Direction Of Arrival Estimation Research Articles

A High-Precision DOA Estimator for Low-Frequency Signals Using Ultra-Dense Small-Aperture Microphone Arrays

Abstract Accurate Direction of Arrival (DOA) estimation is critical for the effectiveness of Unattended Ground Sensor (UGS) systems, as it enhances sound localization, situational awareness, resource optimization, and facilitates integration with other sensor data for comprehensive monitoring. With the growing demand for lightweight and miniaturized sensors suitable for diverse environments, challenges arise in DOA estimation of low-frequency signals using dense small-aperture microphone arrays, especially under noisy conditions. Despite advancements in deep learning, both conventional and existing neural network methods struggle with this task. In this paper, we present the Multi-Resblock DOA Network (MRDNet), a novel neural network designed for precise DOA estimation of low-frequency sounds in noisy environments using small-aperture arrays. MRDNet was evaluated under simulations involving Brownian and Gaussian noise, representing wind and general background disturbances. The results demonstrate that MRDNet achieves superior accuracy, with a Mean Angular Error (MAE) of 2.797 degrees, significantly outperforming baseline methods by 24.93\%. Furthermore, we show that increasing the number of microphones within a constant array size using MRDNet effectively enhances DOA accuracy in the context of deep learning.

Triple extended coprime array for single‐snapshot DoA estimation

AbstractThe direction‐of‐arrival (DoA) estimation methods based on coprime array (CA) largely rely on having a sufficient number of snapshots. However, under single‐snapshot conditions typical of vehicle‐mounted imaging radar, CA‐based DoA estimation often suffers from ambiguity leakage, resulting in significant degradation in performance. This paper thoroughly analyses the mechanism of ambiguity leakage in CA by re‐deriving the covariance matrix model under single‐snapshot conditions. To suppress the ambiguity leakage, a triple extended coprime array composed of three pairwise coprime sub‐arrays enhanced coprime constraint is designed. Building on this design, a DoA estimation algorithm based on an iterative adaptive approach is proposed. By leveraging the power spectrum distribution from iterative adaptive approach, a reduced‐noise signal is constructed by retaining only the high‐energy components. Next, the noise subspace using a multi‐stage Wiener filter, and finally, achieve super‐resolution DoA estimation through multiple signal classification spectrum analysis.

Off-grid DOA estimation for metasurface antenna systems using sparse Bayesian learning

Direction-of-arrival (DOA) estimation is a classic research topic with numerous applications in the field of signal processing. However, multiple radio frequency channels are required to receive array signals in order to achieve excellent performance, which is complicated in hardware to be applied to portable or cost-effective equipment. In this paper, we investigate the DOA estimation for transmissive metasurface antenna systems, where the signals are modulated by metasurface elements before reaching the receiving antennas. Then, we proposed an off-grid sparse Bayesian learning algorithm for metasurface aided systems, where the DOA estimation process consists of three stages, i.e., off-grid operation, calculation of posterior probability, and iterative update for hyperparameters using expectation maximization algorithm. Simulation results show that the proposed method can obtain superior estimation performance with a low number of snapshots and low signal-to-noise ratio. Meanwhile, it can achieve satisfactory performance even when the angle interval of the incoming signal is small.

Performance Analysis of Cardioid and Omnidirectional Microphones in Spherical Sector Arrays for Coherent Source Localization

Traditional spherical sector microphone arrays using omnidirectional microphones face limitations in modal strength and spatial resolution, especially within spherical sector configurations. This study aims to enhance array performance by developing a spherical sector array employing first-order cardioid microphones. A model based on spherical sector harmonic (SSH) functions is introduced to extend the benefits of spherical harmonics to sector arrays. Modal strength analysis demonstrates that cardioid microphones in open spherical sectors enhance nonzero-order strengths and eliminate the nulls associated with spherical Bessel functions. We find that the spatial resolution of spherical cap arrays depends on the array’s maximum order and the limiting polar angle, but is independent of the microphone gain pattern. We assess direction-of-arrival (DOA) estimation performance for coherent wideband sources using the array manifold interpolation method, and compare cardioid and omnidirectional arrays through simulations in both open and rigid hemispherical configurations. The results indicate that cardioid arrays outperform omnidirectional ones on DOA estimation tasks, with performance improving alongside increased microphone directivity in the open hemispherical configuration. Specifically, hypercardioid microphones yielded the best results in the open configuration, while subcardioid microphones (without nulls) were optimal in rigid configurations. These findings demonstrate that spherical sector arrays of first-order cardioid microphones offer improved modal strength and DOA estimation capabilities over traditional omnidirectional arrays, providing significantly enhancing performance in spherical sector array processing.

