Azimuth-elevation Direction Finding Research Articles

Azimuth-Elevation Direction Finding With a Pair of Acoustic Vector Sensors in the Presence of a Reflecting Boundary

This paper is aiming at addressing an azimuth-elevation direction-finding algorithm using a pair of identically oriented acoustic vector sensors located near a reflecting boundary. Two fourth-order cumulant matrices related in terms of a translationally invariant structure are formed for recovering the acoustic vector sensor steering vectors in the particle-velocity coarray domain. Afterward, source azimuth-elevation directions are extracted in closed-form from the estimates of the coarray steering vectors. The identifiability study shows that the algorithm proposed herein can uniquely resolve up to 13 sources, thereby being applicable to underdetermined scenarios, where the number of sources exceeds that of the sensors. This capability constitutes the primary advantage over the many seminal works Hawkes and Nehorai (2000); Wu et al. (2016); Ahmadi-Shokouh and Keshavarz (20007); Tao et al. (2007); Xu and Liu (2007) that pioneered AVS array processing involving reflecting boundaries. Finally, numerical examples are provided to verify the theoretical analysis and demonstrate the efficacy of the proposed algorithm.

A higher-order "figure-8" sensor and an isotropic sensor-For azimuth-elevation bivariate direction finding.

A "p-u probe" (also known as a "p-v probe") comprises one pressure-sensor (which is isotropic) and one uni-axial particle-velocity sensor (which has a "figure-8" bi-directional spatial directivity). This p-u probe may be generalized, by allowing the figure-8 bi-directional sensor to have a higher order of directivity. This higher-order p-u probe has not previously been investigated anywhere in the open literature (to the best knowledge of the present authors). For such a sensing system, this paper is first (1) to develop closed-form eigen-based signal-processing algorithms for azimuth-elevation direction finding; (2) to analytically derive the associated Cramér-Rao lower bounds (CRB), which are expressed explicitly in terms of the two constituent sensors' spatial geometry and in terms of the figure-8 sensor's directivity order; (3) to verify (via Monte Carlo simulations) the proposed direction-of-arrival estimators' efficacy and closeness to the respective CRB. Here, the higher-order p-u probe's two constituent sensors may be spatially displaced.

Azimuth-elevation direction finding, using three uni-axial velocity sensors as an arbitrarily sparse linear array

A tri-axial velocity sensor measures the acoustic particle-velocity vector, by all three of its Cartesian components. This particle-velocity vector equals the spatial gradient of the acoustic pressure field. Song & Wong [1] has advanced an algorithm to estimate an incident source's azimuth-elevation (θ, Φ) direction-of-arrival using three uni-axial velocity sensors that are orthogonally oriented among themselves and placed arbitrarily in three-dimensional space. This work will focus on a particular array geometry whereby the three uni-axial velocity sensors are placed on a straight line in three-dimensional space but the inter-element spacings may be entirely arbitrary. This work will show how to estimate a far-field emitter's azimuth-elevation direction-of-arrival, despite the three elements’ spatial separation, and despite the separation's arbitrary length and possible sparseness. Furthermore, the Cramer-Rao Bounds (CRB) will be presented analytically for the case of the linear array being aligned along the x-axis. This work differs from [2], which requires an additional pressure-sensor. [1] Y. Song & K. T. Wong, “Acoustic direction finding using a spatially spread tri-axial velocity sensor,” IEEE Trans. Aerosp. Electron. Syst. 51(2), 834–842 (2015). [2] Y. Song & K. T. Wong, “Azimuth-elevation direction finding, using one four-component acoustic vector-sensor spread spatially along a straight line,” Proc. of Meetings on Acoustics—Meeting of the ASA, Pittsburgh, U.S.A., May 18–22, 2015.

The hybrid Cramer-Rao bound of direction finding by a uniform circular array of isotropic sensors that suffer stochastic dislocations

Consider azimuth-elevation direction finding by a uniform circular array of isotropic sensors. In the real world, the sensors may dislocate from their nominal positions. These dislocations could be modeled as random variables having an a priori known distribution. This paper investigates how the dislocations would affect azimuth-elevation direction finding by deriving the corresponding hybrid Cramer-Rao bounds. Maximum a posteriori estimators are derived and Monte Carlo simulations are conducted to validate the derived hybrid Cramer-Rao bounds.

Azimuth-elevation direction finding using one four-component acoustic vector-sensor spread spatially as a parallelogram array

An acoustic vector-sensor (a.k.a. a vector hydrophone) consists of three uni-axial velocity-sensors (which are oriented perpendicularly with regard to each other) and one pressure-sensor. Song and Wong have demonstrated how to space these four component-sensors apart in three-dimensional space, in order to extend the overall spatial aperture spanned by them, while improving the accuracy in estimating the azimuth-elevation direction-of-arrival of an acoustic emitter incident from the far field. This paper will focus on a special spatial geometry—where the four component-sensors occupy the four corners of a parallelogram in three-dimensional space.

