Direction Cosine Estimates Research Articles

2D-DOD and 2D-DOA Estimation Using Sparse L-Shaped EMVS-MIMO Radar

It is well-known that EMVS-MIMO radar is an emerging technique that it allows for 2D-DOD and 2D-DOA estimation. Unfortunately, existing array geometries on the EMVS-MIMO radar can rarely reach a good compromise between the estimation accuracy and the computational burden. This paper is aimed at proposing an L-shaped sparse array topology for a bistatic EMVS-MIMO radar, whose inter-element distance is much larger than half-wavelength. A fast algorithm proposed herein to estimate the 2D-DOD and 2D-DOA. Firstly, the direction cosine estimates are obtained via the rotational invariance properties of the sparse subarrays, which are ambiguous yet exhibit high-resolution. Thereafter, the direction cosine estimates are achieved via the vector cross-product of the normalized Poynting vectors, which are unambiguous but have low-resolution. The unambiguous high-resolution direction cosine estimates are determined by combining the previous results, following which the 2D-DOD and 2D-DOA can be easily recovered. It is shown that the proposed framework can obtain a better accuracy of estimation than the other existing methods. Moreover, it is more flexible than the current sparse array methodologies. Finally, the theoretical derivations have been validated by simulation results.

Joint 2D-DOA and polarization estimation for sparse nonuniform rectangular array composed of spatially spread electromagnetic vector sensor

In this paper, a sparse nonuniform rectangular array based on spatially spread electromagnetic vector sensor (SNRA-SSEMVS) is introduced, and a method for estimating 2D-direction of arrival (DOA) and polarization is devised. Firstly, according to the special structure of the sparse nonuniform rectangular array (SNRA), a set of accurate but ambiguous direction-cosine estimates can be obtained. Then the steering vector of spatially spread electromagnetic vector sensor (SSEMVS) can be extracted from the array manifold to obtain the coarse but unambiguous direction-cosine estimates. Finally, the disambiguation approach can be used to get the final accurate estimates of 2D-DOA and polarization. Compared with some existing methods, the SNRA configuration extends the spatial aperture and refines the parameters estimation accuracy without adding any redundant antennas, as well as reduces the mutual coupling effect. Moreover, the proposed algorithm resolves multiple sources without the priori knowledge of signal information, suffers no ambiguity in the estimation of the Poynting vector, and pairs the x-axis direction cosine with the y-axis direction cosine automatically. Simulation results are given to verify the effectiveness and superiority of the proposed algorithm.

Joint DOA and Polarization Estimation with Two Parallel Sparse Dipole Arrays

Electromagnetic vector sensors (EMVS) have attracted growing attention in recent years. However, the mutual coupling effects in practical EMVS arrays may seriously degrade the parameter estimation performance. In order to solve this problem, a novel array configuration consisting of two parallel sparse dipole arrays is proposed. Based on the spatially rotational invariance property between the two parallel arrays and the interdipole spacing inside each array, highly accurate but ambiguous direction-cosine estimates, coarse direction-of-arrival (DOA) estimates, and polarization parameter estimation can be obtained jointly. The coarse DOA estimates are then employed to disambiguate the phase ambiguities in the fine estimates. Compared with collocated EMVS, the proposed array overcomes the mutual coupling problem. Moreover, the DOA estimation accuracy is promoted due to the sparse array aperture extension. Simulation results demonstrate the effectiveness of the proposed algorithm.

Two-dimensional direction estimation of multiple signals using two parallel sparse linear arrays

In this paper, we focus on the problem of estimating the two-dimensional (2-D) direction-of-arrival (DOA) of multiple signals and propose a novel approach for 2-D DOA estimation using two parallel sparse arrays structured by two sparse uniform linear arrays (ULAs) and an auxiliary sensor. Firstly, we obtain automatically paired direction cosine estimates along the x and y axes by using the mutual and internal shift-invariance properties of two sparse ULAs and the propagator method, where the direction cosine estimates along the y-axis are cyclically ambiguous due to the fact that the inter-element spacings of two sparse ULAs exceed a half-wavelength. Then, we extract unambiguous direction cosine estimates by means of the auxiliary sensor and a novel disambiguation procedure. Finally, we use the unambiguous direction cosine estimates to calculate the elevation and azimuth angles. The proposed method does not require extra pair-matching process and can achieve automatic pairing for 2-D DOA estimation. Moreover, it has a low computational complexity without any spectral search. Simulation results demonstrate that the proposed method outperforms the existing methods based on the two-parallel ULA, especially for small number of sensors case.

Eigenstructure-based ambiguity resolution algorithm for distributed subarray antennas VHF radar

Distributed subarray antennas (DSAs) have been proposed to enhance angular resolution and the accuracy of direction of arrival (DOA) estimation. This results in the well-known grating lobes in the array beampattern or ambiguities in DOA estimation. Presented is a slanting DSA composed of two widely-separated uniform rectangular arrays. By exploiting the translational invariance and the aperture coupling in the DSA configuration, a novel ambiguity resolution algorithm is proposed. It can provide closed-form, low-variance and automatically paired 2D direction cosine estimates. Simulation results are presented to verify the efficacy of the ambiguity resolution algorithm.