Deep learning-enhanced atomic norm minimization for DOA estimation of coherent and incoherent sources using coprime array

Abstract In the field of array signal processing, accurate direction of arrival (DOA) estimation is crucial for handling both coherent and incoherent mixed signal sources. This paper proposes a deep learning-enhanced atomic norm minimization (DLEANM) algorithm, designed to improve DOA estimation for coprime arrays. The algorithm first models the mixed signal scenarios realistically and employs interpolation to transform coprime arrays into virtual uniform linear arrays, which facilitates the formulation of the atomic norm minimization problem. Solving this problem reconstructs an augmented Hermitian Toeplitz covariance matrix. To further enhance the accuracy of DOA estimation, we developed a multi-scale convolutional neural network with an attention mechanism, which uses the covariance matrix as input to better capture signal variations across different frequencies and spatial distributions. By processing multi-scale inputs in parallel, the model improves adaptability and robustness in estimating mixed signal sources. Simulation results show that, under equivalent SNR and snapshot conditions, the DLEANM algorithm achieves lower estimation errors, more accurate multi-target DOA estimation, and relatively faster computation speed compared to conventional methods. Field experiments further confirm the effectiveness of the proposed algorithm. Therefore, after training, the algorithm is able to accurately identify the directions of unknown signals received by sensor arrays.

Sparse Bayesian Learning with Jeffreys’ Noninformative Prior for Off-Grid DOA Estimation

Sparse Bayesian learning (SBL) algorithms are attractive methods for direction-of-arrival (DOA) estimation and have certain advantages over other sparse representation-based DOA estimation methods. In this paper, a new computationally efficient SBL algorithm for DOA estimation is developed which considers a noninformative prior for hyperparameters. This noninformative prior is obtained using the well-known Jeffreys’ rule which is based on the Fisher information and the hyperparameters are powers of the source signals. The Jeffreys’ prior that is obtained for the hyperparameters is different from the conventional Jeffreys’ prior used in the literature. Moreover, a method for refining the DOA estimates obtained by the SBL algorithm is derived to reduce the off-grid error. Analysis indicates that the computational complexity of the proposed SBL algorithm per iteration is less than that of other existing SBL algorithms. Simulation results exhibit the superior performance of the proposed SBL algorithm compared to state-of-the-art SBL algorithms in terms of DOA estimation accuracy and total computational complexity. Moreover, simulations reveal that, unlike certain other state-of-the-art SBL algorithms, the proposed algorithm is robust to changes in noise power.

Joint DOA and distance estimation via spatial diversity wideband signal synthesis calibrated by distance parameter

Wideband signal synthesis is a technique designed to achieve large bandwidth detection capabilities by utilizing multiple relatively narrow bandwidth signals. Traditional single-antenna, time-diversity wideband synthesis method is inefficient, which has led to using Multiple-Input Multiple-Output (MIMO) architectures to introduce spatial diversity. However, this method introduces challenges such as frequency-phase inconsistencies in the self-mixing signals from different array elements due to differences in wave travel distances. In previous research, we studied the calibration of frequency and phase for synthesized sub-signals using DOA parameters, which required additional high-precision direction of arrival (DOA) estimation algorithms. In contrast, this paper proposes a novel spatial-diversity wideband synthesis method that utilizes distance parameter calibration for joint DOA and distance estimation (JDDE). A key advantage of this method is the relative simplicity of obtaining distance parameters. To address the issue where the accuracy of distance parameters does not meet the requirements for synthesis, we proposed a grid search synthesis method in this paper. Furthermore, we introduced a search synthesis based on optimization algorithms to reduce computational load and enhance the synthesis performance. Theoretical analysis and simulations confirm the high accuracy of our JDDE method. Under conditions of high signal-to-noise ratios, our method significantly reduces the DOA's root mean square error—approximately halving it compared to the multiple signal classification algorithm within the same wideband self-mixing framework. Additionally, both distance resolution and range accuracy exceed those achieved with pre-synthesis methods.

Fast DOA Estimation of IGS Noncircular Signals Under Coprime Arrays

Traditional direction-of-arrival (DOA) estimation methods often encounter challenges such as low accuracy and high computational complexity, particularly in complex signal environments with multiple sources. To address these issues, this paper proposes a fast DOA estimation method for improper Gaussian signaling (IGS) non-circular signals, based on a coprime array; this approach involves extending the array model by leveraging the unique properties of non-circular signals. Subsequently, this study introduces the ANCM algorithm, a method designed for fast DOA estimation of IGS non-circular signals within a non-uniform noise background. The proposed ANCM algorithm is then compared to classical algorithms, through simulations in a non-uniform noise environment. Experimental results demonstrate that the ANCM algorithm significantly outperforms traditional methods in such conditions. Therefore, the development of new, efficient DOA estimation methods holds substantial theoretical and practical value.

