Array Manifold Matrix Research Articles

Multi-Target Pairing Method Based on PM-ESPRIT-like DOA Estimation for T/R-R HFSWR

The transmit/receive-receive (T/R-R) synergetic High Frequency Surface Wave Radar (HFSWR) has increasingly attracted attention due to its high localization accuracy, but multi-target pairing needs to be performed before localization in multi-target scenarios. However, existing multi-target parameter matching methods have primarily focused on track association, which falls under the category of information-level fusion techniques, with few methods based on detected points. In this paper, we propose a multi-target pairing method with high computational efficiency based on angle information for T/R-R synergetic HFSWR. To be more specific, a dual-receiving array signal model under long baseline condition is firstly constructed. Then, the amplitude and phase differences of the same target reaching two subarrays are calculated to establish the cross-correlation matrix. Subsequently, in order to extract the rotation factor matrices containing pairing information and improve angle estimation performance, we utilize the conjugate symmetry properties of the uniform linear array (ULA) manifold matrix for generalized virtual aperture extension. Ultimately, azimuths estimation and multi-target pairing are accomplished by combining the propagator method (PM) and the ESPRIT algorithm. The proposed method relies solely on angle information for multi-target pairing and leverages the rotational invariance property of Vandermonde matrices to avoid peak searching or iterations, making it computationally efficient. Furthermore, the proposed method maintains superb performance regardless of whether the spatial angles are widely separated or very close. Simulation results validate the effectiveness of the proposed method.

Multiple ultrasonic partial discharge DOA estimation performance of KPCA Pseudo-Whitening mnc-FastICA

Empirical studies into partial discharge (PD) localization face the difficulty of signal contamination from external noise and interference. To extract relevant information from PD signals collected by acoustic sensor array, Kernel Principal Component Analysis (KPCA) pseudo-whitening with modified noncircular Fast Independent Component Analysis (mnc-FastICA) were used. By this approach, separated matrix and observed signals can be achieved. The reconstructed array manifold matrix created from the separated matrix generated by KPCA-mnc-FastICA may be used in the Direction of Arrival (DOA) estimation approach. An angle error correction matrix is designed to compensate for the sensor's phase inaccuracy. The simulation results show that angle identification accuracy is outstanding, with mistakes limited to a small margin of 2°. Furthermore, the results of trials show that this technique can efficiently isolate individual target signals even when they are polluted with significant noise and interference. The average errors in azimuth and pitch angle are less than 2° and 1.1°, respectively. These data support the effectiveness of the approach for effectively separating signals and estimating DOA of numerous signal sources.

Assistant vehicle locating based on DOA estimation of deep unfolded network

In view of the decline in the positioning accuracy of the vehicles with small snapshots, this paper proposes a direction of arrival(DOA) estimation method based on deep unfolded network to assist the global positioning system to achieve high-precision locating. Firstly, the signal emitted from the on board unit installed on the vehicle is received by the array antenna of the road side unit(RSU), then RSU transmits the array data to cloud service platform, in which the traditional fixed point continuation algorithm is improved by using l1 norm instead of l2 norm, and the adaptive outlier point tracking algorithm is used to deal with the problem of symbol flipping caused by noise. Then we unfold the improved fixed point continuous algorithm for obtaining a neural network. In order to improve the DOA estimation performance and convergence speed, this paper uses the black widow optimization algorithm to determine the soft threshold shrinkage parameters. According to the mapping between the signal and the array manifold matrix, the DOA of the target is estimated, and its location can be evaluated from the geometry relation between vehicle and RSU. The simulation results show that the algorithm proposed in this paper has better direction finding performance and improves the vehicle positioning accuracy under small snapshots and high signal-to-noise ratio effectively.

Off-Grid Based DOA Estimation Algorithm Using Auto-Regression (1) Sparse Bayesian Learning with Linear Interpolation Model

On-grid approaches for DOA estimation majorly exhibits the problem of grid mismatch. Coarse grid leads to reduced estimation accuracy and dense grid leads to increased algorithm complexity and performance degradation due to highly correlated array manifold matrix. In this paper, a fixed off-grid DOA estimation algorithm is proposed to overcome this grid mismatch problem. Firstly, a sparsity based linear interpolation model for array manifold matrix is proposed to avoid the above limitation by introducing a bias parameter into the estimation framework. To solve this model, an Auto-regression (1) (AR (1)) based sparse Bayesian learning algorithm is proposed. To exploit the temporal correlation property of unknown DOA spatial spectrum in a MMV case, we develop this AR (1) model along with SBL to estimate the unknown DOA spectrum and expectation maximization (EM) framework to update the hyper-parameters. The results section shows that the proposed algorithm enjoys good estimation resolution and accuracy in the cases of fewer snapshots available, highly correlated signal sources, very low SNR and very closely spaced sources.

