors, in order to speed up the signal-processing involved. For example, the Fresnel approximation is a second order Taylorseries approximation. Such intentional approximation introduces a systemic error in the algorithm's modeling of the actual objective reality from which the measured data arise. A mismatch thus exists between the algorithm's presumptions versus the data it processes. This modeling-mismatch will introduce a systematic bias in the bearing-range estimates of the near-field source-localization algorithm. This bias is non-random, and adds towards the random estimation-errors due to the additive and/or multiplicative noises. The open literature currently offers no rigorous mathematical analysis on this issue. This proposed project aims to fill this literature gap, by deriving explicit formulas of the degrading effects in three-dimensional source-localization, due to approximating the source/sensor geometry by any order of the Taylor's series expansion.Index Terms-Acoustic interferometry, array signal processing, direction of arrival estimation, interferometry, linear arrays, nearfield far-field transformation, phased arrays, sonar arrays, underwater acoustic arrays.

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“…This concurs with the specification in[4] (on page 74) of "the region of validity for the Fresnel approximation" as .…”

supporting

confidence: 80%

Section: Mismatch Of Near-field Bearing-range Spatial Geometry In Soumentioning

confidence: 99%

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Mismatch of Near-Field Bearing-Range Spatial Geometry in Source-Localization by a Uniform Linear Array

Hsu

Wong

Yeh

2011

IEEE Trans. Antennas Propagat.

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“…According to [31], the necessary condition for the validity of the Fraunhofer approximation, which is utilized by the steering vector definition in (1), can be expressed as (42) where is the distance from the calibrator source to the center of the array, and denotes the maximum distance from the array elements to the array center. As an example, for a standard 50 50 URA in a 3-D sonar imaging system, if it were assumed that and 10 mm (similar systems can be found in [32]), then the calibrator source should be artificially placed at a location more than 4.7 m away from the array.…”

Section: F Practical Setup Of the Proposed Methods In 3-d Underwater mentioning

confidence: 99%

“…For any fixed values of and , if were chosen as (27) equation (26) would become (28) An important feature of is that the sum of all the elements of remains unchanged for various and , which helps to simplify the MAP approach as will be shown in (31).…”

Section: Adjustment Of Doa and Phase Estimations With The Map Apprmentioning

confidence: 99%

Gain and Phase Autocalibration of Large Uniform Rectangular Arrays for Underwater 3-D Sonar Imaging Systems

Yuan

Jiang

Chen

2014

IEEE J. Oceanic Eng.

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In this paper, a new calibration method for gain and phase errors in large uniform rectangle arrays is proposed for underwater 3-D sonar imaging systems. It requires only one calibrator source at an unknown position in the far field. An efficient and speedy three-step-iteration algorithm is performed first to provide a robust direction-of-arrival (DOA) estimator in the presence of gain and phase errors. It then follows with the gain and phase errors estimation using a spatial matched filter. Finally, a maximum a posteriori (MAP) exercise is executed to further adjust the estimated phase parameters and the source direction. The statistical performance of the proposed algorithm will be demonstrated and compared to representative methods. It will be shown that the proposed method is computationally effective and asymptotically efficient in Monte Carlo simulations.Index Terms-Array signal processing, autocalibration, gain and phase error, underwater 3-D sonar imaging, uniform rectangular array (URA).

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A Weighted Fresnel Approximation for the Delays Used in Focused Beamforming

Trueco

Murino

1997

Acoustical Imaging

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Three necessary conditions for the validity of the Fresnel phase approximation for the near-field beam pattern of an aperture

Cited by 38 publications

References 3 publications

Mismatch of Near-Field Bearing-Range Spatial Geometry in Source-Localization by a Uniform Linear Array

Mismatch of Near-Field Bearing-Range Spatial Geometry in Source-Localization by a Uniform Linear Array

Gain and Phase Autocalibration of Large Uniform Rectangular Arrays for Underwater 3-D Sonar Imaging Systems

A Weighted Fresnel Approximation for the Delays Used in Focused Beamforming

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