Accurate Direction Of Arrival Research Articles

Combined Keyword Spotting and Localization Network Based on Multi-Task Learning

The advent of voice assistance technology and its integration into smart devices has facilitated many useful services, such as texting and application execution. However, most assistive technologies lack the capability to enable the system to act as a human who can localize the speaker and selectively spot meaningful keywords. Because keyword spotting (KWS) and sound source localization (SSL) are essential and must operate in real time, the efficiency of a neural network model is crucial for memory and computation. In this paper, a single neural network model for KWS and SSL is proposed to overcome the limitations of sequential KWS and SSL, which require more memory and inference time. The proposed model uses multi-task learning to utilize the limited resources of the device efficiently. A shared encoder is used as the initial layer to extract common features from the multichannel audio data. Subsequently, the task-specific parallel layers utilize these features for KWS and SSL. The proposed model was evaluated on a synthetic dataset with multiple speakers, and a 7-module shared encoder structure was identified as optimal in terms of accuracy, direction of arrival (DOA) accuracy, DOA error, and latency. It achieved a KWS accuracy of 94.51%, DOA error of 12.397°, and DOA accuracy of 89.86%. Consequently, the proposed model requires significantly less memory owing to the shared network architecture, which enhances the inference time without compromising KWS accuracy, DOA error, and DOA accuracy.

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.

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.

Research on the vector DOA estimation method with limited number of snapshots

The number of sample snapshots of array signals directly affects the performance of direction of arrival (DOA) estimation methods, and smaller snapshots often cannot represent all the features of array signals. However, in practical applications, owing to short-time abrupt changes, low intensity, large noise interference, and other factors of the target signal, the acoustic vector array sometimes cannot obtain sufficient signal data, making it difficult to achieve accurate DOA estimation. Therefore, this study proposes a transfer-learning-based DOA estimation method for acoustic vector arrays. This method extracts the spatial–temporal features of existing signal data by constructing a pre-trained network model based on a convolutional neural network (CNN) and long short-term memory (LSTM), and transfers the trained model to scenes with limited snapshot data through model fine-tuning, achieving the goal of improving the DOA estimation accuracy under a small number of snapshots. Simulation experiments show that the accuracy and RMSE of the proposed DOA estimation method are superior to those of traditional methods when only 1% of the target data are used. This indicates that the pre-training model based on LSTM and CNN can preserve the effective information of signal data and provides a new solution for the real-time prediction of acoustic vector arrays in scenes with a limited number of snapshots through transfer learning.

RDCSAE-RKRVFLN: A unified deep learning framework for robust and accurate DOA estimation

This paper introduces an innovative unified deep learning (DL) model, “reduced deep convolutional stack autoencoder (RDCSAE)-robust kernel-based random vector functional link network (RKRVFLN)” (RDCSAE-RKRVFLN), for addressing practical challenges like phase and gain uncertainty, mutual coupling effects, and element position errors in direction of arrival (DOA) estimation. The RDCSAE utilizes deep convolutional neural network (DCNN) and stack autoencoder (SAE) for robust feature extraction. The RKRVFLN integrates a concise SAE output with kernel-based learning. Thus, the integration of RDCSAE (suitable for unsupervised feature extraction) and RKRVFLN (for supervised learning) in the developed model results in efficient use of limited training data. Performance metrics of this method include among others the accuracy (separation between sources), root mean square error (RMSE), signal-to-noise ratio (SNR), etc. The method performs better than existing data driven methods in terms of computational efficiency, faster learning speed, enhanced model generalization, higher accuracy, and shorter event regression time and empirical methods. In the presence of above mentioned four perturbations, this method successfully resolves multiple sources with a resolution of 0.3° with a RMSE of 0.00376. For real time application, the paper implements RDCSAE-RKRVFLN on a high-speed reconfigurable Xilinx Virtex-5 field-programmable gate array (FPGA) realizing a digital DOA estimator for one source. The hardware estimates the DOA with a maximum error of 0.01953125 which follows closely the simulation results indicating the efficiency and feasibility of the method.

