Direction Of Arrival Estimation Accuracy Research Articles

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°.

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.

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.

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.

Direction‐of‐arrival estimation in coprime linear array using three uniform linear arrays considering mutual coupling

AbstractNowadays, sparse arrays have been a focus for direction‐of‐arrival (DOA). The existing arrays can achieve high degree of freedom (DOF) bigger than the number of sensors when using the spatial smoothing methods. However, the small inter‐element spacing degrades the DOA estimation accuracy when facing severe mutual coupling. In order to alleviate mutual coupling, a coprime linear array using three uniform linear arrays (CLA‐U3) is proposed. The expression of sensor locations is given, and the analysis of DOF is considered. The minimum subarray inter‐element spacing in CLA‐U3 is bigger than that of the existing arrays, which means that CLA‐U3 can be less sensitive to mutual coupling. Moreover, the difference co‐subarrays can fill each other's holes, so CLA‐U3 and other sparse arrays composed of three subarrays have close DOF. Simulation experiments prove the favourable performance of DOA estimation.

An effective DOA estimation method for low SIR in small-size hydrophone array

The estimation ability of traditional direction of arrival (DOA) estimation methods is relatively fragile in small-size hydrophone arrays with limited space. Especially in low signal to interference ratio (SIR), the strong interference signals may submerge some weak signals of interest (SOI) and make DOA estimation difficult in response to this issue. This paper introduces an improved sparse DOA estimation method for practical multi-objective DOA estimation in complex scenarios. The main work is to introduce a noise weight constraint in the sparse iterative covariance process. It leads the algorithm to output sparse peaks and smooth spatial energy spectra and achieve faster fitting while reducing the probability of false peaks. The algorithm can complete DOA estimation of the multi-target reliably without prior information of sources. Then, we propose a fast region grid refinement method based on allocation reconstruction to increase angle resolution. The method increases the accuracy of multi-objective DOA estimation while reducing computational costs. Finally, simulation and experiment have verified the method's effectiveness.

DOA estimation of coherent signals in underdetermined problems using sparse-based Toeplitz covariance reconstruction

Direction-Of-Arrival (DOA) estimation in environments with coherent sources is a challenging problem, when the number of narrowband sources is more than elements and current coherent algorithms cannot accurately overcome such underdetermined problems. In this paper, we propose the Sparse-based Toeplitz Covariance Reconstruction (STCR) algorithm, which obtains a hole-free extended-aperture array with increased Degrees of Freedom (DOF) by exploiting a minimum redundancy array. This method provides superiority in estimating coherent sources by Toeplitz covariance matrix reconstruction. Also, using a Sparse Signal Representation (SSR) framework makes the DOA estimator stronger in source detection and robust to the noise power. Numerical results show the effectiveness of the proposed method even at low SNRs for over- and underdetermined DOA estimators compared to well-known methods. Also, it has high accuracy in DOA estimation of closely-located coherent sources using a small number of snapshots.

Fast and accurate wideband sparse spatial spectrum estimation in an underwater strong interference environment.

Wideband sparse spatial spectrum estimation is an important direction-of-arrival (DOA) estimation method that can obtain a high resolution with few snapshots and a low signal-to-noise ratio. However, in an underwater strong interference environment, the accuracy of DOA estimation may be seriously affected, and even the weak targets could be completely masked. In this paper, we propose a fast matrix filter design method based on truncated nuclear norm regularization to attenuate strong interferences while passing weak targets. The matrix filter operator and the exact covariance matrix after filtering can be obtained simultaneously by solving a convex optimization problem that contains the output power term and non-Toeplitz error propagation control term. Then the modified sparse spectrum fitting algorithm based on the matrix filter is used to estimate spatial spectrum over closely spaced wideband signals. Compared with existing methods, the proposed method achieves higher DOA estimation accuracy and lower computational time for matrix filter design. Meanwhile, the estimation accuracy of the proposed method is verified with the experimental results.

