Direction Of Arrival Estimation Algorithm Research Articles

An automated multi-layer perceptron discriminative neural network based on Bayesian optimization achieves high-precision one-source single-snapshot direction-of-arrival estimation

This paper proposes an innovative global solution which is a pioneering work applying automated machine learning algorithms to remarkable precision sparse underwater direction-of-arrival (DOA) estimation that views the subaquatic sparse-sampling DOA estimation problem as a classification prediction task. The proposed solution, termed automated multi-layer perceptron discriminative neural network (AutoMPDNN), is built upon a Bayesian optimization framework. AutoMPDNN transforms sparsely sampled time-domain signals into the complex domain, preserving essential components in a one-source single-snapshot scenario. Leveraging Bayesian optimization principles, the algorithm embeds necessary hyperparameters into the loss function, effectively defining it as a maximum likelihood problem using the upper confidence bound function and incorporating sparse signal features. We also explore the model space architecture and introduce variants of AutoMPDNN, denoted as AutoMPDNNs_ln (n = 2,3,4). Through a series of plane wave simulation experiments, it is demonstrated that AutoMPDNN achieves the highest prediction performance for one-source single-snapshot scenarios compared to classical DOA estimation algorithms that incorporate sparse representation approaches, as well as contemporary deep learning DOA methods under varying conditions.

Direction of arrival estimation using the rotating equatorial microphone

Introduction: Direction of arrival (DOA) estimation of sound sources is an essential task of sound field analysis which typically requires two or more microphones. In this study, we present an algorithm that allows for DOA estimation using the previously designed Rotating Equatorial Microphone prototype, which is a single microphone that moves rapidly along a circular trajectory, introducing DOA-dependent periodic distortions in the captured signal.Methods: Our algorithm compensates for the induced spectral distortions caused by the REM’s circular motion for multiple DOA candidates. Subsequently, the best DOA candidate is identified using two distortion metrics. We verify our approach through numerical simulations and practical experiments conducted in a low-reverberant environment.Results: The proposed approach localizes unknown single-frequency sources with a mean absolute error of 23 degrees and unknown wideband sources with a mean absolute error of 5.4 degrees in practice. Two sources are also localizable provided they are sufficiently separated in space.Conclusion: Whilst previous work only allowed for DOA estimation of a single monochromatic sound source with a known frequency, our DOA estimation algorithm enables localization of unknown and arbitrary sources with a single moving microphone.

Research on Direction Finding Method under Impulsive Noise Based on Nonuniform Linear Array

Direction of arrival (DOA) estimation under impulsive noise has always been an important research area in array signal processing. The traditional methods under impulsive noise mostly rely on prior parameters and have high computational complexity. Based on the filtering theory, we present an effective pretreatment filtering technology to cut out the impulse mixed in the array received data and employ the nonuniform linear array to improve the estimation performance further. First, according to the amplitude characteristics of impulse noise, the pretreatment filtering technology is proposed to cut out the impulse based on the median filter and sliding average filter, which is valid for both strong and weak impulsive noise. Second, the minimum redundant array is adopted to carry out array virtual expansion so that the array aperture can be increased and the estimation performance can be improved. Finally, based on the idea of matrix reconstruction, we propose the improved estimation of signal parameters via rotational invariance techniques algorithm and an improved root multiple signal classification algorithm for DOA estimation. Theoretical analysis and simulation results show that the proposed method has a simple processing process, small calculation load, good array expansion ability, and excellent noise adaptability. Moreover, the proposed methods greatly improve the direction-finding performance under the condition of low signal-to-noise ratio and strong impulsive noise.

Robust Sparse Recovery Based Vehicles Location Estimation in Intelligent Transportation System

An architecture for vehicle position estimation is introduced in this paper to tackle the issue of vehicles positioning in traffic congestion of intelligent transportation system (ITS). The introduced architecture is related to three unmanned aerial vehicles (UAVs) equipped with uniform linear array (ULA), ITS center and the terminal of position estimation, in which the UAV collect data from the ULA, the ITS center store data and the terminal is responsible for executing the corresponding direction of arrival (DOA) estimation algorithm to estimate the vehicle position. In the introduced architecture, DOA estimation is the crucial issue, hence a robust sparse recovery framework based on the optimal weighted subspace fitting is put forward for DOA estimation in the presence of direction-dependent unknown mutual coupling. Firstly, a data model can be obtained by a new transformation approach. Then, a sparse recovery algorithm based on the weighted subspace fitting is used to estimate the desired DOAs. The proposed DOA estimation algorithm can achieve superior performance in both coherent and incoherent signals in the environment of direction-dependent mutual coupling, and this environment often occurs in traffic congestion. Based on the DOA estimation results obtained from the proposed efficient regularized sparse recovery algorithm, the position of vehicles is final estimated by a weighted three-points cross-positioning method. The results of various simulation experiments fully demonstrate the robustness and superiority of the proposed architecture and algorithm.