Multiplicative Basis Function Based Adaptive DOA Estimation in Optimal MIMO Sparse Antenna Reconfiguration Model

Direction of arrival (DOA) estimation using sparse signal representation has gained significant attention in recent decades. The spatial signals utilized for DOA estimation are reconstructed through a novel compressive sensing (CS) approach. In this study, we used a CS approach to ascertain the adaptive underdetermined DOA for multiple inputs and multiple output (MIMO) sparse media. Accurate DOA estimation through the CS approach contributes to enhanced signal investigation and the suppression of undesired noise in a sparse channel. The method proposed herein encompasses the development and execution of a novel multiplicative basis function known as the multi-kernel supported non-negative sparse Bayesian learning (NNSBL) algorithm, which is implemented on predefined grid values. Concurrently, stochastic grey wolf optimization (GWO) is virtually applied to increase the degrees of freedom (DOF) on a minimum redundancy array (MRA) while considering an optimal antenna reconfiguration model. The advantages of this proposed approach include the generation of a distinct manifold matrix for precise beam steering, resulting in improved DOA estimation accuracy. Additionally, an augmentation of DOF using GWO was observed, with low computational complexity. The simulated result of proposed algorithm leads to the attainment of optimal minimum root mean square error (RMSE) across various optimal wavelengths of the stochastic sources. Finally, a comparative analysis of RMSE and convergence plots confirms the superior performance and high potentiality of the proposed method in comparison to existing techniques across different SNR values. Notably, there is significant reduction in RMSE which is suitable for precise DOA estimation in signal processing applications.

Improving the Accuracy of Direction of Arrival Estimation with Multiple Signal Inputs Using Deep Learning.

In this paper, an innovative cyclic noise reduction method and an improved CAPON algorithm (also the called minimum variance distortionless response (MVDR) algorithm) are proposed to improve the accuracy and reliability of DOA (direction of arrival) estimation. By processing the eigenvalues obtained from the covariance matrix of the received signal, the signal-to-noise ratio (SNR) can be increased by up to 5 dB by the cyclic noise reduction method, which will improve the DOA estimation accuracy. The improved CAPON algorithm has a convolution neural network (CNN) structure, whose input is the processed covariance matrix of the received signal, and the CAPON spectral value is used as the training label to obtain the estimated spatial spectrum. It retains the advantages of the CAPON algorithm, which can achieve blind source estimation, and simulations show that the proposed algorithm exhibits a better performance than the traditional algorithm in conditions of various SNRs and snapshot numbers. The simulation results show that, based on a certain SNR, the root mean square error (RMSE) of the improved CAPON algorithm can be reduced from 0.86° to 0.8° compared to traditional algorithms, and the angle estimation error can be decreased by up to about 0.3°. With the help of the cyclic noise reduction method, the angle estimation error decreases from 0.04° to 0.02°.

A Novel Weighted Block Sparse DOA Estimation Based on Signal Subspace under Unknown Mutual Coupling

A Novel Weighted Block Sparse DOA Estimation Based on Signal Subspace under Unknown Mutual Coupling

Design and Algorithm Integration of High-Precision Adaptive Underwater Detection System Based on MEMS Vector Hydrophone.

Real-time DOA (direction of arrival) estimation of surface or underwater targets is of great significance to the research of marine environment and national security protection. When conducting real-time DOA estimation of underwater targets, it can be difficult to extract the prior characteristics of noise due to the complexity and variability of the marine environment. Therefore, the accuracy of target orientation in the absence of a known noise is significantly reduced, thereby presenting an additional challenge for the DOA estimation of the marine targets in real-time. Aiming at the problem of real-time DOA estimation of acoustic targets in complex environments, this paper applies the MEMS vector hydrophone with a small size and high sensitivity to sense the conditions of the ocean environment and change the structural parameters in the adaptive adjustments system itself to obtain the desired target signal, proposes a signal processing method when the prior characteristics of noise are unknown. Theoretical analysis and experimental verification show that the method can achieve accurate real-time DOA estimation of the target, achieve an error within 3.1° under the SNR (signal-to-noise ratio) of the X channel of -17 dB, and maintain a stable value when the SNR continues to decrease. The results show that this method has a very broad application prospect in the field of ocean monitoring.

A Reduced Complexity Acoustic-Based 3D DoA Estimation with Zero Cyclic Sum.