Extended Aperture 2-D Direction Finding With a Two-Parallel-Shape-Array Using Propagator Method

In this letter, we propose a two-parallel-shape array geometry, consisting of sensors spaced much farther apart than a half-wavelength, to improve estimation accuracy via aperture extension for two-dimensional (2D) direction finding. First, the subarray parallel with the x-axis is employed to extract automatically paired high-variance but unambiguous y-axis direction cosines and low-variance but cyclically ambiguous x-axis direction cosines. Then, the subarray parallel with the y-axis is employed to extract automatically paired unambiguous x-axis direction cosines and cyclically ambiguous y-axis direction cosines. Finally, the high-variance unambiguous direction cosine estimates are used to resolve the low-variance cyclically ambiguous direction cosine estimates to obtain automatically paired azimuth-elevation angle estimates. The propagator method, which requires only linear operations but involves no eigen-decomposition or singular-value decomposition into signal/noise subspaces, is adapted to derive the direction cosines. Therefore, the proposed technique offers high estimation precision with low computational complexity.

Self-initiating MUSIC-based direction finding in underwater acoustic particle velocity-field beamspace

This paper introduces a novel blind MUSIC-based (MUltiple SIgnal Classification) source localization algorithm applicable to an arbitrarily spaced three-dimensional array of vector hydrophones, each of which comprises two or more co-located and orthogonally oriented velocity hydrophones plus an optional pressure hydrophone. This proposed algorithm: (1) exploits the incident sources' angular diversity in the underwater acoustic particle velocity field; (2) adaptively forms velocity-field beams at each vector-hydrophone; (3) uses ESPRIT to self-generate coarse estimates of the sources' arrival angles to start off its MUSIC-based iterative search with no a priori source information; and (4) automatically pairs the x-axis direction-cosine estimates with the y-axis direction-cosine estimates. Simulation results verify the efficacy of this proposed scheme.

Self-initiating MUSIC-based direction finding and polarization estimation in spatio-polarizational beamspace

A novel self-initiating multiple signal classification (MUSIC)-based direction-finding (DF) and polarization-estimation algorithm in spatio-polarizational beamspace is presented for an arbitrarily spaced array of identically oriented electromagnetic vector sensors. An electromagnetic vector sensor, already commercially available, is composed of six colocated, but diversely polarized, antennas distinctly measuring all six electromagnetic-field components of a multisource incident wave field. This proposed algorithm: (1) exploits the incident sources' polarization diversity; (2) decouples the estimation of the sources' arrival angles from the estimation of the sources' polarization parameters; (3) uses ESPRIT on pairs of vector sensors to self-generate coarse estimates of the arrival angles to start off its MUSIC-based iterative search without any a priori information on the incident sources' parameters; (4) estimate the sources' polarization states; and (5) automatically pairs the x-axis direction-cosine estimates with the y-axis direction-cosine estimates and with the polarization estimates. Monte Carlo simulation results verify the efficacy of the proposed method.

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.

Visualization of complex geological structures using 3-D Bézier construction tools

Various 3-D visualization methods use structural field data to constrain geological models. One approach is to employ 3-D β-Splines, a class of Bézier curves, to densify point data sets too sparse and clustered for direct spatial interpolation. Bézier curves are implemented to act as construction lines that respect the constraints imposed by structural orientation data. These 3-D construction lines are defined by tangents to local planar features, and the projection of key geologic structures. A method is presented that estimates the local strike and dip of vertices along elevation registered 3-D curvilinear geological features. The local direction cosine estimates derived along the surface traces of geological structures are interpolated, and linearly projected to depth. In regions where subparallel relationships exist between local and regional scale structures it is possible to constrain modeled regional geometry to the field data. The success of any 3-D geological modeling exercise is dependent on the data density, clustering and depth variability of known structural observations, and the geological relationship of local structures to regional bounding surfaces. Ultimately, methodologies to generate geological models from regions of sparse data will need to be able to combine computer aided geometric design (CAGD) tools with constraining software, which respects structural field observations. Several examples are given to emphasize this point.

Direction-finding with sparse rectangular dual-size spatial invariance array

A novel sparse array geometry embedding two sizes of spatial invariances is presented for use with a new ESPRIT-based (estimation of signal parameters via rotational invariance techniques) algorithm for aperture extension. The half-wavelength invariance yields unambiguous but high-variance direction cosine estimates to disambiguate low-variance but cyclically ambiguous estimates from the larger invariance. With larger invariance at 60 half-wavelengths, resolution threshold for two closely spaced emitters is reduced by 50 dB and estimation error by 100-fold. Array design formulas are also presented.

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 source's directions-of-arrival are determined from the source's acoustical particle velocity components, which are extracted by decoupling the data covariance matrix's 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 ESPRIT's 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.