Range-Angle Decoupling and Estimation for FDA Radar With Non-Uniform Frequency Offset

Frequency diverse array (FDA) radar with non-uniform frequency increasing offset is the most potent method to decouple the range-angle dependent beampattern and form a dot-shaped beampattern. However, little known empirical research has focused on the joint range-angle estimation of FDA radar with non-uniform frequency offset. The aim of this letter is to investigate a decoupling model and propose a range-angle estimation algorithm of FDA radar with uniform or non-uniform frequency offset. First, the blind source separation algorithm is performed to process the observation signal and obtain the separation matrix. Then, the array manifold matrix of observation signal is estimated by separation matrix correction. Next, a decoupling model is formulated to separate the range and angle component from the estimated array manifold matrix. Finally, an independent range and angle estimation algorithm via pulse-pair technique is developed. The numerical simulations are performed to indicate the effectiveness and superior performance.

Equal Sinusoidal Division of Array Manifold Matrix Based Direction-of-Arrival Estimation for Dual-functional Radar-communication

In view of the large computational complexity and poor real-time performance of l1 norm convex optimization process for DOA estimation based on compressed sensing sparse reconstruction, the SAMP greedy algorithm is used to replace the l1 norm to obtain the approximate solution of l0 norm optimization in DOA estimation. The array manifold matrix is divided by equal sinusoidal, which satisfies the MIP criterion better. An iterative regularization sparsity adaptive matching pursuit (IR-SAMP) algorithm is proposed, which makes the SAMP algorithm better approximate the signal sparsity and reduces the estimation error. IR-SAMP algorithm uses regularization method and backtracking screening, and eliminates the inappropriate atoms in the backtracking stage, so as to better approximate the signal source sparsity. Simulation results show that the proposed IR-SAMP algorithm in single snapshot DOA estimation under equal sinusoidal sparse division is better. At the same time, IR-SAMP algorithm has low computational complexity, as for coherent signal source, which also has a better estimation effect.

A novel multi-site damage localization method based on near-field signal subspace fitting using uniform linear sensor array

Damage diagnose imaging methods based on guided waves have been widely developed to depict the position and area of damage in structural health monitoring (SHM). Among them, compact sensor array based imaging methods have been gradually applied with high accuracy, such as phased array imaging, spatial filter imaging, multiple signal classification imaging and so on. However, when the multi-site damage appears nearly, the performance of these methods usually degrades. On one hand, limited to the array aperture, traditional methods cannot distinguish adjacent damage sites. On another hand, some subspace decomposition based methods also fail, suffering from the correlation between scattered array signals from different damage sites. To realize localization of multi-site damage, a novel near-field signal subspace fitting based multi-site damage localization method is proposed in this paper. This method constructs the cost function, which describe the equivalence relation between the signal subspace and array manifold matrix. Then localization of multi-site damage could be realized through multidimensional search for the optimization of cost function. The proposed method is verified on the aluminum panel with 3 damage sites. Experimental results show that the proposed method can realize multi-site damage localization with the angle errors less than 4° and the distance errors less than 35 mm.

Lightweight CNNs-Based Interleaved Sparse Array Design of Phased-MIMO Radar

Conventional transmit subarray partitioning schemes of phased-MIMO radar will cause several problems, the reduction of array aperture, the increase of feeding network complexity and optimization algorithms time cost. Focus on the problems above, this paper proposes a deep learning-based interleaved sparse transmit subarray partitioning method. Firstly, the training data is generated by phased-MIMO array manifold matrix. Secondly, a dimensionality reduction method for radar data is introduced to reduce the dimensionality of the sample data while minimizing information loss. Then, a lightweight convolutional neural network is constructed for training and the optimal array structures is selected by classification. Finally, linear and plane arrays experiment results show that our proposed method can achieve 97.95% classification accuracy, better than other conventional dimensionality reduction methods and neural networks; compared with the traditional SCP partitioning method, our proposed method has similar beampattern sidelobe level and DOA estimation accuracy, but the time cost is greatly reduced.