4D High-Resolution Imagery of Point Clouds for Automotive mmWave Radar

In the community of automotive millimeter wave radar, the recently developed concept of four-dimensional (4D) radar can provide high-resolution point clouds image with enhanced imaging performance. Currently, the density of point clouds for single-frame image is usually too sparse to satisfy the demands of target classification and recognition due to the limitation of Doppler and angle resolutions. To address the aforementioned issues, a novel algorithm is proposed for 4D high-resolution imagery generation of point clouds with extremely high Doppler and angle resolutions in this paper. For high Doppler resolution with high-dynamic, a novel velocity ambiguity resolution algorithm is proposed using a dual pulse repetition frequency (dual-PRF) waveform design embedded in an innovative time-division multiplexing & Doppler-division multiplexing MIMO (TDM-DDM-MIMO) framework. Meanwhile, an attractive complex-valued deep convolutional network (CV-DCN) of super-resolution direction-of-arrival (DOA) estimation is proposed only using single-frame data. To be specific, a spatial smoothing operator on array data is applied as input of the network, and a CV-DCN is designed to learn the transformation of the spatial spectrum from the end-to-end to effectively protect the spectrum extraction. Furthermore, experimental analysis is performed to confirm the effectiveness of the proposed super-resolution DOA estimation algorithm. Finally, the 4D high-resolution imagery of point clouds is obtained by experiments in the parking lot.

Structural-Missing Tensor Completion for Robust DOA Estimation with Sensor Failure

Array sensor failure poses a serious challenge to robust direction-of-arrival (DOA) estimation in complicated environments. Although existing matrix completion methods can successfully recover the damaged signals of an impaired sensor array, they cannot preserve the multi-way signal characteristics as the dimension of arrays expands. In this paper, we propose a structural-missing tensor completion algorithm for robust DOA estimation with uniform rectangular array (URA), which exhibits a high robustness to non-ideal sensor failure conditions. Specifically, the signals received at the impaired URA are represented as a three-dimensional incomplete tensor, which contains whole fibers or slices of missing elements. Due to this structural-missing pattern, the conventional low-rank tensor completion becomes ineffective. To resolve this issue, a spatio-temporal dimension augmentation method is developed to transform the structural-missing tensor signal into a six-dimensional Hankel tensor with dispersed missing elements. The augmented Hankel tensor can then be completed with a low-rank regularization by solving a Hankel tensor nuclear norm minimization problem. As such, the inverse Hankelization on the completed Hankel tensor recovers the tensor signal of an unimpaired URA. Accordingly, a completed covariance tensor can be derived and decomposed for robust DOA estimation. Simulation results verify the effectiveness of the proposed algorithm.

Coherent DOA Estimation Algorithm with Co-Prime Arrays for Low SNR Signals

The Direction of Arrival (DOA) estimation of coherent signals in co-prime arrays has become a popular research topic. However, traditional spatial smoothing and subspace algorithms fail to perform well under low signal-to-noise ratio (SNR) and small snapshots. To address this issue, we have introduced an Enhanced Spatial Smoothing (ESS) algorithm that utilizes a space-time correlation matrix for de-noising and decoherence. Finally, an Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is used for DOA estimation. In comparison to other decoherence methods, when the SNR is −8 dB and the number of snapshots is 150, the mean square error (MSE) of the proposed algorithm approaches the Cramér–Rao bound (CRB), the probability of resolution (PoR) can reach over 88%, and, when the angular resolution is greater than 4°, the estimation accuracy can reach over 90%.

