Direction Of Arrival Estimation Research Articles

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.

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

Purpose This 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/approach Initially, 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. Findings Simulation 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/value To 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.

A high-resolution method for direction of arrival estimation based on an improved self-attention module.

The high-resolution direction of arrival (DOA) estimation is a prominent research issue in underwater acoustics. The existing high-resolution methods include subspace methods and sparse representation methods. However, the performance of subspace methods suffers from low signal-to-noise ratio (SNR) and limited snapshots conditions, and the computational complexity of sparse representation methods is too high. The neural network methods are emerging high-resolution methods. However, insufficient support for big data is frequently observed in underwater acoustics, and conventional network structures present challenges in further enhancing performance. To address the aforementioned problems, we propose a neural network method based on an improved self-attention module to achieve high accuracy and robust DOA estimation. First, we design a multi-head self-attention module with large-scale convolutional kernels and residual structures to improve the estimated accuracy. Second, we propose an improved input feature to enhance the robustness to non-uniform noise and unequal-intensity targets. The simulations demonstrate that the proposed method exhibits superior angle resolution compared to sparse representation methods under the same simulation conditions. The proposed method demonstrates exceptional accuracy and robustness in DOA estimation under challenging conditions of low SNR, limited snapshots, and unequal-intensity targets. The experimental results further prove the effectiveness of the proposed method.

Reliable underwater multi-target direction of arrival estimation with optimal transport using deep models.

Multi-target direction of arrival (DoA) estimation is an important and challenging task for sonar signal processing. In this study, we propose a method called learning direction of arrival with optimal transport (LOT) to accurately estimate the DoAs of multiple sources with a single deep model. We model the DoA estimation problem as a multi-label classification task and introduce an optimal transport (OT) loss based on the OT theory to capture the intrinsic continuity within the angular categories. We design a cost matrix for the OT loss in LOT approach to characterize the order and periodicity of the angular grid. The LOT approach encourages reliable predictions closer to the ground truth and suppresses spurious targets. We also propose a lightweight channel mask data augmentation module for deep models that use items related to the covariance matrix as input. The proposed methods can be seamlessly integrated with different model architectures and we indicate the portability with experiments on several typical network backbones. Experiments across various scenarios using different measurements show the effectiveness and robustness of our approaches. Results on SwellEx-96 experimental data demonstrate the practicality in real applications.

Estimating direction of arrival in reverberant environments for wake-word detection using a single structural vibration sensora).

The vibrational response of an elastic panel to incident acoustic waves is determined by the direction-of-arrival (DOA) of the waves relative to the spatial structure of the panel's bending modes. By monitoring the relative modal excitations of a panel immersed in a sound field, the DOA of the source may be inferred. In reverberant environments, early acoustic reflections and the late diffuse acoustic field may obscure the DOA of incoming sound waves. Panel microphones may be especially susceptible to the effects of reverberation due to their large surface areas and long-decaying impulse responses. An investigation into the effect of reverberation on the accuracy of DOA estimation with panel microphones was made by recording wake-word utterances in eight spaces with reverberation times (RT60s) ranging from 0.27 to 3.00 s. The responses were used to train neural networks to estimate the DOA. Within ±5°, DOA estimation reliability was measured at 95.00% in the least reverberant space, decreasing to 78.33% in the most reverberant space, suggesting an inverse relationship between RT60 and DOA accuracy. Experimental results suggest that a system for estimating DOA with panel microphones can generalize to new acoustic environments by cross-training the system with data from multiple spaces with different RT60s.

Direction of Arrival Estimation Based on DNN and CNN

The accuracy of Direction of Arrival (DOA) estimation primarily depends on the precision of the data. When the receiver uses a low-precision analog-to-digital converter (ADC), traditional DOA estimation algorithms exhibit poor accuracy. To face the challenge of multi-target DOA estimation in scenarios with low-precision ADC quantized sampling, this paper proposes a novel DOA estimation algorithm for quantized signals based on classification problems. A deep learning network was constructed using Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs), divided into the quantized signal recovery framework and the DOA estimation framework. The DNN network is utilized to recover signals that have undergone low-precision quantization, while the CNN network addresses the classification problem to estimate the DOA from received data with an unknown number of signal sources. A comprehensive analysis of the impact of signal-to-noise ratio (SNR), the number of array elements, and the number of quantization bits on the proposed algorithm was conducted. Simulation results indicate that the proposed algorithm exhibits superior DOA estimation performance in low-precision scenarios, characterized by reduced computational complexity, thereby facilitating real-time DOA estimation.

