High-resolution Direction Research Articles

Conditional and Unconditional Cramér–Rao Bounds for Near-Field Source Localization

Near-field source localization problem by a passive antenna array makes the assumption that the time-varying sources are located near the antenna. In this context, the far-field assumption (i.e., planar wavefront) is, of course, no longer valid and one has to consider a more complicated model parameterized by the bearing (as in the far-field case) and by the distance, named range, between the source and a reference coordinate system. One can find a plethora of estimation schemes in the literature, but their ultimate performance in terms of mean square error (MSE) have not been fully investigated. To characterize these performance, the Cramer-Rao bound (CRB) is a popular mathematical tool in signal processing. The main cause for this is that the MSE of several high-resolution direction of arrival algorithms are known to achieve the CRB under quite general/weak conditions. In this correspondence, we derive and analyze the so-called conditional and unconditional CRBs for a single time-varying near-field source. In each case, we obtain non-matrix closed-form expressions. Our approach has two advantages: i) due to the fact that one has to inverse the Fisher information matrix, the computational cost for a large number of snapshots (in the case of the conditional CRB) and/or for a large number of sensors (in the case of the unconditional CRB), of a matrix-based CRB can be high while our approach is low and ii) some useful information can be deduced from the behavior of the bound. In particular, an explicit relationship between the conditional and the unconditional CRBs is provided and one shows that closer is the source from the array and/or higher is the signal carrier frequency, better is the range estimation.

Autocalibration algorithm for mutual coupling of planar array

With few exceptions, high resolution direction of arrival (DOA) estimation algorithms suffer a lot from the mutual coupling between different array elements. In order to compensate this effect, two autocalibration methods are proposed for the 2-D DOA estimation on a planar array. Both of them can estimate the DOAs without any iterative process or calibration sources. We prove that the effect of mutual coupling can be automatically eliminated by the inherent mechanism of the proposed methods. Moreover, they can also achieve an obvious performance improvement even when there is a coupling model mismatch. After getting the DOA estimations, two methods are proposed to estimate the mutual coupling coefficients. Moreover, these coefficient estimates can be used to further improve the accuracy of DOA estimations. The Cramer–Rao lower bound (CRB) for the parameter estimations are also presented as the benchmark. Simulation results demonstrate the effectiveness of the proposed algorithms.

Robust Adaptive Trimming for High-Resolution Direction Finding

The presence of impulsive noise can severely degrade the accuracy performance of conventional direction of arrival (DOA) estimation algorithms, such as MUSIC and ESPIRIT. We propose a two-stage robust adaptive trimming approach. We first apply Shapiro-Wilk's goodness-of-fit <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> test for Gaussianity, as a preprocessing stage. We then robustly estimate the covariance matrix in order to minimize the impact of impulsive noise on conventional DOA estimation algorithms. Numerical simulations are presented to illustrate the efficacy of the proposed approach for high resolution direction finding in highly-impulsive environments.

High-Resolution Through-the-Wall Radar Imaging Using Beamspace MUSIC

The MUSIC algorithm is a high-resolution direction finding technique which has been successfully applied to enhance radar imaging in inverse synthetic aperture radar (ISAR). Although this signal subspace-based method has proven effective when dealing with point targets and high signal-to-noise ratio (SNR), it may fail to work when directly applied to extended targets or target returns of low SNR. The Beamspace MUSIC (BS-MUSIC), in which the MUSIC algorithm is applied to multiple beams, is capable of locating spatially extended targets in low SNR environments. In this paper, we consider BS-MUSIC as an image formation method for indoor radar imaging problems and sensing through-the-wall applications. We compare BS-MUSIC performance to conventional beamforming and element-space MUSIC. Imaging results, using both synthesized and real data, demonstrate the advantages of the proposed algorithm in depicting targets behind walls.

Comparative Study of Wideband Subspace Direction of Arrival (DOA) estimation methods

Signal subspace Methods like ESPRIT, MUSIC and MATRIX PENCIL, provides high resolution Direction Of Arrival (DOA) estimation in comparison to traditional Delay and Sum and Capon methods, which are limited by sensor spacing. However underwater Acoustics signals are inherently wideband in nature and most of these Subspace methods works on narrowband signals. Currently modified version of these methods for wideband signals are emerging. These methods are broadly classified as Coherent and Incoherent methods depending upon how signals of different frequencies have been merged. Performances of these methods are evaluated using extensive Monte‐Carlo simulations under various protocols by comparing there Mean Square Error in DOA estimation and by their respective resolution power. This comparison study is also complemented with real acoustic data from public domain.