2D DOA Estimation of Coherently Distributed Sources for Planar Arrays Based on Blind Signal Separation

A novel method is presented to estimate the direction-of-arrival (DOA) of coherently distributed (CD) sources for planar arrays. In the proposed method, the two-dimensional (2D) angular parameters are obtained by making use of the estimated generalized array manifold matrix, which is separated from the received observation data based on blind signal separation algorithm. The proposed method offers a number of advantages. First, the 2D central DOAs and angular spread variances can be estimated simultaneously. Second, the deterministic angular distributed functions (DADFs) of the CD sources do not need to know. Third, the special array geometries are not required, as the method is applicable to planar arrays. Computer simulations are shown to verify the efficacy of the proposed method.

Marginal Likelihood Maximization Based Fast Array Manifold Matrix Learning for Direction of Arrival Estimation

By exploiting the sparsity of signal sources in the spatial domain, compressive sensing (CS) based directional of arrival (DOA) estimation has emerged as a promising approach especially in the case of a limited number of snapshots. However, due to the use of a large overcomplete dictionary obtained from a predefined grid, CS-based DOA estimation methods normally suffer from high computational complexity and the grid mismatch problem. Many methods, in particular sparse Bayesian learning (SBL) based off-grid methods, have been developed to address the grid mismatch problem at the cost of high complexity. In this work, we develop a new method for DOA estimation based on marginal likelihood maximization, where the array manifold matrix is learned incrementally, which is in contrast to the use of overcomplete dictionaries or grid matrices in existing CS or SBL based methods. We show that the problem of marginal likelihood maximization over multiple variables can be greatly simplified to maximization of a simple cost function over a sole variable (angle), which enables the learning of the manifold matrix and the development of an efficient solver. The grid mismatch problem is circumvented and the manifold matrix during learning is kept in a small size (slightly larger than the number of sources), leading to low computational complexity. Simulations results demonstrate the merits of the proposed method in terms of performance and computational complexity, compared to state-of-the-art SBL-based methods.

Deep Networks for Direction-of-Arrival Estimation in Low SNR

In this work, we consider direction-of-arrival (DoA) estimation in the presence of extreme noise using Deep Learning (DL). In particular, we introduce a Convolutional Neural Network (CNN) that is trained from mutli-channel data of the true array manifold matrix and is able to predict angular directions using the sample covariance estimate. We model the problem as a multi-label classification task and train a CNN in the low-SNR regime to predict DoAs across all SNRs. The proposed architecture demonstrates enhanced robustness in the presence of noise, and resilience to a small number of snapshots. Moreover, it is able to resolve angles within the grid resolution. Experimental results demonstrate significant performance gains in the low-SNR regime compared to state-of-the-art methods and without the requirement of any parameter tuning. We relax the assumption that the number of sources is known a priori and present a training method, where the CNN learns to infer the number of sources jointly with the DoAs. Simulation results demonstrate that the proposed CNN can accurately estimate off-grid angles in low SNR, while at the same time the number of sources is successfully inferred for a sufficient number of snapshots. Our robust solution can be applied in several fields, ranging from wireless array sensors to acoustic microphones or sonars.

A Novel Block Sparse Reconstruction Method for DOA Estimation With Unknown Mutual Coupling

In this letter, we consider the direction-of-arrival (DOA) estimation in the presence of unknown mutual coupling in application to uniform linear arrays (ULAs). A novel method is proposed that treats the DOA estimation as a block sparse signal reconstruction problem with a modified array manifold matrix which utilizes the information of entire array output. A block smoothed $\ell _{0}$ norm approximation technique is introduced to solve the problem. Finally, an iterative proximal algorithm is proposed. Simulation results are presented that show the superiority of the proposed method against other known techniques.

Source separation and localisation via tensor decomposition for distributed arrays

This study focuses on the problem of power spectra separation and localisation of multiple sources using distributed arrays. First, the array structure and signal model are discussed. By cross-correlating the multi-channel received signals in time-domain, a third tensor is constructed. Then, utilising the multi-dimensional characteristic, the tensor is decomposed to separate the array manifold matrix and the power spectra matrix through alternating least square (ALS) method. Finally, the sources are located using the relative x-y plane relationship between the distributed arrays and the direction of arrival (DOA), which can be estimated by spectrum analysis of each column of the array manifold matrix. The effectiveness and superiority of the proposed method is demonstrated by simulation results.

A Simple Modification of ESPRIT

In this letter, a manifold reconstruction based ESPRIT algorithm is devised for direction-of-arrival (DOA) estimation. Unlike the standard ESPRIT approach, the proposed method employs two smaller overlapping subarrays to construct the rotational invariance equation, which is then used to recover the array manifold matrix. This way, the DOA estimation can be split into K single-source DOA estimation problems, where each DOA is estimated by minimizing a nonlinear least squares fitting criterion that is solved via a computationally efficient Newton's method. Numerical results are included to validate the effectiveness of the proposed algorithm.