Robust Underwater Direction-of-Arrival Estimation Method Using Acoustic Sensor Array under Unknown Swing Deviation Elements

This paper presents a strategy called the alternating iterative minimization method (AIMM), aimed at enhancing the precision of direction of arrival (DOA) estimation when utilizing an acoustic vector sensor array (AVSA) with unknown swing deviation elements (SDEs). The AVSA model with unknown SDEs is formulated by incorporating the swing deviation parameter. Later, to estimate the swing deviation matrix (SDM) and the sparse signal power by using the alternating iteration method, the auxiliary cost functions with respect to SDM and the sparse signal power are formulated based on the regularized weighted least squares (RWLS) and regularized covariance matrix fitting (RCMF) criteria. Furthermore, their analytical expressions have also been quantified. In order to mitigate the effect of unknown SDEs on the accuracy of DOA estimation, any sub-time segment (STS) in the dataset is selected as the reference to convert the received data of different STS into the reference STS using the estimated SDM. The simulation and experimental outcomes conclusively represent the effectiveness of the suggested TSIM approach using AVSA in handling unknown SDEs.

Motion coprime array-based DOA estimation considering phase disturbance of sensor array

To address the phase disturbance issue faced by sensor arrays in practical applications, a cascaded deep convolutional neural network structure is proposed to achieve direction-of-arrival (DOA) estimation for motion coprime arrays. Firstly, the synthesized covariance matrix obtained after motion is inputted into the first-level network for estimating the phase disturbance matrix. Then, we analyze the impact of phase perturbation on the synthesized covariance matrix and utilize the estimated disturbance phase to obtain an undisturbed synthesized covariance matrix. Finally, after phase compensation, the synthesized covariance matrix performs DOA estimation through the second-level network. Furthermore, to acquire three times the virtual unique lags of the coprime array, the synthesis condition about moving distance and unique lags is derived. The proposed method is shown to be effective and superior through the experiment results.

An Improved Unfolded Coprime Linear Array Design for DOA Estimation with No Phase Ambiguity

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method.

A High-Precision, Ultra-Short Baseline Positioning Method for Full Sea Depth

To fulfill the demand for high-precision underwater acoustic positioning at full sea depth, an ultra-short baseline (USBL) positioning method with the square array based on the least squares estimating signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm is presented in this paper. A combination of beam tracking and beamforming is employed to improve the accuracy of direction-of-arrival (DOA) estimation and, consequently, enhance overall positioning accuracy. In order to mitigate the issue of position jumping resulting from phase ambiguity in traditional four-element cross arrays, we have improved the stability of the positioning algorithm by utilizing a multi-element square array and employing the LS-ESPRIT algorithm for DOA estimation. Furthermore, the signal detection method integrating the correlation coefficient and ascending/descending chirp signals is employed to enhance the reliability of the location algorithm. Simulation analysis and experimental results demonstrate that the proposed algorithm effectively enhances positioning accuracy and improves the problem of jumping in positioning results.

Robust Direction Estimation of Terrestrial Signal via Sparse Non-Uniform Array Reconfiguration under Perturbations

