Direction Of Arrival Of Sources Research Articles

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.

Deep learning based 2D-DOA estimation using L-shaped arrays

Direction-of-arrival (DOA) estimation problems arise in many applications such as wireless communication and localization. Recently, a number of deep learning (DL) based methods have been studied for one dimensional (1D) DOA estimation with relatively fewer studies for 2D-DOA estimation. In this study, we propose a low-complexity DL based method to estimate both elevation and azimuth DOAs of sources along with their pairing. To this end, first a classification neural network is proposed to estimate both elevation and azimuth DOAs of multiple sources. Next, a residual classification network is introduced to estimate the pairing between the estimated DOAs. In particular, we consider two perpendicular linear arrays which are located on z-axis and x-axis, respectively. The first proposed network uses the Sample Covariance Matrix (SCM) of the former array to estimate elevation angles and utilizes the latter array to estimate the corresponding azimuth DOAs. The second network, is responsible for estimating the pairing between the estimated elevation and azimuth DOA sets. Numerical simulations demonstrate the enhanced performance of our proposed 2D-DOA estimator scheme, surpassing existing 1D and 2D deep learning (DL) methods. Notably, our approach closely approaches the Ziv–Zakai bound (ZZB), particularly in low signal-to-noise ratio (SNR) and low-angle-difference scenarios, even in the presence of multiple highly correlated signals. Moreover, our complexity analysis validates the superiority of the proposed method.

Direction-of-arrival estimation in closely distributed array exploiting mixed-precision covariance matrices

In this paper, we explore a collaborative direction-of-arrival (DOA) estimation technique that utilizes multiple closely spaced subarrays to maximize the potential of distributed arrays while minimizing communication overhead between the subarrays and the processing center. Each subarray computes its self-covariance matrix using the full-precision data and transmits it, along with a one-bit version of the measured data, to the processing center. The processing center generates one-bit cross-covariance matrices between subarrays, which are combined with full-precision subarray self-covariance matrices to create the mixed-precision covariance matrix of the entire array for source DOA estimation. This approach utilizes the full array aperture and all available degrees of freedom of the entire distributed array. To address missing entries in the full covariance matrix, we employ matrix completion, taking into account its Toeplitz and Hermitian structure. For subarrays that are not positioned on the half-wavelength grid, we propose an iterative DOA estimation method to ensure robust DOA estimation performance. Our proposed approach outperforms scenarios where cross-covariance matrices are unavailable or the entire covariance matrix is not interpolated. With the same communication traffic limitation, it demonstrates superiority over schemes that utilize only full-precision data or only one-bit data.

A DOA Estimation Method Based on an Improved Transformer Model for Uniform Linear Arrays with Low SNR

In this paper, the Star-Transformer model is improved to obtain more accurate direction of arrivals (DOA) estimation of underwater sonar uniform linear array (ULA) under low signal-to-noise ratio (SNR) conditions. The ideal real covariance matrix is divided into three channels: real part channel, imaginary part channel, and phase channel to obtain more input features. In training, the real covariance matrix is used under different SNRs. In testing, the covariance matrix of samples in the real environment is used as input. The on-grid form is used to estimate the DOA of multiple signal sources, which is modelled as a multilabel classification problem. The results show that the model can be effective and can still have a good DOA estimation performance under the conditions of trained and untrained SNRs, different snapshots, signal power mismatch, different separation angles, signal correlation, and so on. It shows that the model has excellent robustness.

Neural-Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.

Enhanced Coprime Array Structure and DOA Estimation Algorithm for Coherent Sources.

This paper presents a new enhanced coprime array for direction of arrival (DOA) estimation. Coprime arrays are capable of estimating the DOA using coprime properties and outperforming uniform linear arrays. However, the associated algorithms are not directly applicable for estimating the DOA of coherent sources. To overcome this limitation, we propose an enhanced coprime array in this paper. By increasing the number of array sensors in the coprime array, it is feasible to enlarge the aperture of the array and these additional array sensors can be utilized to achieve spatial smoothing, thus enabling estimation of the DOA for coherent sources. Additionally, applying the spatial smoothing technique to the signal subspace, instead of the conventional spatial smoothing method, can further improve the ability to reduce noise interference and enhance the overall estimation result. Finally, DOA estimation is accomplished using the MUSIC algorithm. The simulation results demonstrate improved performance compared to traditional algorithms, confirming its feasibility.

