Two-dimensional Multiple Signal Classification Research Articles

Combining circular laser sensing array with MUSIC algorithm for fast damage localization

Large plate shell structures are key supporting components for aerospace and transportation equipment. Rapid localization of damages in large-scale thin-walled structures is an urgently needed technology for on-site detection and maintenance. This paper proposed a rapid damage localization method based on a laser ultrasonic circular arrays, combining the advantages of the circular arrays and the MUSIC algorithm. It does not need reference signals in advance, the direct waves and scattered waves can be quickly distinguished and extracted according to the time of arrival (TOA). Then, the two-dimensional multiple signal classification method(2D-MUSIC) under near-field conditions is used to quickly locate damage, which is a feature subspace algorithm in array signal processing technology. Compared with other commonly used imaging algorithms, this method has great advantages in detection efficiency and angular resolution. According to the detection method proposed in this paper, the position of single damage and multiple incoherent damages within 0.12 m2 can be quickly found within 1.3 s, and the angle error and distance error are not more than 5° and 5 cm. However, for the damage of coherent sources, there may be artifacts interfering with the imaging results.

Binary Radio Tomographic Imaging in Factory Environments Based on LOS/NLOS Identification

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Radio tomographic imaging</i> (RTI) is a technique for estimating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spatial loss fields</i> (SLFs), which maps the quantified attenuation of radio signals at every spatial location within monitored regions. In this study, we investigate RTI techniques in indoor factory environments, where the RTI techniques deteriorate because of severe multipath channels. We propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">binary radio tomographic imaging</i> (binary RTI) method, where the attenuation level of each pixel in a SLF is defined as a binary value. The binary RTI method is suited for factory environments, including metallic objects, because radio signals are almost fully reflected rather than getting absorbed by such objects. In the proposed method, we suppose that transmitted signals are modulated with an orthogonal frequency division multiplexing (OFDM) format, and each receiver is equipped with multiple antenna elements. By adopting the two-dimensional multiple signal classification (MUSIC), the proposed method identifies whether the signals are transmitted in a line-of-sight (LOS) or a non-line-of-sight (NLOS) path. From the LOS/NLOS identification, we propose two algorithms to estimate the binary SLF: a simple greedy algorithm and a relaxation algorithm with low-rank approximation. We evaluate the performance of the proposed method via simulation experiments. To assess the applicability of the proposed method to factory environments, we assume a severe multipath environment where all the objects, wall, and ceiling are perfect electrical conductors, and show that by using an appropriate threshold parameter for the LOS/NLOS identification, the proposed method can estimate the binary SLF in the test environment.

An Indoor Environment Sensing and Localization System via mmWave Phased Array

In this paper, an indoor layout sensing and localization system with testbed in the 60-GHz millimeter wave (mmWave) band, named mmReality, is elaborated. The mmReality system consists of one transmitter and one mobile receiver, both with a phased array and a single radio frequency (RF) chain. To reconstruct the room layout, the pilot signal is delivered from the transmitter to the receiver via different pairs of transmission and receiving beams, so that multipath signals in all directions can be captured. Then spatial smoothing and the two-dimensional multiple signal classification (MUSIC) algorithm are applied to detect the angle-of-departures (AoDs) and angle-of-arrivals (AoAs) of propagation paths. Moreover, the technique of multi-carrier ranging is adopted to measure the path lengths. Therefore, with the measurements of the receiver in different locations of the room, the receiver and virtual transmitters can be pinpointed to reconstruct the room layout. Experiments show that the reconstructed room layout can be utilized to localize a mobile device via the AoA spectrum.

Gain-Phase Error-Calibrated Piezoelectric Sensor Array-Based Impact Localization on Stiffened Curved Composite Structures.