Azimuth-elevation direction finding using one four-component acoustic vector-sensor spread spatially along a straight line

A considerable literature has developed to use the four-component acoustic vector-sensor to estimate the azimuth-elevation direction-of-arrival of incident acoustic sources. A four-component acoustic vector sensor (a.k.a. a “vector hydrophone” in underwater applications) consists of a pressure sensor, plus three identical but perpendicular univariate velocity- sensors, which are often idealized as collocated. One shortcoming of the above acoustic vector sensor is the point-size of its array aperture, due to the spatial collocation of all its four component-sensors. If these four component-sensors are placed at different spatial locations, there would arise spatial phase factors among these component-sensors’ data, and the array-manifold of (1) would be invalid, thus the incident wavefield’s propagation direction is no longer so straight-forwardly obtainable. However, Song & Wong (JASA 4, 2013) shows that how the four component-sensors may be allowed to spread out arbitrarily in three-dimensional space (thus sampling the incident wavefield at different locations), while not just achieving direction finding, but to do so with increased accuracy. This paper will focus on one particular array grid to spread out the four component-sensors—on a straight line in any permutation.

Direction finding using a biaxial particle-velocity sensor

A particle-velocity sensor measures the acoustic particle velocity, instead of the acoustic pressure. A biaxial velocity-sensor (a.k.a. a “u–u probe”) consists of two uniaxial velocity-sensors, oriented orthogonally and (possibly) displaced in space. This paper investigates what orientations of the two axes would allow azimuth-elevation direction finding, what closed-form formulas to achieve this direction finding via eigen-based parameter-estimation algorithms, and what the corresponding Cramér–Rao bounds would be.

Azimuth-elevation direction finding using a microphone and three orthogonal velocity sensors as a non-collocated subarray

An acoustic vector-sensor consists of three identical but orthogonally oriented acoustic particle-velocity sensors, plus a pressure sensor-all spatially collocated in a point-like geometry. At any point in space, this tri-axial acoustic vector-sensor can sample an acoustic wavefield as a 3 × 1 vector, instead of simply as a scalar of pressure. This vector, after proper self-normalization, would indicate the incident wave-field's propagation direction, and thus the incident emitter's azimuth-elevation direction-of-arrival. This "self-normalization" direction-of-arrival estimator is predicated on the spatial-collocation among the three particle-velocity sensors and the pressure-sensor. This collocation constriction is relaxed here by this presently proposed idea, to realize a spatially distributed acoustic vector-sensor, allowing its four component-sensors to be separately located. This proposed scheme not only retains the algorithmic advantages of the aforementioned "self-normalization" direction-of-arrival estimator, but also will significantly extend the spatial aperture to improve the direction-finding accuracy by orders of magnitude.

Direction finding in spatially correlated noise fields with arbitrarily-spaced and far-separated subarrays at unknown locations

A computationally simple azimuth-elevation direction finding algorithm in spatially correlated noise fields using two-far-separated subarray geometry (Li et al. 1995) is presented. We assume one subarray consists of multiple acoustic vector sensors, while another subarray comprises multiple pressure sensors. All sensors are arbitrarily placed at unknown locations. The authors firstly define a cross matrix to eliminate the effect of the spatially correlated noise. Then the so-called propagator method is used to estimate the steering vectors of acoustic vector sensors. Finally, a closed form, automatically paired azimuth-elevation angle estimates are derived. The proposed algorithm requires no eigen decomposition into signal or noise subspaces. In addition, the proposed algorithm does not need 2D iterative searching. Therefore the algorithm shows low computational complexity. Monte Carlo simulations are presented to verify the effectiveness of the proposed algorithm.

Two-dimensional direction finding of acoustic sources by a vector sensor array using the propagator method

This paper considers a new azimuth-elevation direction finding algorithm for multiple acoustic plane wave signals using acoustic vector array. Firstly, a planar-plus-an-isolated sensor array geometry [P. Li, J. Sun, B. Yu, Two-dimensional spatial spectrum estimation of coherent signals without spatial smoothing and eigendecomposition, IEE Proc.-Radar Sonar Navigat. 143(5) (October 1996) 295–299] is exploited and a cross-covariance matrix is defined. Then the propagator method is used to estimate the steering vectors of acoustic vector sensors. Finally, a closed-form, automatically paired azimuth-elevation angle estimates are derived. The presented algorithm shows high azimuth-elevation estimation accuracy due to array aperture extension. In addition, the new algorithm does not need the eigen-decomposition and 2D iterative searching, and is applicable to coherent (fully correlated) signals and spatially correlated noises. Therefore, the algorithm shows low computational complexity and robustness. Monte-Carlo simulations are presented to verify the effectiveness of the proposed algorithm.

Radio interferometer for geosynchronous-satellite direction finding

A radio interferometer capable of azimuth-elevation direction finding for geosynchronous satellites has been developed. The interferometer has two small-diameter antennas and four movable planar mirrors. The movable mirrors reflect the microwaves from the satellite and guide them to the fixed receiving antennas. Two of the movable mirrors are mounted on a rotary arm, so that the baseline of the interferometer can rotate in the horizontal plane. This configuration enables the interferometer to eliminate phase-ambiguity problems and cable-phase errors, resulting in a direction finding accuracy of better than 0.01 deg in the Ku band.