Accurate direction of arrival (DoA) estimation is paramount in various fields, from surveillance and security to spatial audio processing. This work introduces an innovative approach that refines the DoA estimation process and demonstrates its applicability in diverse and critical domains. We propose a two-stage method that capitalizes on the often-overlooked secondary peaks of the cross-correlation function by introducing a reduced complexity DoA estimation method. In the first stage, a low complexity cost function based on the zero cyclic sum (ZCS) condition is used to allow for an exhaustive search of all combinations of time delays between pairs of microphones, including primary peak and secondary peaks of each cross-correlation. For the second stage, only a subset of the time delay combinations with the lowest ZCS cost function need to be tested using a least-squares (LS) solution, which requires more computational effort. To showcase the versatility and effectiveness of our method, we apply it to the challenging acoustic-based drone DoA estimation scenario using an array of four microphones. Through rigorous experimentation with simulated and actual data, our research underscores the potential of our proposed DoA estimation method as an alternative for handling complex acoustic scenarios. The ZCS method demonstrates an accuracy of 89.4%±2.7%, whereas the ZCS with the LS method exhibits a notably higher accuracy of 94.0%±3.1%, showcasing the superior performance of the latter.

Grid-less wideband direction of arrival estimation based on variational Bayesian inference.

Many recent works have addressed the problem of wideband direction of arrival (DOA) estimation using grid-less sparse techniques, and these methods have been shown to outperform the traditional wideband DOA estimation methods. However, these methods often suffer from the problem of requiring manual parameter tuning or high computational complexity, which reduces their practicality. To alleviate this problem, a grid-less wideband DOA estimation method based on variational Bayesian inference is proposed in this paper. The method approximates the posterior probability density function of DOA with the help of variational Bayesian inference, which does not require manual adjustment of parameters and can obtain accurate DOA estimation results with low computational complexity. Numerical simulations and real measurement data processing show that the proposed method has a higher DOA estimation accuracy than other grid-less wideband methods while providing higher computational speed.

Gridless Underdetermined DOA Estimation for Mobile Agents with Limited Snapshots Based on Deep Convolutional Generative Adversarial Network

Deep learning techniques have made certain breakthroughs in direction-of-arrival (DOA) estimation in recent years. However, most of the current deep-learning-based DOA estimation methods view the direction finding problem as a grid-based multi-label classification task and require multiple samplings with a uniform linear array (ULA), which leads to grid mismatch issues and difficulty in ensuring accurate DOA estimation with insufficient sampling and in underdetermined scenarios. In order to solve these challenges, we propose a new DOA estimation method based on a deep convolutional generative adversarial network (DCGAN) with a coprime array. By employing virtual interpolation, the difference co-array derived from the coprime array is extended to a virtual ULA with more degrees of freedom (DOFs). Then, combining with the Hermitian and Toeplitz prior knowledge, the covariance matrix is retrieved by the DCGAN. A backtracking method is employed to ensure that the reconstructed covariance matrix has a low-rank characteristic. We performed DOA estimation using the MUSIC algorithm. Simulation results demonstrate that the proposed method can not only distinguish more sources than the number of physical sensors but can also quickly and accurately solve DOA, especially with limited snapshots, which is suitable for fast estimation in mobile agent localization.

High-Precision DOA Estimation Based on Synthetic Aperture and Sparse Reconstruction.

The direction-of-arrival (DOA) estimation is predominantly influenced by the antenna's aperture size. However, space constraints on flight platforms often necessitate the use of antennas with smaller apertures and fewer array elements. This inevitably imposes limitations on the DOA estimation's resolution and degrees of freedom. To address these precision constraints, we introduce an accurate DOA estimation method based on spatial synthetic aperture model. This method adopts a two-stage strategy to ensure both efficiency and precision in DOA estimation. Initially, the orthogonal matching pursuit (OMP) reconstruction algorithm processes the original aperture data, providing a rough estimate of target angles that guides the aircraft's flight direction. Subsequently, the early estimations merge with the aircraft's motion space samples, forming equivalent spatially synthesized array samples. The refined angle estimation then employs the OMP-RELAX algorithm. Moreover, with the off-grid issue in mind, we devise an estimation method integrating Bayesian parameter estimation with dictionary sequence refinement. The proposed technique harnesses the spatial synthetic aperture for pinpoint estimation, effectively addressing the challenges of atomic orthogonality and angular off-grid on estimation accuracy. Importantly, the efficiency of deploying sparse reconstruction for angle estimation is bolstered by our phased strategy, eliminating the necessity for fine grid analysis across the entire observation scene. Moreover, the poor estimation accuracy caused by coherent source targets and angular-flickering targets is improved by sparse reconstruction. Through simulation and experiment, we affirm the proposed method's efficacy in angle estimation. The results indicate that target angle estimation errors are limited to within 1°. Furthermore, we assess the impact of variables such as target state, heading angle, spatial sampling points, and target distance on the estimation accuracy of our method, showcasing its resilience and adaptability.

