Direction Of Arrival Estimation Approach Research Articles

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.

Sparse Bayesian learning for sparse signal recovery using [formula omitted]-norm

Sparse signal recovery is an important technique for acoustic direction-of-arrival (DOA) estimation which is widely used in applications such as humanoid robots and voice control loudspeakers. However, the estimation accuracy performance is limited by the size of platform and the sound wavelength. To improve the accuracy performance, we propose a sparse signal recovery approach for acoustic DOA estimation based on a hierarchical formulation of the generalized Gaussian prior with a shape parameter q=1/2. Specifically, a sparse Bayesian learning (SBL) framework is built using ℓ1/2-norm priors to efficiently utilize the space sparsity nature of acoustic sources. The priors, built primarily based on a hierarchical structure with a couple of layers, are used for modeling the sparse signals. Then, an expectation–maximization algorithm is proposed for inference and parameter learning. The estimation accuracy performance of the proposed approach is verified in terms of sparse signal recovery and acoustic DOA estimation. The experimental results exhibit that the proposed method achieves the highest recovery accuracy performance and has the lowest root mean square error (RMSE) in contrast with the state-of-the-art sparse signal recovery methods.

YOLO-DoA: A New Data-Driven Method of DoA Estimation Based on YOLO Neural Network Framework

Direction-of-arrival (DoA) estimation is one of the most promising technologies in array signal processing. Existing data-driven methods for DoA estimation are usually implemented by classification networks, which suffer from insufficient utilization about features of sources and require spectral peak-search stage. In this letter, we reframe DoA estimation as a target detection problem and propose a novel DoA estimation approach on the basis of the you only look once v3 (YOLOv3) framework, namely YOLO-DoA. DoAs of sources with confidence scores are directly predicted from the spectrum proxy with YOLO-DoA and an end-to-end estimation is realized. By combining squeeze-and-excitation operation, cross stage partial connections, and an improved loss function for bounding box regression, the performance of YOLO-DoA is enhanced. Simulation results demonstrate that the proposed approach outperforms several state-of-the-art methods in terms of network size, computational cost, prediction time, and accuracy of DoA estimation.

A Novel DOA Estimation for Low-Elevation Target Method Based on Multiscattering Center Equivalent Model

The multipath in very high-frequency (VHF)radar will reduce the direction-of-arrival (DOA) estimation accuracy for the low-angle target following. Since the target and multipath signals have strong coherence in the spatial domain, it is challenging to distinguish them accurately. Especially in some terrain complex regions, various scattering media cause the multipath echo exhibit the multi-channel and nonuniform energy distribution features. Therefore, the single multipath DOA estimation methods will mismatch the actual signal, resulting in inaccurate DOA estimation. The current letter presents a new DOA estimation approach using a multiple scattering center model in complex terrain to solve the mentioned issue. In the presented method, multiple multipath is analogous to a single one based on the multipath signal’s spatial coherence. The equivalent model represents the DOA estimation problem with a parametric optimization problem, and the accurate estimation results can be attained using the Newton optimization approach. Compared with the conventional sparse reconstruction method, the presented method is not restricted by the Restricted Isometry Property (RIP), and employs a robust parameter estimation method to solve the angle super-resolution problem under the low signal-to-noise ratio (SNR). The experimental results reflect that the presented model and approach can efficiently promote the DOA estimation precision and calculational performance compared to conventional DOA estimation approaches.

Radioactive Direction of Arrival Estimation Using Neural Networks Approach

In this paper, we present a comprehensive investigation into improving Direction of Arrival (DOA) estimation for gamma-emitting isotopes using deep neural networks. The direction of arrival estimation is most valuable for Home Land Security (HLS) applications or increased safety in Decontamination and Decommissioning (D&amp;D). Traditional methods, such as beamforming (BF), have limitations in accuracy and sensitivity to noise and background variations. In recent years, data-driven approaches utilizing deep neural networks, including Convolutional Neural Network (CNN) and Gated Recurrent Unit (GRU) models, have shown promise in enhancing DOA estimation. By considering the full energy spectrum and augmenting recorded data, our neural network models outperform traditional BF methods and exhibit greater resilience in diverse background scenarios. The 2-layer CNN model, in particular, achieves up to 40% improvement in estimation accuracy. Our research provides a reliable and data-driven approach for precise DOA estimation with potential applications in nuclear security and safety in D&amp;D.