Stiffened structure-induced gain-phase errors degrade the performance of the high-resolution two-dimensional multiple signal classification (2D-MUSIC) algorithm, which makes it impossible to ensure the high accuracy of impact localization results. To eliminate the localization bias caused by these errors, a calibrated 2D-MUSIC-based impact localization method is first introduced. Firstly, time-frequency characteristics of the non-stationary impact signals are evaluated by experiment to obtain a clear first wave packet or a wave packet that purely corresponds to a single mode through continuous wavelet transform (CWT). Then, the uniform linear array covariance matrix with gain-phase errors is calibrated to be constructed as a Toeplitz structural matrix. By reconstructing covariance matrix R, 2D-MUSIC-based impact localization is calibrated for stiffened curved composite structures. Experimental research on the stiffened curved composite panel is carried out, and these impact localization results demonstrate the validity and effectiveness of the calibrated 2D-MUSIC-based method.

FEM simulation based adaptive sensors array error compensation method for impact monitoring on stiffened composite structures

To eliminate the sensor array based impact localization bias on stiffened composite structures, a finite element method (FEM) simulation based adaptive sensors array errors compensation method for impact monitoring is introduced. Firstly, detailed analysis and comparison discussion about Lamb wave propagation errors between the simple and stiffened plate are provided using FEM simulation, and the gain-phase errors obtained are structured as a array error matrix. Secondly, array error matrix is substituted into the steering vector of standard two-dimensional Multiple Signal Classification (2D-MUSIC) algorithm to compensate the stiffener effect. And then initial estimates of impact could be estimated by the compensated 2D-MUSIC algorithm. Finally substituting these initial estimates, the cost function is minimized by adaptive iterative to calculate the reasonable location of the impact source. The experiments on a carbon fiber composite stiffened plate demonstrate the validity and effectiveness of the proposed method.

Low-Complexity 2D-MUSIC for Joint Range and Angle Estimation of Frequency Modulated Continuous-Wave Radar

A pre-processing technique is proposed to reduce the complexity of two-dimensional multiple signal classification (2D-MUSIC) for the joint range and angle estimation of frequency-modulated continuous-wave (FMCW) radar systems. By using the central symmetry of the angle steering vector from a uniform linear array (ULA) antenna and the linearity of the beat signal in the FMCW radar, this preprocessing technique transforms 2D-MUSIC from complex values into real values. To compare the computational complexity of the proposed algorithm with the conventional 2D-MUSIC, we measured the CPU processing time for various numbers of snapshots, and the evaluation results indicated that the 2D-MUSIC with the proposed pre-processing technique is approximately three times faster than the conventional 2D-MUSIC.

Performance Analysis of Joint Range-Velocity Estimator With 2D-MUSIC in OFDM Radar

To achieve high resolution, orthogonal frequency division multiplex (OFDM) radars deploy two-dimensional multiple signal classification (2D-MUSIC) in the joint range-velocity estimator. However, it is obvious that both of the signal reconstruction and 2D smoothing affect the noise statistical distribution and virtual array aperture in the joint range-velocity estimator with 2D-MUSIC. Therefore, the conventional accuracy analysis methods for the MUSIC are no longer suitable. In this paper, we propose an estimation accuracy analysis for the joint range-velocity estimator with 2D-MUSIC. Firstly, we present that the noise statistical distribution of the signals being reconstructed and 2D smoothed has a 2-fold Hankel structure. Then, the closed-forms of the range and velocity estimation accuracies are derived, respectively, which both show that the estimation accuracies highly depend on the 2D smoothing and could be improved by properly choosing the 2D smoothing window. Further, we formulate the smoothing optimization and propose the quasi-optimal size of the 2D smoothing window. Finally, both theoretical analyses and simulations validate that the proposed smoothing optimization could significantly improve the estimation accuracies with a lower computational burden than the conventional smoothing.