High-resolution DOA estimation in the hydrophone array shape with uncertainty based on dynamic compressed sensing

Compressed sensing (CS) technology is a popular method for the direction of arrival (DOA) estimation of underwater acoustic radiation noise due to its high resolution. However, in practical applications such as buried arrays and other arrays, uncertainty in the hydrophone array shape can lead to model mismatch which significantly reduces DOA estimation accuracy. This paper focuses on high-resolution wideband DOA estimation in the radiated noise from underwater targets of interest using dynamic compressed sensing. The study introduces phase error into the signal model to simulate the model mismatch, and improves DOA estimation accuracy by jointly estimating both the DOA and phase error. Simulation results demonstrate that the proposed algorithm is effective in improving the accuracy of DOA estimation.

Robust Sparse Bayesian Two-Dimensional Direction-of-Arrival Estimation with Gain-Phase Errors

To reduce the influence of gain-phase errors and improve the performance of direction-of-arrival (DOA) estimation, a robust sparse Bayesian two-dimensional (2D) DOA estimation method with gain-phase errors is proposed for L-shaped sensor arrays. The proposed method introduces an auxiliary angle to transform the 2D DOA estimation problem into two 1D angle estimation problems. A sparse representation model with gain-phase errors is constructed using the diagonal element vector of the cross-correlation covariance matrix of two submatrices of the L-shaped sensor array. The expectation maximization algorithm derives unknown parameter expression, which is used for iterative operations to obtain off-grid and signal precision. Using these parameters, a new spatial spectral function is constructed to estimate the auxiliary angle. The obtained auxiliary angle is substituted into a sparse representation model with gain and phase errors, and then the sparse Bayesian learning method is used to estimate the elevation angle of the incident signal. Finally, according to the relationship of the three angles, the azimuth angle can be estimated. The simulation results show that the proposed method can effectively realize the automatic matching of the azimuth and elevation angles of the incident signal, and improves the accuracy of DOA estimation and angular resolution.

UNet-rootMUSIC: A high accuracy direction of arrival estimation method under array imperfection

In the practical direction-finding systems, the accuracy and resolution of the direction of arrival (DOA) estimation are affected not only by the Gaussian noise and array size but also by hardware configuration imperfections, such as errors in element manufacturing and mounting. These impairments cause phase and amplitude errors in estimating the DOA of signal sources. To address this issue, this paper proposes to combine a U-shape deep neural network (UNet) with the multiple signal classification via the root of the polynomial (rootMUSIC) algorithm (so-called UNet-rootMUSIC) to improve the DOA estimation accuracy. In this approach, the UNet model plays a role in converting a covariance matrix of received signals containing phase and gain errors into a nearly perfect one of the ideal antenna array. The rootMUSIC algorithm is then employed to estimate the signal DOA based on the converted covariance matrix. The DOA estimation performance of the uniform linear array of eight elements with an inter-element distance of λ/2 is analyzed through experimental simulations. The simulation results demonstrate that our method can significantly reduce the root mean square error of DOA estimation compared to the conventional MUSIC, rootMUSIC, ESPRIT methods and two deep neural network-based angular classification methods.

Fast DOA Estimation Algorithms via Positive Incremental Modified Cholesky Decomposition for Augmented Coprime Array Sensors.

This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling on the augmented array to generate a non-uniform, discontinuous virtual array. It then utilizes interpolation to convert this into a uniform, continuous virtual array. Based on this, the problem of DOA estimation is equivalently formulated as a gridless optimization problem, which is solved via atomic norm minimization to reconstruct a Hermitian Toeplitz covariance matrix. Furthermore, by positive incremental modified Cholesky decomposition, the covariance matrix is transformed from positive semi-definite to positive definite, which simplifies the constraint of optimization problem and reduces the complexity of the solution. Finally, the Multiple Signal Classification method is utilized to carry out statistical signal processing on the reconstructed covariance matrix, yielding initial DOA angle estimates. Experimental outcomes highlight that the PI-CANM algorithm surpasses other algorithms in estimation accuracy, demonstrating stability in difficult circumstances such as low signal-to-noise ratios and limited snapshots. Additionally, it boasts an impressive computational speed. This method enhances both the accuracy and computational efficiency of DOA estimation, showing potential for broad applicability.

Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

Deep learning-based DOA estimation for hybrid massive MIMO receive array with overlapped subarrays

As massive MIMO is a key technology in the future sixth generation (6G), the large-scale antenna arrays are widely considered in direction-of-arrival (DOA) estimation for they can provide larger aperture and higher estimation resolution. However, the conventional fully digital architecture requires one radio-frequency (RF) chain per antenna, and this is challenging for the high hardware costs and much more power consumption caused by the large number of RF chains. Therefore, an overlapped subarray (OSA) architecture-based hybrid massive MIMO array is proposed to reduce the hardware costs, and it can also have better DOA estimation accuracy compared to non-overlapped subarray (NOSA) architecture. The simulation results also show that the accuracy of the proposed OSA architecture has 6^{circ } advantage over the NOSA architecture with signal-to-noise ratio (SNR) at 10 dB. In addition, to improve the DOA estimation resolution, a deep learning (DL)-based estimator is proposed by combining convolution denoise autoencoder (CDAE) and deep neural network (DNN), where CDAE can remove the approximation error of sample covariance matrix (SCM) and DNN is used to perform high-resolution DOA estimation. From the simulation results, CDAE-DNN can achieve the accuracy lower bound at textrm{SNR}=-8 dB and the number of snapshots N=100, this means it has better performance in poor communication situation and can save more software resources compared to conventional estimators.

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.

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.

Single acoustic vector sensor DOA enhanced by unsaturated bistable stochastic resonance with linear amplitude response constrained

Acoustic vector sensors (AVS) are increasingly utilized for remote target passive perception, but accurate direction-of-arrival (DOA) estimation remains a formidable challenge, particularly in the presence of heavy background noise. In this paper, we propose a novel DOA estimation method that utilizes complex acoustic intensity measurements (CAIM) and unsaturated bistable stochastic resonance with linear amplitude response constrained (LAR-UBSR). The proposed method aims to exploit the excellent denoising performance of stochastic resonance (SR) to enhance the accuracy of DOA estimation. The proposed LAR-UBSR method is based on the theoretical analysis of the signal pre-processing requirements of CAIM, which determines the linear amplitude response and fixed phase shift. LAR-UBSR achieves a stable phase shift and linear amplitude response by utilizing the unsaturated potential well and limited potential parameters adjustment method of SR. We analyze the amplitude response linearity of LAR-UBSR under different signal-to-noise ratios (SNRs) and a wide range of frequencies, demonstrating a larger linear amplitude response interval that meets the signal pre-processing requirements of CAIM. Numerical analysis and application verification show that the proposed DOA method outperforms existing methods, particularly under low SNR conditions. The results suggest the potential for high-accuracy DOA estimation using nonlinear signal processing strategies in the presence of heavy background noise.

A Novel Nested Array Structure for DOA Based on CCM of Subarrays

An innovative nested array structure that can notably increase the DOF and the linear arrays’ direction of arrival (DOA) estimated performance is proposed. For the conventional nested array, we vectorize the ACM’s output of the whole array and then remove the repeated rows to get a virtual array’s output. In contrast with classical nested arrays, the superiority of the new nested array is that it utilizes the combination of reverse ordering and conjugation of the inner uniform linear array (ULA) for one of the two subarrays and the sparse outer ULA for another to increase the array aperture. This means the outer sparse ULA’s sensor spacing is approximately the length of the entire inner ULA in the classical nested array structure. Yet, it is about twice the length in the new nested array structure. We generate one lengthy consecutive virtual uniform array excluding any redundant virtual sensors by vectorizing the two subarrays’ cross-correlation matrix (CCM), which is mentioned above. With the export signal of the virtual array and its conjugate form of it, an equivalent covariance matrix of full rank is constructed, which is called the Toeplitz matrix, to compensate for the rank lack of the virtual array’s ACM. For the sake of obtaining the DOA of input signals, the conventional DOA estimation method will be implemented on the ACM. The increase in outer sparse ULA’s sensor spacing ensures an increase in virtual array aperture in principle, which means it is capable of increasing the number of DOA estimations, which is called DOF, and optimizing the DOA estimated performance in contrast with the ULA and classical nested arrays. Results from trials certify the preponderance of the proposed structure in the aspect of DOF and the accuracy of DOA estimation.