Fast Direction Finding Using Modified Pseudocovariance Matrix

A modified pseudocovariance matrix is described which can improve the performance of Kim 's (Fast DOA estimation algorithm using pseudocovariance IEEE Trans. Antennas Propagat., vol. 53, no. 4, pp. 1346-1351, Apr. 2005) algorithm to realize the fast direction finding with single snapshot in coherent or uncorrelated case. By adding the backwards formulation of pseudocovariance matrix, the rank of pseudocovariance matrix is enhanced. Then a set of pseudocovariance matrices are constructed by circularly shifting the matrix. By weighted averaging, a modified pseudocovariance matrix is reconstructed whose noise is reduced. The proposed matrix has less array element loss than that of the original matrix. Moreover, this algorithm can be applied in the lower signal-noise-ratio (SNR) through noise preprocessing. The new matrix has expanded the application of high-resolution direction finding to nonuniform linear array (NLA), since traditional methods usually assume the array is uniform linear when handling coherent sources. Simulations are conducted to compare the performance of the modified method and the original method. The results illustrate that the high performance of DOA estimate could be obtained rapidly

High-Resolution Direction Finding From Higher Order Statistics: The$2rm q$-MUSIC Algorithm

From the beginning of the 1980s, many second-order (SO) high-resolution direction-finding methods, such as the MUSIC method (or 2-MUSIC), have been developed mainly to process efficiently the multisource environments. Despite of their great interests, these methods suffer from serious drawbacks such as a weak robustness to both modeling errors and the presence of a strong colored background noise whose spatial coherence is unknown, poor performance in the presence of several poorly angularly separated sources from a limited duration observation and a maximum of N-1 sources to be processed from an array of N sensors. Mainly to overcome these limitations and in particular to increase both the resolution and the number of sources to be processed from an array of N sensors, fourth-order (FO) high-resolution direction-finding methods have been developed, from the end of the 1980s, to process non-Gaussian sources, omnipresent in radio communications, among which the 4-MUSIC method is the most popular. To increase even more the resolution, the robustness to modeling errors, and the number of sources to be processed from a given array of sensors, and thus to minimize the number of sensors in operational contexts, we propose in this paper an extension of the MUSIC method to an arbitrary even order 2q (qges1), giving rise to the 2q-MUSIC methods. The performance analysis of these new methods show off new important results for direction-finding applications and in particular the best performances, with respect to 2-MUSIC and 4-MUSIC, of 2q-MUSIC methods with q>2, despite their higher variance, when some resolution is required

Robust DOA estimation and array calibration in the presence of mutual coupling for uniform linear array

The presence of unknown mutual coupling between array elements is known to significantly degrade the performance of most high-resolution direction of arrival (DOA) estimation algorithms. In this paper, a robust subspace-based DOA estimation and array auto-calibration algorithm is proposed for uniformly linear array (ULA), when the array mutual coupling is present. Based on a banded symmetric Toeplitz matrix model for the mutual coupling of ULA, the algorithm provides an accurate and high-resolution DOA estimate without any knowledge of the array mutual couplings. Moreover, a favorable estimate of mutual coupling matrix can also be achieved simultaneously for array auto-calibration. The algorithm is realized just via one-dimensional search or polynomial rooting, with no multidimensional nonlinear search or convergence burden involved. The problem of parameter ambiguity, statistically consistence and efficiency of the new estimator are also analyzed. Monte-Carlo simulation results are also provided to demonstrate the effectiveness and behavior of the proposed algorithm.

Estimating angle of arrival with non‐uniformly spaced array

AbstractThe present direction‐finding equipment has insufficient accuracy and resolution, so that accurate evaluation of the direction of arrival and the position cannot be carried out. Although each radar signal has a narrow bandwidth, the entire bandwidth for various radars used exceeds four octaves. In order to search all of these, equipment for each bandwidth is used at present so that the entire frequency range is covered. However, it is more effective from the standpoint of equipment size and cost to cover the entire spectrum with a single kind of equipment. It is desirable to realize high‐accuracy high‐resolution direction finding over a broad bandwidth. In realization, broadband antennas are used, and high‐gain antennas are also needed in a low‐S/N environment. Since the dimensions of high‐gain and broadband antennas are large, an array configuration with a half‐wave spacing may not physically be possible. Thus, the array spacing becomes more than a half‐wavelength. If the range of direction estimation is −90 to +90°, the phase difference exceeds 360° so that ambiguity occurs. As a method to resolve this ambiguity problem, a nonuniformly spaced array is effective. In this paper, the array conditions for a nonuniformly spaced array are determined in the case of one arriving wave. Next, the case of several arriving waves is discussed and the array conditions for several arriving waves are derived. © 2001 Scripta Technica, Electron Comm Jpn Pt 1, 85(3): 1–8, 2002