Deep Learning-Enabled Improved Direction-of-Arrival Estimation Technique

This paper provides a simple yet effective approach to improve direction-of-arrival (DOA) estimation performance in extreme signal-to-noise-ratio (SNR) conditions. As an example, a multiple signal classification (MUSIC) algorithm with a deep learning (DL) approach is used. First, brief research into the existing DOA estimation techniques is provided, followed by a demonstration of a simulation environment created on the MATLAB platform to generate and resolve signals from a uniform rectangular array of antenna elements. Following that is an attempt to improve the estimation accuracy of these signals by training various DL approaches, including multi-layer perceptron and one- and two-dimensional convolutional neural networks, using the generated dataset. Key findings include the cases where the developed DL approach can resolve signals and provide accurate DOA estimations that the MUSIC algorithm cannot.

DOA estimation of underwater acoustic co-frequency sources for the coprime vector sensor array

A coprime array with fewer sensors can achieve the same resolution as a uniform linear array. However, when detecting co-frequency targets, there can be prominent false alarms due to overlaps between the main and grating lobes of subarrays. This study proposes a direction-of-arrival (DOA) estimation method to obtain the co-frequency target directions from high grating lobes. The method utilizes joint processing of sound pressure and vibration velocity data from vector hydrophones of a coprime vector hydrophone array and designs joint-cross terms (JCTs) using channel combinations. Based on JCTs, we establish a characteristic data point identification algorithm. The method in this paper can stably and accurately acquire co-frequency target directions from high grating lobes without decoherence operation. Simulation results demonstrate that the proposed algorithm achieves accurate DOA estimation even with reduced signal-to-noise ratio (SNR) and fewer data points. Additionally, a sea experiment confirms the rationality and efficiency of the proposed algorithm, providing new ideas for co-frequency source detection using coprime vector sensor arrays.

Direction finding method via acoustic vector sensor array with fluctuating misorientation

In this paper, we consider the direction-of-arrival (DOA) estimation problem under fluctuating misorientation via acoustic vector sensor array (AVSA). A covariance matrix focusing fitting (CMFF) method is proposed to tackle this issue. Firstly, a new AVSA data model is created by incorporating the fluctuation parameter into different time segments. Then, to overcome the deterioration of DOA estimation performance under fluctuating misorientation in the total observation time, a covariance matrix focusing technique is formulated. By using the covariance matrix focusing technique, different time segments with fluctuating misorientation are converted into the desired data sets. Finally, to obtain more accurate DOA estimation performance, an iterative weighted covariance matrix fitting method is presented. Simulation and experimental results are carried out to demonstrate the superiority and robustness of our proposed method in the case of fluctuating misorientation for an AVSA.

A GNSS Spoofing Detection and Direction-Finding Method Based on Low-Cost Commercial Board Components

The Global Navigation Satellite System (GNSS) is vulnerable to deliberate spoofing signal attacks. Once the user wrongly locks on the spoofing signal, the wrong position, velocity, and time (PVT) information will be calculated, which will harm the user. GNSS spoofing signals are difficult to carry out spoofing attacks in the direction of arrival (DOA) of the real signal, so the spoofing detection method based on DOA is very effective. On the basis of identifying spoofing signals, accurate DOA information of the signal can be further used to locate the spoofer. At present, the existing DOA monitoring methods for spoofing signals are mainly based on dedicated antenna arrays and receivers, which are costly and difficult to upgrade and are not conducive to large-scale deployment, upgrade, and maintenance. This paper proposes a spoofing detection and direction-finding method based on a low-cost commercial GNSS board component (including an antenna). Based on the traditional principle of using a multi-antenna carrier phase to solve DOA, this paper innovatively solves the following problems: the poor direction-finding accuracy caused by the unstable phase center of low-cost commercial antennas, the low success rate of spoofing detection in a multipath environment, and the inconsistent sampling time among multiple low-cost commercial GNSS boards. Moreover, the corresponding prototype equipment for spoofing detection and direction-finding is developed. The measured results show that it can effectively detect spoofing signals in open environments. Under a certain false alarm rate, the detection success rate can reach 100%, and the typical direction-finding accuracy can reach 5°.