DOA (Direction of Arrival), as an important observation parameter for accurately locating the Signals of Opportunity (SOP), is vital for navigation in GNSS-challenged environments and can be effectively obtained through sparse arrays. In practical application, array perturbations affect the estimation accuracy and stability of DOA, thereby adversely affecting the positioning performance of SOP. Against this backdrop, we propose an approach to reconstruct non-uniform arrays under perturbation conditions, aiming to improve the robustness of DOA estimation in sparse arrays. Firstly, we theoretically derive the mathematical expressions of the Cramér–Rao Bound (CRB) and Spatial Correlation Coefficient (SCC) for the uniform linear array (ULA) with perturbation. Then, we minimize CRB as the objective function to mitigate the adverse effects of array perturbations on DOA estimation, and use SCC as a constraint to suppress sidelobes. By doing this, the non-uniform array reconstruction model is formulated as a high-order 0–1 optimization problem. To effectively solve this nonconvex model, we propose a polynomial-time algorithm, which can converge to the optimal approximate solution of the original model. Finally, through a series of simulation experiments utilizing frequency modulation (FM) signal as an example, the exceptional performance of this method in array reconstruction has been thoroughly validated. Experimental data show that the reconstructed non-uniform array excels in DOA estimation accuracy compared to other sparse arrays, making it particularly suitable for estimating the direction of terrestrial SOP in perturbed environments.

Computationally Efficient Direction Finding for Conformal MIMO Radar.

The use of conformal arrays offers a significant advancement in Multiple-Input-Multiple-Output (MIMO) radar, enabling the placement of antennas on irregular surfaces. For joint Direction-of-Departure (DOD) and Direction-of-Arrival (DOA) estimation in conformal-array MIMO radar, the current spectrum-searching methods are computationally too expensive, while the existing rotation-invariant method may suffer from phase ambiguity caused by the non-Nyquist spacing of the sensors. In this paper, an improved rotationally invariant technique is proposed. The core function of the proposed algorithm is to estimate the phase differences between the adjacent sensors; then, it eliminates phase ambiguity via the previous estimated standard phase difference. Thereafter, DODs and DOAs are obtained via Least Squares (LS) fitting. The proposed method provides closed-form estimates for joint DOD and DOA estimation, which is much more efficient than the existing spectrum-searching techniques. Numerical simulations show that the proposed algorithm can accurately determine 2D DODs and DOAs of targets, only requiring approximately 1% of the running time required by existing spectrum-searching approaches.

Trackable Electronic Deception Enabled by Space‐Time Coding Metasurface

AbstractSpace‐time coding metasurfaces (STCMs) have gained a great deal of achievements in the fields of radar and communication, but they have rarely been explored in the field of electronic jamming. The existing researches use time‐varying surface or phase‐switched screens to realize electronic deceptions, but the deceptions are completely passive and are limited in the time‐frequency domain. Here, a mechanism of STCM‐based deceptions is presented in the space and the time‐frequency domains, and precise designs of the STCM‐based deceptions are achieved by performing shifting operations on the space‐time coding sequences of the STCM. Moreover, STCM‐based DOA (direction‐of‐arrival) estimation is integrated with the deception procedure to achieve trackable electronic deception which cannot be realized by completely passive electronic jamming. A prototype system of the STCM‐based deception is built to verify the deception performance, and the experimental results agree well with the numerical simulations. This work extends the research and the applications of the STCMs, hence showing great scientific and engineering significance.

High-Resolution and Robust One-Bit Direct-of-Arrival Estimation via Reweighted Atomic Norm Estimation.

In recent years, one-bit quantization has attracted widespread attention in the field of direction-of-arrival (DOA) estimation as a low-cost and low-power solution. Many researchers have proposed various estimation algorithms for one-bit DOA estimation, among which atomic norm minimization algorithms exhibit particularly attractive performance as gridless estimation algorithms. However, current one-bit DOA algorithms with atomic norm minimization typically rely on approximating the trace function, which is not the optimal approximation and introduces errors, along with resolution limitations. To date, there have been few studies on how to enhance resolution under the framework of one-bit DOA estimation. This paper aims to improve the resolution constraints of one-bit DOA estimation. The log-det heuristic is applied to approximate and solve the atomic norm minimization problem. In particular, a reweighted binary atomic norm minimization with noise assumption constraints is proposed to achieve high-resolution and robust one-bit DOA estimation. Finally, the alternating direction method of multipliers algorithm is employed to solve the established optimization problem. Simulations are conducted to demonstrate that the proposed algorithm can effectively enhance the resolution.