Adaptive Sensor Array Error Calibration Based Impact Localization on Composite Structure

Gains and phases delay induced by sensor position error would significantly degrade the performance of high-resolution two-dimensional multiple signal classification (2D-MUSIC) algorithm, which resulting in low positioning estimation accuracy and poor imaging. In this study, adaptive piezoelectric sensor array calibration based method is proposed for impact localization on composite structure. First, observed signal vector from the sensor array is represented by error calibration matrix with unknown gains and phases, and then it used to construct the cost function including sensor array parameters. Second, a 2D-MUSIC algorithm based on linear attenuation calibration is applied for estimating the initial estimate of impact location. Finally, substituting the initial estimate, the cost function is minimized by adaptive iterative to calculate the sensor array error parameters and the exact location of the impact source. Both finite element method (FEM) simulation and experimental results on carbon-fiber composite panel demonstrate the validity and effectiveness of the proposed method.

DOA estimation of multiple sources for a moving array in the presence of phase noise

The authors investigate the issue of direction of arrival (DOA) estimation in the presence of phase noise for multiple sources with a synthetic linear array, which is synthesised by a short moving array. The extended towed array measurements (ETAM) method can extend the array aperture greatly, but can only be applied to multiple coherent sources and requires the array to move with constant velocity. To tackle the problems, the authors generalise the ETAM method to multiple incoherent sources and array non-uniform motion case. The authors first formulate the manifold of the extended synthetic array (SA) moving with known velocity in a straight line. Then the initial DOA estimates and phase correction factors are estimated successively by two-dimensional multiple signal classification (2D-MUSIC) spectrum search using adjacent measurements sampled by the moving array. Moreover, to reduce the complexity, the authors also propose a reduced dimensional MUSIC (RD-MUSIC) method to turn the two-dimensional peak search to one-dimensional. As the array aperture is extended by proper compensation, the DOA estimation performance of the proposed SA method improves. Besides, the proposed method can resolve more number of sources than sensors since every two measurements are used for estimation in each process. Simulation results validate the effectiveness of the proposed method.

Localization Performance Analysis of FDA Radar Receiver With Two-Stage Estimator

Frequency diverse array (FDA) has received much attention, but little work about FDA receiver architectures and receiver processing algorithms have been reported. In this paper, we analyze the localization performance of FDA radar with a two-stage estimator. Three FDA receive architectures are discussed and compared with the phased-array (PA). In order to overcome disadvantages of the monochromatic FDA radar signal model adopted in the literature that ignores the coherent transmit gain in FDA radar, we formulate a bandwidth model for a general FDA radar received signals including both nonoverlapping and overlapping spectra. The localization performance are assessed by the Cramer–Rao bound (CRB) and receive signal noise ratio. The proposed model provides more accurate representation of FDA radar received signals and more reasonable comparisons between FDA and PA radars. Additionally, a fast two-stage estimator is proposed to reduce the two-dimensional multiple signal classification computation complexity. All proposed methods are verified by both theoretical analysis and numerical results.

Multiple Signal Classification-Based Impact Localization in Composite Structures Using Optimized Ensemble Empirical Mode Decomposition

Multiple signal classification (MUSIC) algorithm-based structural health monitoring technology is a promising method because of its directional scanning ability and easy arrangement of the sensor array. However, in previous MUSIC-based impact location methods, the narrowband signals at a particular central frequency had to be extracted from the wideband Lamb waves induced by each impact using a wavelet transform. Additionally, the specific center frequency had to be obtained after carefully analyzing the impact signal, which is time consuming. Aiming at solving this problem, this paper presents an improved approach that combines the optimized ensemble empirical mode decomposition (EEMD) and two-dimensional multiple signal classification (2D-MUSIC) algorithm for real-time impact localization on composite structures. Firstly, the impact signal at an unknown position is obtained using a unified linear sensor array. Secondly, the fast Hilbert Huang transform (HHT) with an optimized EEMD algorithm is introduced to extract intrinsic mode functions (IMFs) from impact signals. Then, all IMFs in the whole frequency domain are directly used as the input vector of the 2D-MUSIC model separately to locate the impact source. Experimental data collected from a cross-ply glass fiber reinforced composite plate are used to validate the proposed approach. The results show that the use of optimized EEMD and 2D-MUSIC is suitable for real-time impact localization of composite structures.