High-resolution direction finding: the missing data case

This paper considers the problem of estimating the direction-of-arrival (DOA) of one or more signals using an array of sensors, where some of the sensors fail to work before the measurement is completed. Methods for estimating the array output covariance matrix are discussed. In particular, the maximum-likelihood (ML) estimate of this covariance matrix and its asymptotic accuracy are derived and discussed. Different covariance matrix estimates are used for DOA estimation together with the MUSIC algorithm and with a covariance matching technique. In contrast to MUSIC, the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix, and it is demonstrated that this yields a significant performance gain.

Direction Finding Based on Spatial Time-Frequency Distribution Matrices

Amin, Moeness G., and Zhang, Yimin, Direction Finding Based on Spatial Time-Frequency Distribution Matrices, Digital Signal Processing10 (2000), 325–339.Spatial time-frequency distributions (STFDs) have been recently introduced as the natural means to deal with source signals that are localizable in the time-frequency domain. It has been shown that improved estimates of the signal and noise subspaces are achieved by constructing the subspaces from the time-frequency signatures of the signal arrivals rather than from the data covariance matrices, which are commonly used in conventional subspace estimation methods. This paper discusses the application of STFD to high-resolution direction finding. We focus on both the role and the effect of crossterms in angle estimation when multiple time-frequency points are incorporated. Simulation examples are presented to compare the performance of joint block-diagonalization and time-frequency averaging techniques for incorporating multiple autoterm and crossterm points in subspace estimation.

Direction of arrival estimation based on phase differences using neural fuzzy network

A new high-resolution direction of arrival (DOA) estimation technique using a neural fuzzy network based on phase difference (PD) is proposed. The conventional DOA estimation method such as MUSIC and MLE, are computationally intensive and difficult to implement in real time. To attack these problems, neural networks have become popular for DOA estimation. However, the normal neural networks such as the multilayer perceptron (MLP) and radial basis function network (RBFN) usually produce the extra problems of low convergence speed and/or large network size (i.e., the number of network parameters is large). Also, the may to decide the network structure is heuristic. To overcome these defects and take use of neural learning ability, a powerful self-constructing neural fuzzy inference network (SONFIN) is used to develop a new DOA estimation algorithm. By feeding the PDs of the received radar-array signals, the trained SONFIN can give high-resolution DOA estimation. The proposed scheme is thus called PD-SONFIN. This new algorithm avoids the need of empirically determining the network size and parameters in normal neural networks due to the powerful on-line structure and parameter learning ability of SONFIN. The PD-SONFIN can always find itself an economical network size in the fast learning process. Our simulation results show that the performance of the new algorithm is superior to the RBFN in terms of convergence accuracy, estimation accuracy, sensitivity to noise, and network size.

Two-Dimensional Direction-Based Interpolation with Local Centered Moments

Interpolation is generally needed to visualize medical images from a limited number of sliced tomographic images such as CT. In this paper, a novel gray-scale image interpolation method, for interpolating two-dimensional images accurately and efficiently, called direction-based interpolation, is investigated. In this method, the digital image is considered a sampling of the underlying continuous function, which is also called the image field. If the image is interpolated along the isovalue curves in the image field, instead of along the coordinate axes, both the edges and the internal structures of the objects in the image are well preserved. Initially, the isovalue direction at each point is calculated from the local centered moments of the image. A specific type of image, called the direction image, is composed from the isovalue directions. Then, the direction image is interpolated into a high-resolution direction image. The isovalue curve through any point in the image field is determined from the high-resolution direction image using a path-finding technique. A high-resolution gray-scale image with satisfactory object structure is then generated by interpolating the original image linearly along the isovalue curves. Experiments on a set of CT images show that this method not only preserves the shapes of complicated structures but also has an efficient computation. The comparison between the digitally reconstructed radiographs generated from the interpolated result using the direction-based interpolation method, the traditional linear interpolation method, and the traditional cubic spline interpolation method shows the promise of the proposed method in radiation treatment planning.

DOA estimation of wide-band signals based on time-frequency analysis

A numerical study on an approach based on the time-frequency analysis is performed for the high-resolution direction finding applications of wide-band signals. In this method, the direction of arrival (DOA) is estimated using a subband of the incoming signal instead of the whole signal spectrum. This treatment forces the DOA of the wide-band signals to be similar to that of the DOA of the narrow-band signals. The reason behind this can be thought of as the after effects of reducing the signal bandwidth, which constrains the signal subspace. An empirical analysis of the performance of the DOA estimator Is also investigated. This is done to compare the correct and estimated angles of separation between the targets, and it is demonstrated that there is a good agreement which implies that the use of prefiltering does not affect the resolution of the DOA estimator.