UNet-rootMUSIC: A high accuracy direction of arrival estimation method under array imperfection

In the practical direction-finding systems, the accuracy and resolution of the direction of arrival (DOA) estimation are affected not only by the Gaussian noise and array size but also by hardware configuration imperfections, such as errors in element manufacturing and mounting. These impairments cause phase and amplitude errors in estimating the DOA of signal sources. To address this issue, this paper proposes to combine a U-shape deep neural network (UNet) with the multiple signal classification via the root of the polynomial (rootMUSIC) algorithm (so-called UNet-rootMUSIC) to improve the DOA estimation accuracy. In this approach, the UNet model plays a role in converting a covariance matrix of received signals containing phase and gain errors into a nearly perfect one of the ideal antenna array. The rootMUSIC algorithm is then employed to estimate the signal DOA based on the converted covariance matrix. The DOA estimation performance of the uniform linear array of eight elements with an inter-element distance of λ/2 is analyzed through experimental simulations. The simulation results demonstrate that our method can significantly reduce the root mean square error of DOA estimation compared to the conventional MUSIC, rootMUSIC, ESPRIT methods and two deep neural network-based angular classification methods.

Simultaneous Correlative Interferometer Technique for Direction Finding of Signal Sources.

In this paper, we propose a novel simultaneous Correlative Interferometer (CI) technique that elaborately estimates the Direction of Arrival (DOA) of multiple source signals incident on an antenna array. The basic idea of the proposed technique is that the antenna-array-based receiver compares the phase of the received signal with one of the candidates at each time sample and jointly exploits these multiple time samples to estimate the DOAs of multiple signal sources. The proposed simultaneous CI-based DOA estimation technique collectively utilizes multiple time-domain samples and can be regarded as a generalized version of the conventional CI algorithm for the case of multiple time-domain samples. We first thoroughly review the conventional CI algorithm to comprehensively explain the procedure of the direction-finding algorithm that adopts the phase information of received signals. We also discuss several technical issues of conventional CI-based DOA estimation techniques that are originally proposed for the case of a single time-domain sample. Then, we propose a simultaneous CI-based DOA estimation technique with multi-sample diversity as a novel solution for the case of multiple time-domain samples. We clearly compare the proposed simultaneous CI technique with the conventional CI technique and we compare the existing Multiple Signal Classification (MUSIC)-based DOA estimation technique with the conventional CI-based technique by using the DOA spectrum as well. To the best of our knowledge, the simultaneous CI-based DOA estimation technique that effectively utilizes the characteristics of multiple signal sources over multiple time-domain samples has not been reported in the literature. Through extensive computer simulations, we show that the proposed simultaneous CI technique significantly outperforms both the conventional CI technique in terms of DOA estimation even in harsh environments and with various antenna array structures. It is worth noting that the proposed simultaneous CI technique results in much better performance than the classical MUSIC algorithm, which is one of the most representative subspace-based DOA estimation techniques.

Direction-of-arrival and power spectral density estimation using a single directional microphone and group-sparse optimization