Direction of Arrival Estimation with Nested Arrays in Presence of Impulsive Noise: A Correlation Entropy-Based Infinite Norm Strategy

Direction of arrival (DOA) estimation with nested arrays has been widely investigated in the field of array signal processing, but most studies assume that the noise is Gaussian white noise. In practical situations, there may exist impulsive noise (a kind of heavy-tailed noise), wherein the performance of traditional subspace-based DOA estimation algorithms deteriorates significantly. In this paper, we propose a correlation entropy-based infinite norm preprocessing algorithm, which can be applicable to any type of impulsive noise. Each snapshot of the sensor array data is processed by an exponential kernel function with the infinite norm, which can effectively combat the outliers. Furthermore, we construct the equivalent second-order covariance matrix and perform DOA estimation using classical subspace methods. Simulation results demonstrate the effectiveness of the proposed method for both symmetric α-stable distribution and the Gaussian mixture model.

Polarization Direction of Arrival Estimation for Vector Array of Unmanned Aerial Vehicle Swarm

Aiming at the problem of the excessive error of direction of arrival (DOA) estimation caused by the position disturbance of a UAV swarm during flight, a robust polarization-DOA estimation method based on sparse Bayesian learning (SBL) is proposed. First, the algorithm decomposes the covariance matrix of the received data of the UAV swarm vector array and then constructs the determination matrix of the UAV position coordinates by exploiting the orthogonality of the eigenvalues and eigenvectors. Then, the optimal solution of the semi-positive definite programming (SDP) problem is solved using the constrained global least square method, and the exact self-positioning coordinates of UAVs are obtained. Second, we construct a spatially discrete grid to model the received data of the UAV group vector array. The SBL theory is then applied to obtain the posterior probability distribution of the sparse signal matrix. The sparsity of the signal matrix is controlled with a hyperparameter, and the estimation of the DOA is conducted using a fixed-point iteration to obtain the maximum posterior estimate of the signal matrix. Finally, according to the estimated DOA, the polarization parameter is obtained from the constructed objective function of the polarization parameter estimation. The simulation results show that the proposed algorithm achieves higher accuracy and robustness than the traditional 2D DOA estimation algorithm in the direction-finding system for UAV swarm vector arrays.

A Gridless DOA Estimation Method for Sparse Sensor Array

Direction-of-arrival (DOA) estimation is still a pivotal research direction in array signal processing. Traditional algorithms based on the signal subspace and compressed sensing theory usually suffer from off-grid and computational complexity. Deep-learning-based methods usually face difficulty in obtaining labeled datasets. With the development of array technology, sparse sensor arrays can effectively reduce the number of sensors, which in turn reduces the complexity of the hardware. Therefore, effective DOA estimation algorithms for sparse sensor arrays need to be further investigated. An unsupervised deep learning method is proposed here to address the above issues. A training model was built based on the residual network structure. The DOA estimation was implemented using Vandermonde decomposition. Finally, the experimental findings confirmed the efficacy of the proposed algorithms presented in this article.

Low frequency three-dimensional DOA estimation for underwater gliders using an arbitrary tetrahedral array

This study proposes a method for estimating the three-dimensional (3-D) direction of arrival (DOA) of low-frequency line spectra with an arbitrary tetrahedral array on a moving underwater platform, such as underwater glider (UG). First, we provide the theoretical derivations of the 3-D DOA estimation algorithm. Four sensors are matched pairwise without duplication and the time difference of arrival (TDOA) of each pair is estimated using the cross-spectral method. The geometric relation between the space coordinate vector of the paired sensors and direction vector of the incoming signal is combined with the TDOA to establish the overdetermined equations. The algorithm solves the overdetermined equations to obtain the azimuth and elevation of the line spectra, and exploits all the information from sensors to enhance the accuracy of DOA estimation. And the Cramer–Rao lower bound (CRLB) of an arbitrary tetrahedral array is derived as a function of the signal-to-noise ratio (SNR), integration time, signal bandwidth, frequency, array arrangement, and DOA of the signal. Second, simulations and a sea trial verify the feasibility of the 3-D DOA estimation algorithm using a tetrahedral array on a moving UG. Finally, several factors that influence the algorithm are analyzed, including the DOA of the source, frequency, SNR, sensor position error and phase error. The upper frequency limit to avoid spatial aliasing is also derived as a function of the array aperture. The study shows that the tetrahedral array is suitable for various underwater mobile platforms owing to its small scale and irregularity.

Satellite Interference Source Direction of Arrival (DOA) Estimation Based on Frequency Domain Covariance Matrix Reconstruction.

