Direction Of Arrival Estimation Algorithm Research Articles

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.

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.

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.

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.

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.

An improved histogram algorithm for DOA estimation based on single vector acoustic system

The integration of a singular vector acoustic system onto an unmanned underwater platform can lead to achieving unambiguous direction finding across the entire space. To enhance the direction-finding capabilities of the single vector acoustic system for low noise target, a refined histogram algorithm utilizing coherent spectrum weighting is suggested. A comparative evaluation and analysis of the target azimuth estimation performance of the enhanced histogram algorithm, traditional frequency-weighted histogram algorithm, and energy-weighted histogram algorithm are carried out. Through computer simulations, it is observed that the three Direction of Arrival (DOA) algorithms exhibit comparable direction-finding capabilities for wideband signals, whereas for single-frequency signals, the improved histogram algorithm surpasses the two conventional algorithms in direction-finding accuracy. Specifically, at a signal-to-noise ratio (SNR) of −40 dB, the azimuth estimation root mean square error (RMSE) is approximately 2°. Findings from sea trials indicate that the improved histogram algorithm displays a narrower spectral peak width and robust resistance to noise interference, thereby substantiating the effectiveness of the enhanced histogram algorithm.

DIRECTION OF ARRIVAL ESTIMATION BASED ON SMOOTH MUSIC ALGORITHM COMBINED SPECTRUM SELECTION TECHNIQUES OF NOISE CHARACTERISTICS OF MARINE TARGETS EQUIPPED PROPELLER

This article demonstrates a proposal for a direction of arrival (DOA) estimation algorithm for passive sonar systems based on the combination of the smooth multiple signal classification (Smooth MUSIC) algorithm and frequency bin selection (BS) of the sound of marine propeller-equipped targets, so-called BS-SMUSIC. The harmonics of propeller shaft and blade frequencies are considered useful information for detecting targets and estimating their parameters, including DOA. Low frequency analysis recording (LOFAR) is utilized to implement BS. By analyzing MUSIC-based algorithm together BS, passive DOA estimation algorithms have been significantly improved. Simulation results have been given in both cases: uncorrelated and correlated sources. Outcomes demonstrate that the BS-SMUSIC algorithm has the best performance in comparison to three MUSIC-based algorithms (MUSSIC, Modified MUSIC and Root MUSIC) in all investigation cases: narrow band signals at 5 dB of signal to noise (SNR); wideband signals at -5 dB of SNR. Besides, BS-SMUSIC algorithm also archives the lowest root mean square error (RMSE) in SNR range -5 dB to 20 dB. In the SNR range, the RMSE of BS-SMUSIC algorithm remains stable and is about 0.3 ◦ at -5 dB of SNR. This performance reflects its ability to ensure stable operation, super resolution and high accuracy of BS-SMUSIC algorithm for the passive sonar systems.

A Novel DOA Estimation Algorithm Based on Robust Mixed Fractional Lower-Order Correntropy in Impulsive Noise

The estimation of direction of arrival (DOA) is paramount in the realm of practical array signal processing systems. Nevertheless, traditional estimation methods often rely heavily on the Gaussian noise assumption, rendering them ineffective in achieving high-precision estimates in environments plagued by strong impulsive noise. To address this challenge, this paper introduces a novel DOA estimation algorithm that leverages mixed fractional lower-order correntropy (MFLOCR) in the context of Alpha-stable distributed impulsive noise. Correntropy is used as a measure of the similarity of the signals, using a Gaussian function to smooth extreme values and provide greater robustness against impulsive noise. By utilizing diverse kernel lengths to jointly regulate the kernel function, the concept of correntropy is expanded and implemented in the fractional lower-order moment (FLOM) algorithm for received signals. Subsequently, the MFLOCR is derived by adjusting the resulting form of correntropy. Finally, an enhanced DOA estimation algorithm is proposed that combines the MFLOCR operator with the MUSIC algorithm, specifically tailored for impulsive noise environments. Furthermore, a proof of boundedness is provided to validate the effectiveness of the proposed approach in such noisy conditions. Simulation experiments confirmed that the proposed method outperforms existing DOA estimation methods in the context of intense impulsive noise, a low generalized signal-to-noise ratio (GSNR), and a smaller number of snapshots.

Joint parameter estimation algorithm for polarization-sensitive channel compression arrays based on atomic norm minimization

To reduce the complexity of direction-of-arrival (DOA) algorithms in polarization-sensitive arrays and maintain high estimation accuracy while decreasing runtime, this paper proposes a channel compression model based on orthogonal dipole arrays. In addition, a DOA estimation algorithm using atomic norm minimization (ANM) is introduced for this model. This algorithm performs eigenvalue decomposition on the covariance matrix of the data received from the polarization-sensitive channel compressed array. A new observation vector is constructed for the ANM problem under the channel compression model using the obtained eigenvalues and eigenvectors. Subsequently, a Toeplitz matrix is constructed from the optimal solution of the semi-positive definite programming (SDP) problem. The Vandermonde decomposition of the Toeplitz matrix provides estimates of the signal DOA parameters. By combining the vectorization result of the covariance matrix and the least-squares calculation, the polarization auxiliary angle and polarization phase angle information of the incident source are also obtained. Simulation experiments compare the root-mean-squared error (RMSE) of each algorithm at different angular intervals and signal-to-noise ratios (SNR) to confirm the validity of estimating DOA and polarization parameters.

Motion-guided large aperture ULA to enhance DOA estimation: An inverse synthetic aperture perspective

Direction-of-arrival (DOA) estimation is a critical issue in array signal processing, especially in radar applications. However, the array aperture of high-frequency radars is constrained by the site and platform, which in turn leads to limited DOA estimation performance. In this paper, inspired by the inverse synthetic aperture radar, we design a novel DOA estimation method based on motion-guided large-aperture uniform linear array (ULA). Referring to the concept of inverse synthetic aperture, the novel method utilizes the relative motion between the radar and the target to construct a larger ULA. We demonstrate that the key condition for reconstructing ULAs is suitable data segmentation and reshaping within the coherent integration time. However, the correct segmentation position is related to the target's motion trajectory. For non-cooperative targets, the uncertain segmentation position is regarded as a mismatch problem between the steering and weighting vectors, such that the spatial spectrum becomes a product of two sinc-like functions. With the analysis of the main lobe and grating lobes, the maximum peak-to-grating-lobe ratio criterion is introduced to find the ambiguity-free DOA. The experimental results demonstrate the performance advantages of the proposed DOA estimation algorithm in terms of noise robustness and resolution.

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.

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

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.