A New Method for Joint Sparse DOA Estimation.

To tackle the issue of poor accuracy in single-snapshot data processing for Direction of Arrival (DOA) estimation in passive radar systems, this paper introduces a method for judiciously leveraging multi-snapshot data. This approach effectively enhances the accuracy of DOA estimation and spatial angle resolution in passive radar systems. Additionally, in response to the non-convex nature of the mixed norm, we propose a hyperbolic tangent model as a replacement, transforming the problem into a directly solvable convex optimization problem. The rationality of this substitution is thoroughly demonstrated. Lastly, through a comparative analysis with existing discrete grid DOA estimation methods, we illustrate the superiority of the proposed approach, particularly under conditions of medium signal-to-noise ratio, varying numbers of snapshots, and close target angles. This method is less affected by the number of array elements, and is more usable in practices verified in real-world scenarios.

Sparse Bayesian learning based multi trajectory tracking algorithm for direction of arrival trajectory estimation

One of the applications of sequential sparse signal reconstruction is multi-target Direction of Arrival (DoA) trajectory estimation. In fact, each member of the support set is equivalent to the DoA of a moving target at each time instant. There is a mapping between the indices of the sparse vector and DoA values in continuous angle space. The key idea of this paper is to use the dynamic information of the continuous angular space to more accurately track sparse vectors and estimate the DoA trajectories of moving sources with time-varying acceleration based on the Sparse Bayesian Learning (SBL) framework. For this purpose, the members of the estimated support set are mapped to the continuous angular space at each instant. Then, the obtained DoAs are assigned to the available DoA trajectories using the Predictive-Description-Length (PDL) algorithm. In the following, the DoA of each source is predicted for the next time using the Kalman filter. Finally, the predicted DoAs are mapped to a sparse vector. The obtained sparse vector is used as the prior information for SBL-based sparse reconstruction. Simulation results show that the proposed algorithm, which is called SBL-MTT (Multi Trajectory Tracking), leads to an accurate reconstruction of successive sparse vectors in application of DoA trajectory estimation of moving sources.

Sparsity-based direction-of-arrival estimation in the presence of near-field and far-field interferences for small-scale platform sonar arrays.

For the sonar arrays mounted on an unmanned underwater vehicle (UUV), the direction-of-arrival (DOA) estimation of the far-field (FF) weak sources is influenced by the near-field (NF) interferences generated from the radiated self-noise of the UUV and the FF interferences simultaneously. To address the problem, a sparsity-based DOA estimation method resistant to the NF and FF interferences is proposed in this paper. This method isolates the FF signals from the NF signals by sparse reconstruction. Additionally, subspace projection is applied to address the masking problem of the weak target signal by the strong interferences in the spatial domain, effectively enhancing the capacity of estimating the DOA of the weak target signal in the presence of strong interferences. Numerical simulations and experimental results demonstrate the effectiveness of the proposed method. Compared to other advanced DOA estimation methods, the proposed method exhibits better DOA estimation performance in the presence of strong NF and FF interferences.

A Class of High-Resolution DOA Estimation Algorithms Based on Hyper-beamforming

In response to the demand for enhanced resolving power in direction-of-arrival (DOA) estimation algorithms and reduced background levels of spatial spectra, we propose a new class of algorithms based on hyper-beamforming (HBF). This class includes three specific algorithms: hyper-beam minimum-variance-distortionless-response (HMVDR), deconvolved hyper-beamforming (DHBF), and deconvolved HMVDR (DHMVDR). The HMVDR algorithm leverages the phase differences between the outputs from the left and right subarray MVDR algorithms and employs hyper-beam operations to construct a weighting factor that achieves high resolution. Both the DHBF and DHMVDR algorithms develop convolution models for the HBF and HMVDR, then apply the Richardson-Lucy method to deconvolve beams and extract the spatial spectra. The paper outlines the detailed steps and principles that underlie the high-resolution performance of these algorithms and examines the impact of the hyper-beam index on each. Through simulation results and the water tank experiment, we demonstrate that these algorithms not only lower the background level of spatial spectra and reduce the beamwidth of the main lobe but also exhibit superior DOA resolution.