Direction of arrival (DOA) estimation is an effective method for detecting various active interference signals during the satellite navigation process. It can be utilized for both interference detection and anti-interference applications. This paper proposes a DOA estimation algorithm for satellite interference sources based on frequency domain covariance matrix reconstruction (FDCMR) to address various types of active interference that may occur in the satellite navigation positioning process. This algorithm can estimate the DOA of coherent signals from multiple frequency points under low signal-to-noise ratio (SNR) conditions. The signals received from the array are transformed from the time domain to the frequency domain using a fast Fourier transform (FFT). The data corresponding to the frequency point of the target signal is extracted from the signal in the frequency domain. The frequency domain covariance matrix of the received array signals is reconstructed by utilizing its covariance matrix property. The spatial spectrum search method is used for the final DOA estimation. Simulation experiments have shown that the proposed algorithm performs well in the DOA estimation under low SNR conditions and also resolves coherency. Moreover, the algorithm's effectiveness is verified through comparison with three other algorithms. Finally, the algorithm's applicability is validated through simulations of various interference scenarios.

Generalised two‐level nested multiple‐input multiple‐output radar direction of arrival estimation with high degrees of freedom and low mutual coupling

AbstractTo address the problems of traditional two‐level nested arrays (TTNA) with low degrees of freedom and high mutual coupling, a generalised two‐level nested MIMO radar array with high degrees of freedom and low mutual coupling for the direction of arrival (DOA) estimation is proposed. First, two coprime expansion factors are introduced in the TTNA to mitigate mutual coupling among array elements and enhance its degrees of freedom. Secondly, the range of consecutive lags and the total number of virtual array elements are derived in closed form under the structures of ‘sum–difference co‐array’. Finally, utilising the atomic norm minimisation theory, the authors address the issue of discrete holes caused by different coprime expansion factors through filling in virtual arrays at discontinuities. Furthermore, a convex optimisation model to recover equivalent received signals from these filled virtual arrays is established, which is combined with a multiple signal classification algorithm for DOA estimation. Simulation results validate the rationality of the array structure and demonstrate the effectiveness of the algorithm.

Joint DoA and CFO Estimation Scheme With Received Beam Scanned Leaky Wave Antenna for Industrial Internet of Things (IIoT) Systems

Direction-of-arrival (DoA) estimation is essential in many industrial internet of things (IIoT) applications where IoT users may require a high-resolution estimation algorithm for features limited to positioning and device localization. The conventional DoA estimation is challenging as the number of antenna arrays increases leading to an increase in design complexity and cost in RF circuitry. As a result, the conventional DoA estimation algorithms may not be suited for IIoT applications. In this work, a joint DOA and carrier frequency offset (CFO) schemes is introduced for typical uplink IIoT systems by equipping the receiver with a leaky-wave antenna (LWA). By considering that the LWA can simultaneously steer its beam direction towards the active user. As a result, each user is estimated independently. The joint algorithm is developed based on the high-resolution MUSIC scheme, which utilizes the LWA properties to compute the DoA spectrum. Furthermore, we develop an iterative CFO estimation approach as the desired solution to a multi-dimensional search. Subsequently, we further formulate the Cramer–Rao lower bounds (CRLB) to serve as a performance benchmark for the accuracy of the proposed scheme. The SDR platform is provided to validate the proposed algorithm in real-time. Finally, the simulation results and the SDR experiments justify that the proposed scheme offers more robustness than conventional counterparts with linear array antenna, which achieves a root mean square error (RMSE) approach to the derived CLRB, especially at a medium signal-to-noise ratio (SNR) range which suited for IIoT applications.

Computationally efficient direction of arrival estimation using adaptive grid selection

AbstractThe authors propose a computationally efficient approach to estimate the directions of arrival of far‐field sources impinging on a sensor array. The proposed estimator is formed using a sparse reconstruction framework, employing a novel adaptive grid selection technique to reduce the dimensionality of the used dictionary matrix. The method further makes use of a SPICE‐inspired dictionary to adaptively select an appropriate regularisation parameter and to select the active grid set. An adaptive stepsize selection strategy is also introduced to reduce computation complexity further. The proposed method allows for accurate direction‐of‐arrival (DOA) estimates using even a single snapshot, also from weak sources. Numerical simulations indicate that the method offers preferable performance in comparison to existing state‐of‐the‐art DOA estimation algorithms.