Joint DOD and DOA estimation for bistatic multiple‐input multiple‐output radar target discrimination based on improved unitary ESPRIT method

Target position estimation of radar system has attracted much attention. Researchers have proposed a variety of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation algorithms over the last few decades for this well-known problem. However, traditional estimation algorithms require a pairing process between the DOD and DOA estimation. In this study, the authors propose an improved unitary estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm for joint DOD and DOA estimation without a pairing operation. The waveforms are transmitted by an array with M sensors and received by two detached sub-arrays with and sensors, respectively. Specifically, the proposed algorithm eliminates a pairing process via sharing the eigenvectors of DOD and DOA. Theoretical derivation demonstrates that the proposed algorithm requires less computational complexity than two-dimensional multiple signal classification (MUSIC), reduced-dimension MUSIC, and ESPRIT. Simulation results show that the proposed algorithm can effectively enhance the accuracy of identifying and locating targets for the bistatic multiple-input multiple-output radar system.

Fast Estimation Method of Space-Time Two-Dimensional Positioning Parameters Based on Hadamard Product

The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA) and direction of arrival (DOA) parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC) algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM) system, and the Cramer-Rao bound (CRB) is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and 2D matrix pencil (MP) algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.

Real-Valued 2D MUSIC Algorithm Based on Modified Forward/Backward Averaging Using an Arbitrary Centrosymmetric Polarization Sensitive Array.

Two-dimensional multiple signal classification (MUSIC) algorithm based on polarization sensitive array (PSA) has excellent performance. However, it suffers a high computational complexity due to a multitude of complex operations. In this paper, we propose a real-valued two-dimensional MUSIC algorithm based on conjugate centrosymmetric signal model, which is applicable to arbitrary centrosymmetric polarization sensitive array. The modified forward/backward averaging, which can be applied to the PSA, is presented. Hence, the eigen-decomposition analysis process and spectrum function computation are converted into real domain, prominently reducing the computational complexity. Then, the direction-of-arrival (DOA) estimation is decoupled from the polarization parameter estimation so that the four-dimensional spectral peak search process is avoided. The theoretical computational complexity is discussed and the Cramer-Rao bound (CRB) of DOA estimation is derived in this paper. The simulation results indicate that the proposed algorithm achieves superior accuracy in DOA estimation and has low computational complexity.

Cognitive FDA‐MIMO radar for LPI transmit beamforming

Active radar is vulnerable to illegal eavesdroppers due to its high-gain beam-scanning signals. To reduce active radar visibility and enhance its low probability of intercept (LPI) capability, this study proposes a cognitive LPI transmit beamforming scheme using frequency diverse array (FDA) and multiple-input multiple-output (MIMO) hybrid array antenna. The achievement of LPI is due to the unique range-angle-dependent transmitting beampattern of FDA-MIMO radar, which minimises the beam power at the target location to reduce its visibility and simultaneously maximise the power at the radar receiver without degrading the radar detection performance. Furthermore, the FDA-MIMO radar operates in a cognitive way: the receiver estimates the target range and the direction of arrival with a two-dimensional multiple signal classification algorithm, and feedbacks their estimates to the transmitter to update the FDA-MIMO transmit beamforming. As the transmit beamforming optimisation is non-convex problem, the authors propose three methods, namely linear combination, non-linear combination and closed form solution. All the proposed methods are verified by simulation results.