Joint 2-D DOA and TOA Estimation for Multipath OFDM Signals Based on Three Antennas

A method for estimating the 2-D direction- and time-of-arrival of orthogonal frequency division multiplexing (OFDM) signals that utilizes only three antennas is proposed. An array manifold matrix is first constructed not only based on the symmetry of circular geometry but also the time diversity of every OFDM subcarrier, so that the array aperture can be greatly increased. A virtual spatial smoothing method is then used to partition the array manifold matrix into structurally identical sub-array manifold matrix, so that coherent multipaths can be correctly estimated by incorporating the eigenstructure-based techniques on the average of the sub-array covariance matrices. Simulation results are provided to demonstrate the effectiveness of the proposed method.

A new DOA estimation algorithm based on compressed sensing

Considering the computational complexity and redundancy of traditional array signal arrival angle (DOA) estimation algorithms, the compressed sensing technology was used to improve the real-time and accurate performance of the DOA estimation algorithm, in which, the space sparse signals were reconstructed from the array data by means of array manifold matrix. Compared with the classical MUSIC algorithm, the compressed sensing DOA estimation method could effectively improve the direction finding accuracy and angle resolution with low SNR and snapshot deficiency. Moreover, the proposed algorithm could achieve the coherent signal estimation correctly, and the simulation results show that its performance was superior to that of traditional algorithm.

Estimation of DOA for Noncircular Signals via Vandermonde Constrained Parallel Factor Analysis

We provide a complete study on the direction-of-arrival (DOA) estimation of noncircular (NC) signals for uniform linear array (ULA) via Vandermonde constrained parallel factor (PARAFAC) analysis. By exploiting the noncircular property of the signals, we first construct an extended matrix which contains two times sampling number of the received signal. Then, taking the Vandermonde structure of the array manifold matrix into account, the extended matrix can be turned into a tensor model which admits the Vandermonde constrained PARAFAC decomposition. Based on this tensor model, an efficient linear algebra algorithm is applied to obtain the DOA estimation via utilizing the rotational invariance between two submatrices. Compared with some existing algorithms, the proposed method has a better DOA estimation performance. Meanwhile, the proposed method consistently has a higher estimation accuracy and a much lower computational complexity than the trilinear alternating least square- (TALS-) based PARAFAC algorithm. Finally, numerical examples are conducted to demonstrate the effectiveness of the proposed approach in terms of estimation accuracy and computational complexity.

Sparse representation-based DOA estimation of coherent wideband LFM signals in FRFT domain

In this paper, the method of direction-of-arrival (DOA) estimation for wideband signals based on sparse representation of FRFT domain is proposed by using the excellent convergence of FRFT to LFM signals. This method focuses the wideband signal to the reference frequency using FRFT, establishes the DOA estimation model and the array manifold matrix in the FRFT domain, and reconstructs the spatial spectral function based on the sparse representation of the spatial angles, so as to realize the wideband LFM signal DOA estimations. The method not only is suitable for non-coherent signals but also can process coherent signals directly without any decoherent operations; in addition, the number of signals is not necessarily known a priori. Simulation results show that the proposed method can achieve better estimation performance and higher angular resolution, especially under low signal-to-noise ratio (SNR) condition.

2-D DOA Estimation for L-Shaped Array With Array Aperture and Snapshots Extension Techniques

A two-dimensional (2-D) direction of arrival estimation method for L-shaped array with automatic pairing is proposed. It exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and the number of virtual snapshots simultaneously, and then applies the principle of MUSIC to construct an angle cost function and transforms the conventional 2-D search into 1-D via a Rayleigh quotient, which can greatly reduce the computation complexity. Finally, the azimuth and elevation angles are estimated without pair matching. Simulation results show that the proposed method has a better performance and can resolve more sources than some existing computationally efficient methods.

Direction-of-Arrival Estimation and Sensor Array Error Calibration Based on Blind Signal Separation

We consider estimating the direction-of-arrival (DOA) in the presence of sensor array error. In the proposed method, a blind signal separation method, the joint approximation and diagonalization of eigenmatrices algorithm, is implemented to separate the signal vector and the mixing matrix consisting of the array manifold matrix and the sensor array error matrix. Based on a new mixing matrix and the reconstruction of the array output vector of each individual signal, we propose a novel DOA estimation and sensor array error calibration procedure. This method is independent of array phase errors and performs well against difference of SNR of signals. Numerical simulations verify the effectiveness of the proposed method.