Kainam Thomas Wong

Closed-form eigenstructure-based direction finding using arbitrary but identical subarrays on a sparse uniform Cartesian array grid

A sparse uniform Cartesian-grid array suffers cyclic ambiguity in its Cartesian direction-cosine estimates due to the spatial Nyquist sampling theorem. The proposed MUSIC-based or MODE-based algorithm improves and generalizes previous disambiguation schemes that populate the thin array grid with identical subarrays-such as electromagnetic vector sensors, underwater acoustic vector hydrophones, or half-wavelength spaced subarrays.

Closed-form direction finding and polarization estimation with arbitrarily spaced electromagnetic vector-sensors at unknown locations

This paper introduces a new closed-form ESPRIT-based algorithm for multisource direction finding and polarization estimation with arbitrarily spaced electromagnetic vector-sensors whose three-dimensional (3-D) locations need not be known. The vector-sensor, already commercially available, consists of six colocated but diversely polarized antennas separately measuring all six electromagnetic-field components of an incident wavefield. ESPRIT exploits the nonspatial interrelations among the six unknown electromagnetic-field components of each source and produces from the measured data a set of eigenvalues, from which the sources electromagnetic-field vector may be estimated to within a complex scalar. Application of a vector cross-product operation to this ambiguous electromagnetic-field vector estimate produces an unambiguous estimate of that sources normalized Poynting vector, which contains as its components the sources Cartesian direction cosines. Monte Carlo simulation results verify the efficacy and versatility of this innovative scheme. This novel method maybe considered as a simplification and a refinement over Lis (1993) work.

ESPRIT-based 2-D direction finding with a sparse uniform array of electromagnetic vector sensors

Aperture extension (interferometry baseline extension) is achieved in this novel ESPRIT-based two-dimensional (2-D) arrival angle estimation scheme using a sparse (a.k.a., thin or thinned) uniform rectangular array of electromagnetic vector sensors spaced much farther apart than a half-wavelength. An electromagnetic vector sensor is composed of six spatially co-located, orthogonally oriented, diversely polarized antennas, distinctly measuring all six electromagnetic-field components of an incident multisource wavefield. Each incident sources direction of arrival (DOA) is estimated from the sources electromagnetic-field vector component and serves as a coarse reference to disambiguate the cyclic phase ambiguities in ESPRITs eigenvalues when the intervector sensor spacing exceeds a half wavelength. Simulations demonstrate the significant performance gain realizable by this method for radar and wireless mobile fading-channel communications.

Root-MUSIC-based azimuth-elevation angle-of-arrival estimation with uniformly spaced but arbitrarily oriented velocity hydrophones

This novel underwater acoustic azimuth-elevation source localization scheme realizes the eigenstructure-based polynomial rooting procedure for an L-shaped uniformly spaced array of diversely oriented and possibly spatially co-located velocity hydrophones and an optional pressure hydrophone. A velocity hydrophone measures a Cartesian component of the acoustic particle velocity vector of the incident wavefield. At each uniformly spaced array grid, one or more co-located and diversely oriented velocity hydrophones and/or a pressure hydrophone are placed, with the number and orientations of velocity hydrophones possibly varying from grid position to grid position in some known prearranged manner. The diverse orientation of the velocity hydrophones, however, disrupts the Vandermonde array manifold structure in each of the two uniform-linear-array legs of the L-shaped array. Nonetheless, ingenuous mathematical manipulations proposed in this paper restore the disrupted Vandermonde algebraic structure, thereby permitting once again the use of polynomial rooting to estimate the directions of arrival. A proposed pairing procedure matches each sources x-axis direction cosine estimate with its corresponding y-axis direction cosine estimate. Simulation results verify the efficacy of the proposed scheme.

Closed-form underwater acoustic direction-finding with arbitrarily spaced vector hydrophones at unknown locations

This paper introduces a novel ESPRIT-based closed form source localization algorithm applicable to arbitrarily spaced three-dimensional arrays of vector hydrophones, whose locations need not be known. Each vector hydrophone consists of two or three identical but orthogonally oriented velocity hydrophones plus one pressure hydrophone, all spatially co-located in a point-like geometry. A velocity hydrophone measures one Cartesian component of the incident sonar wavefields velocity-vector, whereas a pressure hydrophone measures the acoustic wavefields pressure. Velocity-hydrophone technology is well established in underwater acoustics and a great variety of commercial models have long been available. ESPRIT is realized herein by exploiting the nonspatial inter-relations among each vector hydrophones constituent hydrophones, such that ESPRITs eigenvalues become independent of array geometry. Simulation results verify the efficacy and versatility of this innovative scheme.