An improved two-dimensional multiple signal classification approach for impact localization on a composite structure

Efficient impact monitoring techniques are important to be researched to ensure the safety of in-service composite structures. Multiple signal classification–based method is a new promising method. This method uses small aperture sensor array arrangement instead of sparse sensor arrangement. It has the advantage of easy sensor array arrangement. By processing the whole sensor array outputs using the multiple signal classification algorithm, transfer function and material property of the structure are not needed. Although some researches have shown the potential of this new method, most of the current researches have been performed based on the far-field assumption on aluminum structures. In engineering applications, composite structures are the main structures which need impact monitoring. Deep research needs to be addressed. Aiming at these problems, an improved two-dimensional near-field multiple signal classification processing algorithm is presented for impact localization on composite structure in this article. The proposed method can simultaneously estimate the impact occurring direction and distance. A uniform carbon fiber composite plate and a real aircraft oil tank made of carbon composite structure with varied thickness are adopted to evaluate the presented method. To deal with the anisotropy performance of the complex composite, the two-dimensional multiple signal classification processing algorithm is also improved by taking into account the existing anisotropy performance.

Interference Localization via Direction of Arrival Estimation for Satellite with Planar Array

This paper presents the model of satellite planar array, and interference localization via direction of arrival (DOA) estimation. We derive a dimension reduction DOA estimaton algorithm therein. The proposed algorithm, which only requires a one-dimensional local searching, can avoid the high computational cost within two-dimensional multiple signal classification (2D-MUSIC) algorithm. We illustrate that the proposed algorithm has better angle estimation performance than estimation method of signal parameters via rotational invariance technique (ESPRIT) algorithm, and has very close angle estimation performance to 2D-MUSIC algorithm. Furthermore, our algorithm requires no extra pairing. Simulation results present the usefulness of our algorithm.

Maximum Power Waveform Design for Bistatic MIMO Radar System

In this paper we propose a waveform design algorithm that localizes the maximum output power in the target direction. We extend existing monostatic radar optimal waveform design schemes to bistatic multiple-input multiple-output (MIMO) radar systems. The algorithm simultaneously calculates the direction of departure (DoD) and the direction of arrival (DoA) using a two-dimensional multiple signal classification (MUSIC) method, and successfully localizes the maximum transmitted power to the target locations by exploiting the calculated DoD. The simulation results confirm the performance of the proposed algorithm.

Two-dimensional near-field multiple signal classification algorithm–based impact localization

The susceptibility of composite materials to internal damage caused by low-velocity impact is well known and creates a major concern related to structural health monitoring. This research presents a near-field impact monitoring method based on the two-dimensional multiple signal classification method for the composite structure. Since elastic waves attenuate quickly in the complex aircraft composite structures and impacts may happen near the sensors, near-field impact monitoring method is important. However, most of the methods reported are based on the far-field assumption. When impacts occur not far enough from the sensors, this belongs to the near-field situation, where the elastic wave fronts are spherical and the direction estimation method with the plane wave hypothesis is no longer valid. Hence, this article focuses the research of a near-field multiple signal classification–based impact localization method. To verify the proposed method, two experiments are performed on composite structures. The localization results are in good agreement with the actual impact occurring positions in near-field area. Finally, the proposed method is applied to a real aircraft composite oil tank showing its successful performance on complex composite structure.

Direction Finding for Bistatic MIMO Radar with Uniform Circular Array

A method of direction of arrival (DOA) and direction of departure (DOD) angle estimation based on polynomial rooting for bistatic multiple-input multiple-output (MIMO) radar with uniform circular array (UCA) configuration is proposed in this paper. The steering vector of the UCA is firstly transformed into a steering vector with a Vandermonde structure by using the Jacobi-Anger expansion. Then the null-spectrum function of the MIMO radar can be written as an expression in which the transmit and receive steering vectors are decoupled. Finally, a two-step polynomial rooting is used to estimate DOA and DOD of targets instead of two-dimensional multiple signal classification (MUSIC) search method for bistatic UCA MIMO radar. The angle estimation performance of the proposed method is similar to that of the MUSIC spectral search method, but the computation burden of the proposed polynomial rooting algorithm is much lower than that of the conventional MUSIC method. The simulation results of the proposed algorithm are presented and the performances are investigated and analyzed.