In this paper, two approaches are proposed for estimating the direction of arrival (DOA) and power spectral density (PSD) of stationary point sources by using a single, rotating, directional microphone. These approaches are based on a method previously presented by the authors, in which point source DOAs were estimated by using a broadband signal model and solving a group-sparse optimization problem, where the number of observations made by the rotating directional microphone can be lower than the number of candidate DOAs in an angular grid. The DOA estimation is followed by the estimation of the sources’ PSDs through the solution of an overdetermined least squares problem. The first approach proposed in this paper includes the use of an additional nonnegativity constraint on the residual noise term when solving the group-sparse optimization problem and is referred to as the Group Lasso Least Squares (GL-LS) approach. The second proposed approach, in addition to the new nonnegativity constraint, employs a narrowband signal model when building the linear system of equations used for formulating the group-sparse optimization problem, where the DOAs and PSDs can be jointly estimated by iterative, group-wise reweighting. This is referred to as the Group-Lasso with l_1-reweighting (GL-L1) approach. Both proposed approaches are implemented using the alternating direction method of multipliers (ADMM), and their performance is evaluated through simulations in which different setup conditions are considered, ranging from different types of model mismatch to variations in the acoustic scene and microphone directivity pattern. The results obtained show that in a scenario involving a microphone response mismatch between observed data and the signal model used, having the additional nonnegativity constraint on the residual noise can improve the DOA estimation for the case of GL-LS and the PSD estimation for the case of GL-L1. Moreover, the GL-L1 approach can present an advantage over GL-LS in terms of DOA estimation performance in scenarios with low SNR or where multiple sources are closely located to each other. Finally, it is shown that having the least squares PSD re-estimation step is beneficial in most scenarios, such that GL-LS outperformed GL-L1 in terms of PSD estimation errors.

An Improved Toeplitz Approximation Method for Coherent DOA Estimation in Impulsive Noise Environments.

Direction of arrival (DOA) estimation is an important research topic in array signal processing and widely applied in practical engineering. However, when signal sources are highly correlated or coherent, conventional subspace-based DOA estimation algorithms will perform poorly due to the rank deficiency in the received data covariance matrix. Moreover, conventional DOA estimation algorithms are usually developed under Gaussian-distributed background noise, which will deteriorate significantly in impulsive noise environments. In this paper, a novel method is presented to estimate the DOA of coherent signals in impulsive noise environments. A novel correntropy-based generalized covariance (CEGC) operator is defined and proof of boundedness is given to ensure the effectiveness of the proposed method in impulsive noise environments. Furthermore, an improved Toeplitz approximation method combined CEGC operator is proposed to estimate the DOA of coherent sources. Compared to other existing algorithms, the proposed method can avoid array aperture loss and perform more effectively, even in cases of intense impulsive noise and low snapshot numbers. Finally, comprehensive Monte-Carlo simulations are performed to verify the superiority of the proposed method under various impulsive noise conditions.

Multiple co-frequency sources DOA estimation for coprime vector sensor arrays.

For the problem of direction-of-arrival (DOA) estimation using a coprime array, there are high spatial spectrum outputs of false alarms caused by the overlap of main and grating lobes from subarrays. In this paper, a DOA estimation method of more than two co-frequency sources for a coprime vector hydrophone array is proposed. The method is based on vector cross terms (VCTs), making full use of the directivity of channel combinations for vector hydrophones. Based on VCTs, the characteristic data point identification method is conducted and ensures that the bearing data with the characteristic can be preserved. For further interference rejection, the paper designs Queue Selection (QS) method based on inverse beamforming. The influence of grating lobes can be weakened with the QS, further improving the accuracy of direction extraction. The algorithm in this work does not require decoherence processing, and the simulation work shows that it achieves stable DOA estimation with a low signal-to-noise ratio (SNR).

Localization of mixed coherently and incoherently distributed sources based on generalized array manifold

In practice, signals received by an array may be a mixture of coherently distributed (CD) and incoherently distributed (ID) sources, due to some complicated multipath/scattering effects. To localize mixed CD and ID sources, a method based on the generalized array manifold (GAM) is developed in this work. Firstly, source enumeration and source type classification are achieved by jointly employing the minimum description length (MDL) criterion, the covariance matrix difference technique and the second-order statistics of associated eigenvalues. Secondly, with the source enumeration result, the nominal direction of arrival (DOA) of ID sources is estimated by the rank-reduction principle based one-dimensional (1-D) spectral search, where shift invariance of the GAM associated with ID sources is considered. Thirdly, the oblique projection technique is adopted to separate the CD sources from ID ones, and then the nominal DOA of CD sources is estimated via the sparsity-cognizant total least-squares (S-TLS) method. Finally, with aid of the nominal DOA estimates, the corresponding angular spreads are calculated. An analysis of the proposed method is discussed and the approximate Cramér-Rao bound (CRB) is derived. Simulations are provided to demonstrate the performance of the proposed method.