Subspace Pseudointensity Vectors Approach for DoA Estimation Using Spherical Antenna Array in the Presence of Unknown Mutual Coupling

Spherical antenna array (SAA) exhibits the ability to receive electromagnetic (EM) waves with the same signal strength, regardless of the direction-of-arrival (DoA), angle-of-arrival, and polarization. Hence, estimating the DoA of EM signals that impinge on SAA in the presence of mutual coupling requires research consideration. In this paper, a subspace pseudointensity vectors technique is proposed for DoA estimation using SAA with unknown mutual coupling. DoA estimation using an intensity vector technique is appealing due to its computational efficiency, particularly for SAAs. Two intensity vector-based techniques that operate with spherical harmonic decomposition (SHD) of an EM wave obtained from SAA are presented. The first technique employed pseudointensity vectors (PV) and operates quite well under EM conditions when one source is in operation each time, while the second technique employed subspace pseudointensity vectors (SPV) and operates under EM conditions when multi-sources and multiple reflection cause more challenging problems. The degree of correctness in the estimation of the DoA via the PVs and SPVs is measured using baseline methods in the literature via simulations, adding noise to stationary, single-source and multi-source methods. In addition, incorporating mutual coupling effects, data from experiments, which are the generally acceptable ground truth when examining any procedure, are further used to illustrate the robustness and efficiency of the proposed techniques. The results are sufficiently inspiring for the practical deployment of the proposed techniques.

Direction of Arrival Estimation of Acoustic Sources with Unmanned Underwater Vehicle Swarm via Matrix Completion

With the rapid development of vibration and noise reduction technologies, underwater target detection is facing great challenges. Particularly, the task of high-resolution direction of arrival (DOA) estimation with sonar array is becoming more and more tough. In recent years, unmanned underwater vehicles (UUVs) have been developed considerably, with the improvements of target localization performance in terms of adaptability, detection range, operation efficiency, and anti-interference ability. Nevertheless, in general, the size of UUV is small such that current passive sonar systems usually have relatively limited localization accuracy, detection distance, and environmental robustness in complex ocean noise. This motivates us to present a new approach to construct a large-aperture virtual array with multiple small-aperture arrays of unmanned underwater vehicle swarm (UUVS) which consists of multiple UUVs in this paper. However, for the UUVS array, the received data could suffer from unobserved and corrupted samples. This makes it challenging to analyze and process large-aperture array data. Towards this end, the matrix completion technique is employed to recover the unobserved and corrupted data for virtual array construction based on the low rank property of array data matrix. The recovered matrix is then exploited for underwater target bearing estimation using the traditional DOA estimation approach. Numerical results verify that the proposed method is capable of detecting underwater targets with high precision and resolution.

Robust direction‐of‐arrival estimation approach using beamspace‐based deep neural networks with array imperfections and element failure

Direction-of-arrival (DOA) estimation is a fundamental functionality of sensor array systems. Previous methods only consider element failure or array imperfections. In fact, the co-existence of element failure and array imperfections is more in line with the realistic operation conditions of an array system. However, the performance of previous methods degrades significantly in the presence of both array imperfections and element failure. To deal with this problem, a robust DOA estimation method is proposed based on a deep neural network (DNN). The proposed DNN consists of a denoising autoencoder (DAE) and a parallel network. The DAE can restore damaged array signals to “non-corrupted” signals, and the parallel network is able to process signals with different levels of loss to improve DOA estimation accuracy. At the training stage, array imperfections are modelled as a spherical distribution, and the training samples are extracted under this distribution to improve the generalisation capability of the proposed network to various array imperfections. In addition, the authors propose to estimate the spatial spectrum in a virtual array beamspace, which can reduce the computational complexity as well as signal-to-noise ratio resolution threshold, and further enhance the robustness to array imperfections. Numerical results show that the proposed DOA estimation approach works well in the presence of both array imperfections and element failure.