Buried gas pipe leak localization using dual-wave spectrum estimation

To accurately locate leaks in buried gas pipes, a three-dimensional (3D) localization method using dual-wave velocity pairing and multi-array fusion localization was developed in this study to locate leak-induced vibroacoustic sources. Two velocities at which the P1 and S waves propagated along soil were estimated when the peaks of the dual-wave spectrum coincided with each other. Root-MUSIC algorithm was introduced to quickly determine the superimposed peak, thereby reducing the computational complexity. To address the issue of 3D localization using the P1 wave that propagated in soil according to a far-field model, least-squares (LS) estimation for the 3D coordinates was performed using the fusion localization method. A numerical model of geometrical dilution of precision (GDOP) was constructed to analyze the performances of multi-array layouts. A uniform circular array of eight accelerometers was utilized to visualize the leak-induced vibroacoustic source, and the imaging showed that the vibroacoustic source coincided with the leak. Accurate direction of arrival (DOA) estimation under multiple soil conditions was achieved, which proved that the velocity near the array was accurately estimated. An equilateral-triangle multi-array layout was selected using GDOP analyzing, and the results of localization experiments revealed that the equilateral-triangle layouts with 1.5-m and 2-m spacings achieved relatively good accuracy. Compared to the 3D localization method using a single array, the fusion localization method showed better accuracy for the remote leak, and the maximum reduction in error is 84.75 %. GDOP of fusion localization was found less than 0.1 m when the internal pipe pressure ≥ 0.4 MPa and the signal-to-noise ratio (SNR) ≥ 0 dB under the conditions of experiments in this study.

Multitarget 2-D DOA Estimation Using Wideband LFMCW Signal and Triangle Array Composed of Three Receiver Antennas

Direction of arrival (DOA) estimation has been a primary focus of research for many years. Research on DOA estimation continues to be immensely popular in the fields of the internet of things, radar, and smart driving. In this paper, a simple new two-dimensional DOA framework is proposed in which a triangular array is used to receive wideband linear frequency modulated continuous wave signals. The mixed echo signals from various targets are separated into a series of single-tone signals. The unwrapping algorithm is applied to the phase difference function of the single-tone signals. By using the least-squares method to fit the unwrapped phase difference function, the DOA information of each target is obtained. Theoretical analysis and simulation demonstrate that the framework has the following advantages. Unlike traditional phase goniometry, the framework can resolve the trade-off between antenna spacing and goniometric accuracy. The number of detected targets is not limited by the number of antennas. Moreover, the framework can obtain highly accurate DOA estimation results.

Centroid Optimization of DNN Classification in DOA Estimation for UAV

Classifications based on deep learning have been widely applied in the estimation of the direction of arrival (DOA) of signal. Due to the limited number of classes, the classification of DOA cannot satisfy the required prediction accuracy of signals from random azimuth in real applications. This paper presents a Centroid Optimization of deep neural network classification (CO-DNNC) to improve the estimation accuracy of DOA. CO-DNNC includes signal preprocessing, classification network, and Centroid Optimization. The DNN classification network adopts a convolutional neural network, including convolutional layers and fully connected layers. The Centroid Optimization takes the classified labels as the coordinates and calculates the azimuth of received signal according to the probabilities of the Softmax output. The experimental results show that CO-DNNC is capable of acquiring precise and accurate estimation of DOA, especially in the cases of low SNRs. In addition, CO-DNNC requires lower numbers of classes under the same condition of prediction accuracy and SNR, which reduces the complexity of the DNN network and saves training and processing time.