Self-Calibration Method of Sensors Array Errors Based on Rotation Measurement

Array calibration is the premise of successful array signal processing. The active calibration needs to know the direction of arrival (DOA) of calibration source signals accurately; otherwise, the performance will deteriorate. Although the conventional self-calibration does not need accurate DOA of calibration sources, it may suffer from falling into the local extremum since there are too many parameters to be estimated. Thus, we propose a novel self-calibration method based on the rotation measurement. The rotation measurement is that the array receives signals from a fixed source with different array rotation angles. The proposed method jointly estimates array errors and DOAs of the sources by an alternative minimization (AM) algorithm. Through the derivation of a suitable initial value in the AM algorithm, we could improve the robustness and reduce the computational complexity. The proposed method can achieve as high calibration accuracy as the active method even if there is an error in the source DOA information and can apply to arbitrary planar arrays. Both simulation and field experiment results demonstrate the effectiveness of the proposed method.

Self-Calibration of Acoustic Scalar and Vector Sensor Arrays

In this work, we consider the self-calibration problem of joint calibration and direction-of-arrival (DOA) estimation using acoustic sensor arrays. Unlike many previous iterative approaches, we propose solvers that can be readily used for both linear and non-linear arrays for jointly estimating the sensor gain, phase errors, and the source DOAs. We derive these algorithms for both the conventional element-space and covariance data models. We focus on sparse and regular arrays formed using scalar sensors as well as vector sensors. The developed algorithms are obtained by transforming the underlying non-linear calibration model into a linear model, and subsequently by using convex relaxation techniques to estimate the unknown parameters. We also derive identifiability conditions for the existence of a unique solution to the self-calibration problem. To demonstrate the effectiveness of the developed techniques, numerical experiments, and comparisons to the state-of-the-art methods are provided. Finally, the results from an experiment that was performed in an anechoic chamber using an acoustic vector sensor array are presented to demonstrate the usefulness of the proposed self-calibration techniques.

Ziv-Zakai Bound for DOAs Estimation

Lower bounds on the mean square error (MSE) play an important role in evaluating the direction-of-arrival (DOA) estimation performance. Among numerous bounds for DOA estimation, the local Cram <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{\acute{e}}$</tex-math></inline-formula> r-Rao bound (CRB) is only tight asymptotically. By contrast, the existing global tight Ziv-Zakai bound (ZZB) is appropriate for evaluating the single source estimation only. In this paper, we derive an explicit ZZB applicable for evaluating hybrid coherent/incoherent multiple sources DOA estimation. It is first shown that, a straightforward generalization of ZZB from single source estimation to multiple sources estimation cannot keep the bound valid in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> performance region. To derive a global tight ZZB, we then introduce order statistics to describe the change of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> distribution of DOAs caused by ordering process during the MSE calculation. The derived ZZB is for the first time formulated as a function of coherent coefficients between coherent sources, and reveals the relationship between the MSE convergency in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> performance region and the number of sources. Moreover, the derived ZZB also provides a unified tight bound for both overdetermined and underdetermined DOA estimation. Simulation results demonstrate the obvious advantages of the derived ZZB over the CRB on evaluating and predicting the estimation performance for multiple sources DOA.

Robust min-norm algorithms for coherent sources DOA estimation based on Toeplitz matrix reconstruction methods

Most of the classical high-resolution algorithms such as ESPRIT, MUSIC or Min-Norm, demonstrate their ability to estimate the directions by which non-coherent signals are arrived on a sensor array. However, the need to enhance this kind of algorithm is becoming increasingly important in order to obtain good estimation also in coherent environments. In this paper, two different algorithms for Direction-of-Arrival (DOA) estimation are devised. These two new algorithms improve the performance of the Min-Norm algorithm by incorporating decorrelation techniques as a tool to overcome coherent source estimation problems. Simulation examples are conducted to validate the robustness and the effectiveness of the new proposed algorithms compared to the conventional Min-Norm high resolution algorithm.