Iteratively reweighted [formula omitted] norm minimization for DOD and DOA estimation in bistatic MIMO radar under impulsive noise

In this paper, an iterative-reweighting-based algorithm is proposed to improve the performance of direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in bistatic MIMO radar under impulsive noise. The BSUM-RELAX algorithm is generalized to its two dimension and multiple measurement vectors (MMV) version for robust DOD and DOA estimation. The optimization problem is cast to an lp (with 0<p<2) norm minimization problem to alleviate the impact of the impulsive noise, which is iteratively solved by minimizing the objective function based on each variable. Nevertheless, such a problem is of non-convexity and highly depends on a good guess of all the initial values of DODs and DOAs of multiple targets in order to obtain considerable performance. Therefore, an off-grid two-dimensional Newtonized orthogonal matching pursuit (2D-NOMP) algorithm is developed to obtain a near-optimal initial guess. Simulations are conducted to verify the robustness of the proposed approach for DOD and DOA estimation under impulsive noise.

Fast and Accurate Approach for DOA Estimation of Coherent Signals

An algorithm for estimation of direction of arrival (DOA) based on QR decomposition is proposed for coherent signals in this paper. When coherent is present, the rank of the signal covariance matrix is generally less than the signal number, making the estimation of the signal or noise subspace inaccurate. Therefore, we need to eliminate the spatial covariance matrix rank loss. According to the idea of matrix reconstruction, we try to construct three different data matrices, one is the signal covariance matrix, the other is the eigenvector reconstruction matrix of the signal covariance matrix, and the other is reconstructed matrix with the addition of spatial smoothing technology. Based on the resulting data matrix, whereafter, QR decomposition with the iteratively weighted least squares (IWLS) as solver is proposed to reduce the computational complexity of DOA estimation. Compared with other existing algorithms, the simulation results show that our method has high accuracy and great increase in the computational efficiency.

Machine–learning-enabled metasurface for direction of arrival estimation

Abstract Metasurfaces, interacted with artificial intelligence, have now been motivating many contemporary research studies to revisit established fields, e.g., direction of arrival (DOA) estimation. Conventional DOA estimation techniques typically necessitate bulky-sized beam-scanning equipment for signal acquisition or complicated reconstruction algorithms for data postprocessing, making them ineffective for in-situ detection. In this article, we propose a machine-learning-enabled metasurface for DOA estimation. For certain incident signals, a tunable metasurface is controlled in sequence, generating a series of field intensities at the single receiving probe. The perceived data are subsequently processed by a pretrained random forest model to access the incident angle. As an illustrative example, we experimentally demonstrate a high-accuracy intelligent DOA estimation approach for a wide range of incident angles and achieve more than 95% accuracy with an error of less than 0.5 ° $0.5{}^{\circ}$ . The reported strategy opens a feasible route for intelligent DOA detection in full space and wide band. Moreover, it will provide breakthrough inspiration for traditional applications incorporating time-saving and equipment-simplified majorization.

Underdetermined DOA estimation via multiple time-delay covariance matrices and deep residual network

Higher-order statistics based approaches and signal sparseness based approaches have emerged in recent decades to resolve the underdetermined direction-of-arrival (DOA) estimation problem. These model-based methods face great challenges in practical applications due to high computational complexity and dependence on ideal assumptions. This paper presents an effective DOA estimation approach based on a deep residual network (DRN) for the underdetermined case. We first extract an input feature from a new matrix calculated by stacking several covariance matrices corresponding to different time delays. We then provide the input feature to the trained DRN to construct the super resolution spectrum. The DRN learns the mapping relationship between the input feature and the spatial spectrum by training. The proposed approach is superior to existing model-based estimation methods in terms of calculation efficiency, independence of source sparseness and adaptive capacity to non-ideal conditions (e.g., low signal to noise ratio, short bit sequence). Simulations demonstrate the validity and strong performance of the proposed algorithm on both overdetermined and underdetermined cases.