Enhancing robust acoustic DOA estimation against position errors via fast sparse Bayesian learning

Advanced methods for acoustical direction-of-arrival (DOA) estimation leverage sparse signal recovery techniques, which are valued for providing high-resolution results using a limited number of measurement vectors. Although these technologies are capable, they frequently overlook potential errors in sensor positioning, and their computational complexity is excessive, constraining their practical application. This paper introduces a new self-calibrating Bayesian method designed to address this issue. The approach begins by establishing a hierarchical Bayesian model that exploits the sparsity of both signal and position error vectors. Subsequently, a fast algorithm applies a basis selection strategy to efficiently update all variables. Furthermore, the study also explores off-grid estimation. The empirical results indicate that our method outperforms state-of-the-art methods in both accuracy and computational efficiency.

Hyperparameter free sparse estimation for wideband multiple‐input‐multiple‐output radar direction finding without secondary data

AbstractThe estimation of target directions of arrival (DOA) for wideband multiple‐input‐multiple‐output (MIMO) radar is investigated in this article. First, the authors establish a signal model for wideband MIMO radar systems. Then, an algorithm is proposed to estimate the target angles without secondary data (i.e. the training data from slow‐time is not required).The proposed algorithm unitises the spatial sparsity of target signals and it is derived under the Bayesian framework. It can estimate the spatial pseudo‐spectra of the targets through cyclic optimisation. Additionally, it is hyperparameter‐free and guarantees convergence. To analyse the performance of the proposed algorithm, the Cramér‐Rao bound (CRB) is derived for DOA estimation with wideband MIMO radar. Numerical examples demonstrate that even without secondary data, the proposed algorithm can accurately estimate the DOA of the targets.

Research on underwater target signal orientation estimation based on smoothness priors approach

PurposeThis paper aims to address the challenges in hydroacoustic signal detection, signal distortion and target localization caused by baseline drift. The authors propose a combined algorithm that integrates short-time Fourier transform (STFT) detection, smoothness priors approach (SPA), attitude calibration and direction of arrival (DOA) estimation for micro-electro-mechanical system vector hydrophones.Design/methodology/approachInitially, STFT method screens target signals with baseline drift in low signal-to-noise ratio environments, facilitating easier subsequent processing. Next, SPA is applied to the screened target signal, effectively removing the baseline drift, and combined with filtering to improve the signal-to-noise ratio. Then, vector channel amplitudes are corrected using attitude correction with 2D compass data. Finally, the absolute target azimuth is estimated using the minimum variance distortion-free response beamformer.FindingsSimulation and experimental results demonstrate that the SPA outperforms high-pass filtering in removing baseline drift and is comparable to the effectiveness of variational mode decomposition, with significantly shorter processing times, making it more suitable for real-time applications. The detection performance of the STFT method is superior to instantaneous correlation detection and sample entropy methods. The final DOA estimation achieves an accuracy within 2°, enabling precise target azimuth estimation.Originality/valueTo the best of the authors’ knowledge, this study is the first to apply SPA to baseline drift removal in hydroacoustic signals, significantly enhancing the efficiency and accuracy of signal processing. It demonstrates the method’s outstanding performance in the field of underwater signal processing. In addition, it confirms the reliability and feasibility of STFT for signal detection in the presence of baseline drift.

Field Programmable Gate Array (FPGA) Implementation of Parallel Jacobi for Eigen-Decomposition in Direction of Arrival (DOA) Estimation Algorithm

The eigen-decomposition of a covariance matrix is a key step in the Direction of Arrival (DOA) estimation algorithms such as subspace classes. Eigen-decomposition using the parallel Jacobi algorithm implemented on FPGA offers excellent parallelism and real-time performance. Addressing the high complexity and resource consumption of the traditional parallel Jacobi algorithm implemented on FPGA, this study proposes an improved FPGA-based parallel Jacobi algorithm for eigen-decomposition. By analyzing the relationship between angle calculation and rotation during the Jacobi algorithm decomposition process, leveraging parallelism in the data processing, and based on the concepts of time-division multiplexing and parallel partition processing, this approach effectively reduces FPGA resource consumption. The improved parallel Jacobi algorithm is then applied to the classic DOA estimation algorithm, the MUSIC algorithm, and implemented on Xilinx’s Zynq FPGA. Experimental results demonstrate that this parallel approach can reduce resource consumption by approximately 75% compared to the traditional method but introduces little additional time consumption. The proposed method in this paper will solve the problem of great hardware consumption of eigen-decomposition based on FPGA in DOA applications.