Extended-aperture underwater acoustic multisource azimuth/elevation direction-finding using uniformly but sparsely spaced vector hydrophones

Aperture extension is achieved in this novel ESPRIT-based two-dimensional angle estimation scheme using a uniform rectangular array of vector hydrophones spaced much farther apart than a half-wavelength. A vector hydrophone comprises two or three spatially co-located, orthogonally oriented identical velocity hydrophones (each of which measures one Cartesian component of the underwater acoustical particle velocity vector-field) plus an optional pressure hydrophone. Each incident sources directions-of-arrival are determined from the sources acoustical particle velocity components, which are extracted by decoupling the data covariance matrixs signal-subspace eigenvectors using the lower dimensional eigenvectors obtainable by ESPRIT. These direction-cosine estimates are unambiguous but have high variance; they are used as coarse references to disambiguate the cyclic phase ambiguities in ESPRITs eigenvalues when the intervector-hydrophone spacing exceeds a half-wavelength. In one simulation scenario, the estimation standard deviation decreases with increasing intervector-hydrophone spacing up to 12 wavelengths, effecting a 97% reduction in the estimation standard deviation relative to the half-wavelength case. This proposed scheme and the attendant vector-hydrophone array outperform a uniform half-wavelength spaced pressure-hydrophone array with the same aperture and slightly greater number of component hydrophones by an order of magnitude in estimation standard deviation. Other simulations demonstrate how this proposed method improves underwater acoustic communications link performance. The virtual array interpolation technique would allow this proposed algorithm to be used with irregular array geometries.

Direction finding/polarization estimation-dipole and/or loop triad(s)

This paper shows (1) how measurement of the three Cartesian components of the electrical-field or magnetic-field suffices for multisource azimuth/elevation direction finding and polarization estimation, and (2) how the vector cross-product direction-of-arrival estimator is fully applicable even when the dipole triad is arbitrarily displaced from the loop triad.

“Vector Cross-Product Direction-Finding” With an Electromagnetic Vector-Sensor of Six Orthogonally Oriented But Spatially Noncollocating Dipoles/Loops

Direction-finding capability has recently been advanced by synergies between the customary approach of inter ferometry and the new approach of “vector cross product” based Poynting-vector estimator. The latter approach measures the incident electromagnetic wavefield for each of its six electromagnetic components, all at one point in space, to allow a vector cross-product between the measured electric-field vector and the measured magnetic-field vector. This would lead to the estimation of each incident sources Poynting-vector, which (after proper norm-normalization) would then reveal the corresponding Cartesian direction-cosines, and thus the azimuth-elevation arrival angles. Such a “vector cross product” algorithm has been predicated on the measurement of all six electromagnetic components at one same spatial location. This physically requires an electromagnetic vector-sensor, i.e., three identical but orthogonally oriented electrically short dipoles, plus three identical but orthogonally oriented magnetically small loops-all spatially collocated in a point-like geometry. Such a complicated “vector-antenna” would require exceptionally effective electromagnetic isolation among its six component-antennas. To minimize mutual coupling across these collocated antennas, considerable antennas-complexity and hardware cost could be required. Instead, this paper shows how to apply the “vector cross-product” direction-of-arrival estimator, even if the three dipoles and the three loops are located separately (instead of collocating in a point-like geometry). This new scheme has great practical value, in reducing mutual coupling, in simplifying the antennas hardware, and in sparsely extending the spatial aperture to refine the direction-finding accuracy by orders of magnitude.

CramÉr-Rao Bounds for Direction Finding by an Acoustic Vector Sensor Under Nonideal Gain-Phase Responses, Noncollocation, or Nonorthogonal Orientation

An acoustic vector-sensor (also known as vector-hydrophone in underwater applications) is composed of two or three spatially collocated but orthogonally oriented acoustic velocity sensors, plus possibly a collocated acoustic pressure sensor. Such an acoustic vector sensor is versatile for direction-finding, due to its azimuth-elevation spatial responses independence from the incident sources frequency, and bandwidth. However, previously unavailable in the open literature is how the acoustic vector sensors far-field direction-of-arrival estimates may be adversely affected by any unknown nonideality in the acoustic vector sensors gain response, phase response, collocation, or orthogonal orientation among its constituent velocity sensors. This paper pioneers a characterization of how these various unknown nonidealities degrade direction-finding accuracy, via Cramer-Rao bound analysis.

The Acoustic Vector-Sensor's Near-Field Array-Manifold

The acoustic vector-sensor is a practical and versatile sound-measurement system, for applications in-room, open-air, or underwater. Its far-field measurement model has been introduced into signal processing over a decade ago; and many direction-finding algorithms have since been developed for acoustic vector-sensors, but only for far-field sources. Missing in the literature is a near-field measurement model for the acoustic vector-sensor. This correspondence fills this literature gap.