Toeplitz Cyclic-MUSIC Algorithms for DOA Estimation of the SOCS Correlated Signals

This letter addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signal when the second-order cyclic statistics (SOCS) of signals are correlated. We first present a Toeplitz Cyclic-MUSIC algorithm for multichannels receiver by exploiting signal cyclostationarity. Based on cyclic autocorrelation of the received signal, a new pesudocyclic covriance matrix, which is Toeplitz, is constructed. The rank of Toeplitz matrix is equal to the number of signals even if the SOCS of signals are correlated. So the MUSIC algorithm can be used to estimate the DOAs of sources. Moreover, a single channel Toeplitz Cyclic-MUSIC algorithm for the the single-channel receiver is proposed to avoid the affect of channel inconsistency. The effectiveness of the proposed algorithms is verified by computer simulation, and the performance of the proposed algorithms is compared with the existing algorithms correspondingly.

A joint DOA and polarization estimation method based on the conformal polarization sensitive array from the sparse reconstruction perspective

The conformal polarization sensitive array (CPSA) is formed by placing some vector sensors on the conformal array and it has a wide range of practical application in direction of arrival (DOA) and polarization parameters estimation. However, due to the diversity of each sensor’s direction, the performance of the conventional parameters estimation methods based on the CPSA would decrease greatly, especially under the low signal to noise ratio (SNR) and limited snapshots. In order to solve this problem, a unified framework and sparse reconstruction perspective for joint DOA and polarization estimation based on CPSA is proposed in this paper. Specifically, the array received signal model of the CPSA is formulated first and the two-dimensional spatial sparsity of the incident signals is then exploited. Subsequently, after employing the singular value decomposition method to reduce the dimension of array output matrix, the variational sparse Bayesian learning and orthogonal matching pursuit methods are utilized to solve the source DOA estimation, respectively. Finally, the polarization parameters are obtained by the minimum eigenvector method. Simulation results demonstrate that the novel approaches can provide improved estimation accuracy and resolution with low SNR and limited snapshots.

DOA Estimation of Coherent Sources Using Coprime Array via Atomic Norm Minimization

In this letter, we develop an effective algorithm for direction-of-arrival (DOA) estimation of coherent sources with coprime arrays. Firstly, we generate a virtual uniform linear array (ULA) through coprime array interpolation. Subsequently, we derive an augmented noise-free covariance matrix that is constructed using the entries of the covariance matrix of the virtual ULA outputs, and recover the Hermitian Toeplitz matrix by solving an atomic norm minimization problem with multiple measurement vectors. Finally, the DOAs of coherent sources are estimated via MUSIC spectral search. Unlike the state-of-the-art approach, our algorithm is insensitive to the phase differences among sources. Numerical results demonstrate the superiority of the proposed algorithm over several existing techniques.

Application of Differential Geometry to the Array Manifolds of Linear Arrays in Antenna Array Processing

This article deals with the application of differential geometry to the array manifolds of non-uniform linear antenna array (NULA) when estimating the direction of arrival (DOA) of multiple sources present in an environment using far field approximation. In order to resolve this issue, we utilized a doublet linear antenna array (DLA) comprising two individual NULAs, along with a proposed algorithm that chooses correct directions of the impinging sources with the help of the prior knowledge of the ambiguous directions calculated with the application of differential geometry to the manifold curves of each NULA. The algorithm checks the correlation of the estimated direction of arrival (DOAs) by both the individual NULA with its corresponding ambiguous set of directions and chooses the output of the NULA, which has a minimum correlation between their estimated DOAs and corresponding ambiguous DOAs. DLA is designed such that the intersection of all the ambiguous set of DOAs among the individual NULAs are null sets. DOA of sources, which imping signals from different directions on the DLA, are estimated using three direction finding (DF) techniques, such as, genetic algorithm (GA), pattern search (PS), and a hybrid technique that utilizes both GA and PS at the same time. As compared to the existing techniques of ambiguity resolution, the proposed algorithm improves the estimation accuracy. Simulation results for all the three DF techniques utilizing the DLA along with the proposed algorithm are presented using MATLAB. As compared to the genetic algorithm and pattern search, the intelligent hybrid technique, such that, GA–PS, had better estimation accuracy in choosing corrected DOAs, despite the fact that the impinging DOAs were from ambiguous directions.