Improved Direction of Arrival Estimation using Multiple Signal Classification (MUSIC) Algorithm with Decomposition and Normalization

It is important to determine the direction of arrival (DoA) of targets in various applications such as radar and sonar. Multiple Signal Classification (MUSIC), Estimation of Signal Parameters with Rotational In variance Technique (ESPRIT), and Weighted Subspace Fitting (WSF) are subspace-based methods that can be used to improve DoA estimation. MUSIC is effective for high-resolution, uncorrelated signals, but may struggle in cases where there are two nearby targets with a low signal-to-noise ratio (SNR). The goal of this research is to improve the performance of the MUSIC algorithm for DoA estimation with low SNR signals. The proposed solution involves decomposing and normalizing the signal during transmission. Simulations were conducted to test the modified procedure with MUSIC algorithm for DoA estimation, and it was found that received signal power improved though there is noisy environment as well as system can detect more number of targets. The proposed technique of decomposition and normalization could also be applied in other areas such as WiFi communication, autonomous vehicles and biomedical signal and image processing etc.

Adaptive Direction-of-Arrival Estimation Using Deep Neural Network in Marine Acoustic Environment

Deep learning is widely used for target detection and direction-of-arrival (DOA) estimation due to its powerful data fitting capability. However, limited by different environments and number of sound sources, it is difficult to be applied to complex underwater environments. We propose a two-stage approach called Beam-Network for underwater acoustic DOA estimation. In the first stage, local beam patterns with different data augmentation methods, carrying the essential information required for target detection, are used as the input feature to our model. In the second stage, an adaptive convolutional neural network (CNN) is proposed to construct a classification model. Only single-source data are required for model training and data from multi sources can be tested. What’s more, the model is suitable for arrays with different numbers of hydrophones in different geometrical arrangements. The performance of the proposed method is evaluated by comparing with mainstream DOA estimation algorithms such as CBF, MUSIC, MVDR, and SBL. In three simulation scenarios and two sets of recorded data from different marine environments, the proposed method has higher directivity and lower angular root-mean-squared error (RMSE).

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

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

EM and SAGE Algorithms for DOA Estimation in the Presence of Unknown Uniform Noise.

The existing expectation maximization (EM) and space-alternating generalized EM (SAGE) algorithms are only applied to direction of arrival (DOA) estimation in known noise. In this paper, the two algorithms are designed for DOA estimation in unknown uniform noise. Both the deterministic and random signal models are considered. In addition, a new modified EM (MEM) algorithm applicable to the noise assumption is also proposed. Next, these EM-type algorithms are improved to ensure the stability when the powers of sources are not equal. After being improved, simulation results illustrate that the EM algorithm has similar convergence with the MEM algorithm, the SAGE algorithm outperforms the EM and MEM algorithms for the deterministic signal model, and the SAGE algorithm cannot always outperform the EM and MEM algorithms for the random signal model. Furthermore, simulation results show that processing the same snapshots from the random signal model, the SAGE algorithm for the deterministic signal model can require the fewest computations.

DOA Estimation for Multiple Speech Sources Based on Flexible Single-Source Zones and Concentration Weighting

Direction of arrival (DOA) estimation is the key to many audio applications. Recently, sparse component analysis (SCA)-based methods have attracted much attention, in which single-source points (SSPs) and single-source zones (SSZs) where one source is dominant over the others in time-frequency domain are usually detected to construct the pooled histogram containing multi-source DOA information. Nonetheless, the SSZ size in existing methods is fixed and empirically predetermined, which cannot accommodate to the varying spectro-temporal property of speech sources. Furthermore, higher SSP concentration in a SSZ implies a locally stronger dominant source as well as more reliable DOA information extracted therein, which however is also not taken into account yet. To address these problems, a DOA estimation algorithm for multiple speech sources based on flexible SSZs and concentration weighting is presented in this paper. First, in each frame, correlation coefficients of time delay vectors across adjacent frequency bins are calculated to identify SSPs, followed by flexible SSZs construction using varying number of SSPs located at consecutive frequency bins. Next, the number of SSPs in each flexible SSZ is considered as a proxy of corresponding concentration degree, and employed as weighting factor to form the pooled histogram. Finally, a matching pursuit (MP)-based approach is utilized to obtain multi-source DOA estimates. Simulation results reveal that the proposed method significantly outperforms existing approaches in terms of noise floor in pooled histogram, angular resolution, and performance under various signal-to-noise ratio and reverberant conditions. Real-world experiments also verify its effectiveness, and meanwhile demonstrate considerably reduced computational complexity.