MI効果を利用した高分解能な薄膜磁界センサ

A Magneto-Impedance (MI) effect was found in CoSiB/Cu/CoSiB thin film elements fabricated by RF magnetron sputtering. In these elements very large impedance change ratios were achieved when an external magnetic field was applied to the longitudinal direction. These ratios were much higher than those of any other element with MI effect. Therefore, it is useful for the high resolution direction sensing .

Matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts

The performance of high-resolution direction of arrival (DOA) estimation methods significantly degrades in several practical situations where the wavefronts have imperfect spatial coherence. The original solution to this problem was proposed by Paulraj and Kailath (1988), but their technique requires a priori knowledge of the matrix characterizing the loss of wavefront coherence along the array aperture. A novel solution to this problem is proposed, which does not require a priori knowledge of the spatial coherence matrix.

A fast MEM algorithm for high resolution direction spectrum estimation

From the point of view of reducing computation and improving performance, this paper discusses the Maximum Entropy Method (MEM) in array data processing and proposes a fast modified MEM (MMEM) on account of noise power cancellation. The simulation results show that the MMEM has better directional performance and higher angular resolution than the MEM. The required (SNR) can be reduced by 7–10 dB and the error of the root-mean square of angle estimation is greatly decreased.

The Gaussian scale-space paradigm and the multiscale local jet

A representation of local image structure is proposed which takes into account both the image's spatial structure at a given location, as well as its "deep structure", that is, its local behaviour as a function of scale or resolution (scale-space). This is of interest for several low-level image tasks. The proposed basis of scale-space, for example, enables a precise local study of interactions of neighbouring image intensities in the course of the blurring process. It also provides an extrapolation scheme for local image data, obtained at a given spatial location and resolution, to a finite scale-space neighbourhood. This is especially useful for the determination of sampling rates and for interpolation algorithms in a multilocal context. Another, particularly straightforward application is image enhancement or deblurring, which is an instance of data extrapolation in the high-resolution direction. A potentially interesting feature of the proposed local image parametrisation is that it captures a trade-off between spatial and scale extrapolations from a given interior point that do not exceed a given tolerance. This trade-off suggests the possibility of a fairly coarse scale sampling at the expense of a dense spatial sampling (large relative spatial overlap of scale-space kernels). The central concept developed in this paper is an equivalence class called the multiscale Zocal jet, which is a hierarchical, local characterisation of the image in a full scale-space neighbourhood. For this local jet, a basis of fundamental polynomials is constructed that captures the scale-space paradigm at the local level up to any given order.

Rietveld refinement of dry-synthesized Rb2ZnSi5O12 leucite by synchrotron X-ray powder diffraction. Erratum

Analysis of a high-resolution synchrotron X-ray powder direction pattern of a dry-synthesized rubidium zinc silicate, leucite analogue Rb 2 ZnSi 5 O 12 , showed that this material has a cubic Ia3d structure. The structure of this material has been refined by the Rietveld method. Si and Zn atoms are disordered on tetrahedral framework sites and Rb occupies large channel sites along the [111] direction

Image compression using wavelet transform and multiresolution decomposition

Schemes for image compression of black-and-white images based on the wavelet transform are presented. The multiresolution nature of the discrete wavelet transform is proven as a powerful tool to represent images decomposed along the vertical and horizontal directions using the pyramidal multiresolution scheme. The wavelet transform decomposes the image into a set of subimages called shapes with different resolutions corresponding to different frequency bands. Hence, different allocations are tested, assuming that details at high resolution and diagonal directions are less visible to the human eye. The resultant coefficients are vector quantized (VQ) using the LGB algorithm. By using an error correction method that approximates the reconstructed coefficients quantization error, we minimize distortion for a given compression rate at low computational cost. Several compression techniques are tested. In the first experiment, several 512x512 images are trained together and common table codes created. Using these tables, the training sequence black-and-white images achieve a compression ratio of 60-65 and a PSNR of 30-33. To investigate the compression on images not part of the training set, many 480x480 images of uncalibrated faces are trained together and yield global tables code. Images of faces outside the training set are compressed and reconstructed using the resulting tables. The compression ratio is 40; PSNRs are 30-36. Images from the training set have similar compression values and quality. Finally, another compression method based on the end vector bit allocation is examined.