Maximum Element Dichotomous Coordinate Descent Based Minimum Variance Distortionless Response DoA Estimator

In this paper, we devise an efficient approach for estimating the direction of arrival (DoA). The proposed DoA estimation approach is based on minimum variance distortionless response (MVDR) criteria within a recursive least squares (RLS) framework. The dichotomous coordinate descent algorithm is used to modify the calculation of the output power spectrum, and a diagonal loading term is applied to improve the robustness of the DoA estimator. These modifications allow us to both reduce the computational complexity of the RLS DoA estimator and increase the estimation performance. A numerical comparison confirms that the proposed DoA estimator outperforms the conventional RLS DoA estimator in terms of the computational complexity and DoA estimation error. Finally, the proposed theoretical DoA estimator is implemented on a field-programmable gate array (FPGA) board to verify the feasibility of the method. The numerical results of a fixed-point implementation demonstrate that the performance of the proposed method is very close to that of its floating-point counterpart.

DOA Estimation for Coprime Array With Mixed Noise Scenario via Phased Fractional Low-Order Moment

Direction of arrival (DOA) estimation with coprime array is an important topic in array signal processing. In this letter, the coprime array technique is extended to mixed noise (white Gaussian noise and impulsive noise). Since the second order covariance matrix does not exist in presence of mixed noise, the phased fractional low-order moment (PFLOM) is used to replace the data covariance matrix of the received signals from coprime array, and then a DOA estimation approach based on toeplitz method with coprime array is applied. The feasibility of PFLOM with mixed noise scenario of coprime array is theoretically derived, and the simulation results show that the proposed method has better estimation performance than that of the existing methods, especially in the low generalized signal-to-noise ratio (GSNR) environment.

Direction‐of‐arrival estimation using estimator banks in low‐angle tracking for S‐band radar

AbstractTracking low‐angle targets over an uneven surface are challenging because of the highly correlated, complicated, and volatile multipath signals encountered in radar. Especially, in the context of irregular reflector modulated by rough sea, which results in performance depravation of the existing direction‐of‐arrival (DOA) estimation methods. An effective DOA estimation approach is based on maximum likelihood (ML) estimator which is referred to as optimal synthetic vector maximum likelihood (OSVML) method. The approach is essentially different, multipath signals are present that without known prior information of ideal model. The optimal projection space in estimator banks is spanned with direct subspace and indirect subspace to match the signals received by S‐band radar. Then, the performance of the proposed method is evaluated by simulations in terms of the signal‐to‐noise ratio (SNR) and snapshot. Finally, field data sets acquired from S‐band radar are carried out to verify the practicability of the proposed method in a naval environment.

Block Newtonised orthogonal matching pursuit for off‐grid DOA estimation in the presence of unknown mutual coupling

Mutual coupling (MC) between array elements can lead to severe accuracy degradation in direction-of-arrival (DOA) estimation. In this study, an off-grid compressed sensing (CS) approach for DOA estimation in the presence of unknown MC is proposed using block Newtonised orthogonal matching pursuit (NOMP). First, the model of DOA estimation with MC is block sparsely represented to fully utilise the whole array aperture. Then, a block NOMP algorithm with multiple measurement vectors (MMV) is developed to achieve the estimates of DOA, in which the Newton refinement procedure is presented by deriving the first- and second-order derivatives of the block steering matrix with respect to the angle grid. Compared with the subspace-based and sparse recovery-based methods with MC, the proposed block NOMP approach has robustness in a small number of snapshots and owns no grid-mismatch effect. Meanwhile, in comparison to several existing off-grid DOA estimation methods with MC, it can achieve higher estimation accuracy and similarly low computational complexity. The superior performance of the proposed approach is shown via numerical simulations.

Direction-of-Arrival Estimation over Sea Surface from Radar Scattering Based on Convolutional Neural Network

Conventional direction-of-arrival (DOA) estimation methods are primarily used in point source scenarios and based on array signal processing. However, due to the local scattering caused by sea surface, signals observed from radar antenna cannot be regarded as a point source but rather as a spatially dispersed source. Besides, with the advantages of flexibility and comparably low cost, synthetic aperture radar (SAR) is the present and future trend of space-based systems. This paper proposes a novel DOA estimation approach for SAR systems using the simulated radar measurement of the sea surface at different operating frequencies and wind speeds. This article’s forward model is an advanced integral equation model (AIEM) to calculate the electromagnetic scattered from the sea surface. To solve the DOA estimation problem, we introduce a convolutional neural network (CNN) framework to estimate the transmitter’s incident angle and incident azimuth angle. Results demonstrate that the CNN can achieve a good performance in DOA estimation at a wide range of frequencies and sea wind speeds.