Noncircular Distributed Source DOA Estimation with Nested Arrays via Reduced-Dimension MUSIC

This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to be reconsidered for CD sources with sparse arrays and many problems arise. One thorny problem is the disappearance of displacement invariance of the virtual array manifold constructed by the virtualization technique. To deal with this issue, a nested array processing method for CD sources transmitting noncircular signals is proposed in this paper. Firstly, we construct the virtual sum-and-difference co-array by leveraging the noncircular quality of signals with a nested array. Then, an approximation is made to degrade CD sources into point sources. In this way, spatial smoothing techniques can be applied to restore the rank. Finally, in order to reduce the complexity, we modify the reduced-dimension MUSIC to estimate DOAs through a one-dimensional peak-searching procedure. The simulation results prove the superiority of our algorithm against other competitors.

Gridless DOA Estimation Method for Arbitrary Array Geometries Based on Complex-Valued Deep Neural Networks

Gridless direction of arrival (DOA) estimation methods have garnered significant attention due to their ability to avoid grid mismatch errors, which can adversely affect the performance of high-resolution DOA estimation algorithms. However, most existing gridless methods are primarily restricted to applications involving uniform linear arrays or sparse linear arrays. In this paper, we derive the relationship between the element-domain covariance matrix and the angular-domain covariance matrix for arbitrary array geometries by expanding the steering vector using a Fourier series. Then, a deep neural network is designed to reconstruct the angular-domain covariance matrix from the sample covariance matrix and the gridless DOA estimation can be obtained by Root-MUSIC. Simulation results on arbitrary array geometries demonstrate that the proposed method outperforms existing methods like MUSIC, SPICE, and SBL in terms of resolution probability and DOA estimation accuracy, especially when the angular separation between targets is small. Additionally, the proposed method does not require any hyperparameter tuning, is robust to varying snapshot numbers, and has a lower computational complexity. Finally, real hydrophone data from the SWellEx-96 ocean experiment validates the effectiveness of the proposed method in practical underwater acoustic environments.

DOA Estimation Method for Vector Hydrophones Based on Sparse Bayesian Learning.

Through extensive literature review, it has been found that sparse Bayesian learning (SBL) is mainly applied to traditional scalar hydrophones and is rarely applied to vector hydrophones. This article proposes a direction of arrival (DOA) estimation method for vector hydrophones based on SBL (Vector-SBL). Firstly, vector hydrophones capture both sound pressure and particle velocity, enabling the acquisition of multidimensional sound field information. Secondly, SBL accurately reconstructs the received vector signal, addressing challenges like low signal-to-noise ratio (SNR), limited snapshots, and coherent sources. Finally, precise DOA estimation is achieved for multiple sources without prior knowledge of their number. Simulation experiments have shown that compared with the OMP, MUSIC, and CBF algorithms, the proposed method exhibits higher DOA estimation accuracy under conditions of low SNR, small snapshots, multiple sources, and coherent sources. Furthermore, it demonstrates superior resolution when dealing with closely spaced signal sources.

Multi-microphone simultaneous speakers detection and localization of multi-sources for separation and noise reduction

This paper addresses the challenge of online blind speaker separation in a multi-microphone setting. The linearly constrained minimum variance (LCMV) beamformer is selected as the backbone of the separation algorithm due to its distortionless response and capacity to create a null towards interfering sources. A specific instance of the LCMV beamformer that considers acoustic propagation is implemented. In this variant, the relative transfer functions (RTFs) associated with each speaker of interest are utilized as the steering vectors of the beamformer. A control mechanism is devised to ensure robust estimation of the beamformer’s building blocks, comprising speaker activity detectors and direction of arrival (DOA) estimation branches. This control mechanism is implemented as a multi-task deep neural network (DNN). The primary task classifies each time frame based on speaker activity: no active speaker, single active speaker, or multiple active speakers. The secondary task is DOA estimation. It is implemented as a classification task, executed only for frames classified as single-speaker frames by the primary branch. The direction of the active speaker is classified into one of the multiple ranges of angles. These frames are also leveraged to estimate the RTFs using subspace estimation methods. A library of RTFs associated with these DOA ranges is then constructed, facilitating rapid acquisition of new speakers and efficient tracking of existing speakers. The proposed scheme is evaluated in both simulated and real-life recordings, encompassing static and dynamic scenarios. The benefits of the multi-task approach are showcased, and significant improvements are evident, even when the control mechanism is trained with simulated data and tested with real-life data. A comparison between the proposed scheme and the independent low-rank matrix analysis (ILRMA) algorithm reveals significant improvements in static scenarios. Furthermore, the tracking capabilities of the proposed scheme are highlighted in dynamic scenarios.