A Two-Step Compressed Sensing Approach for Single-Snapshot DOA Estimation of Closely Spaced Signals

Single-snapshot direction-of-arrival (DOA) estimation plays an important role in dynamic target detection and tracking applications. Because a single-snapshot signal provides few information for statistics calculation, recently compressed sensing (CS) theory is applied to solve single-snapshot DOA estimation, instead of the traditional DOA methods based on statistics. However, when the unknown sources are closely located, the spatial signals are highly correlated, and its overcomplete dictionary is made up of dense grids, which leads to a serious decrease in the estimation accuracy of the CS-based algorithm. In order to solve this problem, this paper proposed a two-step compressed sensing-based algorithm for the single-snapshot DOA estimation of closely spaced signals. The overcomplete dictionaries with coarse and refined grids are used in the two steps, respectively. The measurement matrix is constructed by using a very sparse projection scheme based on chaotic sequences because chaotic sequences have determinism and pseudo-randomness property. Such measurement matrix is mainly proposed for compressing the overcomplete dictionary in preestimation step, while it is well designed by choosing the steering vectors of true DOA in the accurate estimation step, in which the neighborhood information around the true DOAs partly solved in the previous step will be used. Monte Carlo simulation results demonstrate that the proposed algorithm can perform better than other existing single-snapshot DOA estimation methods. Especially, it can work well to solve the issues caused by closely spaced signals and single snapshot.

Direction of Arrival Estimation of Wideband Sources Using Sparse Linear Arrays

In this paper, we study the problem of wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs), where a number of uncorrelated wideband signals impinge on an SLA and the data is collected from multiple frequency bins. To boost the performance and perform underdetermined DoA estimation, the difference co-array response matrices for all frequency bins are constructed first. Then, to merge the data from different frequency bins, we resort to the Jacobi-Anger approximation to transform the co-array response matrices of all frequency bins into a single virtual uniform linear array (ULA) response matrix. The major advantage of this approach is that the transformation matrices are all signal independent. For the special case where all sources share an identical distribution of the power spectrum, we develop two super-resolution off-the-grid DoA estimation approaches based on atomic norm minimization (ANM), one with and one without prior knowledge of the power spectrum. Our solution is able to resolve more sources than the number of antennas but also more than the number of degrees of freedom (DoF) of the difference co-array of the SLA. For the general case where each source has an arbitrary power spectrum, we propose a multi-task ANM method to exploit the joint sparsity from all frequency bins. Simulation results show that our proposed methods present a clear performance advantage over existing methods, and achieve an estimation accuracy close to the associated Cramér-Rao bounds (CRBs).

Wideband modal orthogonality: A New approach for broadband DOA estimation

Wideband direction of arrival (DOA) estimation techniques for sensors array have been studied extensively in the literature. Nevertheless, needing prior information on the number and directions of sources or demanding heavy computational load makes most of these techniques less useful in practice. In this paper, a low complexity subspace-based framework for DOA estimation of broadband signals, named as wideband modal orthogonality (WIMO), is proposed and accordingly two DOA estimators are developed. First, a closed-form approximation of spatial-temporal covariance matrix (STCM) in the uniform spectrum case is presented. The eigenvectors of STCM associated with non-zero eigenvalues are modal components of the wideband source in a given bandwidth and direction. WIMO idea is to extract these eigenvectors at desired DOAs from the approximated STCM and test their orthogonality to estimated noise subspace. In the non-uniform spectrum case, WIMO idea can be applied by approximating STCM through numerical integration. Fortunately, STCM approximation and modal extraction can be performed offline. WIMO provides DOA estimation without the conventional prerequisites, such as spectral decomposition, focusing procedure and, a priori information on the number of sources and their DOAs. Several numerical examples are conducted to compare the WIMO performance with the state-of-the-art methods. Simulations demonstrate that the two proposed DOA estimators achieve superior performance in terms of probability of resolution and estimation error along with orders of magnitude runtime speedup.