Direction Of Arrival Estimation Problem 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.

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.

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

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.

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.

Data-Driven DOA Estimation Methods Based on Deep Learning for Underwater Acoustic Vector Sensor Array

Abstract Direction of arrival (DOA) estimation is a fundamental problem in underwater acoustic vector sensor array signal processing. Because of the advantages of deep learning technology, this paper proposes two categories of data-driven DOA estimation methods for underwater acoustic vector sensor array, which transform the DOA estimation problem into a neural network classification problem. Specifically, one is the DOA estimation method of convolutional neural network based on teacher-student noise reduction (TS-CNN), which considers the covariance matrix as the training data set; the other is a DOA estimation method based on long-short term memory network and attention mechanism (LSTM-ATT), which applies the time-domain signal as the training data set. The experimental simulation results show that: 1) when the number of array elements is small, the accuracy of the DOA estimation method based on TS-CNN is equivalent to that of traditional methods, and it can effectively suppress the influence of noise when the signal-to-noise ratio (SNR) is low; 2) the accuracy of DOA estimation method based on LSTM-ATT is much higher than that of traditional Multiple Signal Classification method, especially in the case of low SNR, which also proves the importance of temporal characteristics for DOA estimation in a real environment.

A Robust Direction of Arrival Estimation Method for Coherently Distributed Sources in an Impulsive Noise Environment

In this work, a computationally efficient evolutionary algorithm is proposed for estimating the direction of arrival (DOA) of coherently distributed sources corrupted by additive impulsive noise. The typical method, such as distributed signal parameter estimation method, requires a two-dimensional spectral peak search, and cannot allow for coherent signals. The proposed method in this paper employs an infinite norm normalization combined with the maximum likelihood criteria. The resulting cost function is solved using the introduced multimodal quantum-inspired benchmarking algorithm, which obviously reduces the computational complexity without grid errors. The Cramér-Rao bound for the considered DOA estimation problem is also derived. Finally, numerical simulations are conducted to show that our algorithm can perform superior robustness and allow for coherent signals without any additional process compared to alternative approaches for the considered scenarios. In addition, the proposed scheme can be popularized to address other DOA estimation problems and promote the development of DOA estimation.

Bayesian Direction of Arrival Estimation with Prior Knowledge from Target Tracker

The performance of traditional direction of arrival (DOA) estimation methods always deteriorates at a low signal-to-noise ratio (SNR) or without sufficient observations. This paper investigates the Bayesian DOA estimation problem aided by the prior knowledge from the target tracker. The Bayesian Cramér–Rao lower bounds (CRLB) and the expected CRLB are first derived to evaluate the theoretical performance of Bayesian DOA estimation. Based on the maximum a posterior (MAP) estimator in the Bayesian framework, two methods are proposed. One is a two-step grid search method for a single target DOA case. The other is a gradient-based iterative solution for multiple targets DOA case, which extends the traditional Newton method by incorporating the prior knowledge. We also propose a minimum mean square error (MMSE) estimator using a Monte Carlo method, which requires trading off accuracy against computational complexity. By comparing with the maximum likelihood (ML) estimators and the MUSIC algorithm, the proposed three Bayesian estimators improve the DOA estimation performance in low SNR or with limited snapshots. Moreover, the performance is not affected by the correlation between sources.

Cramer-Rao bound investigation of a novel virtually extended nested arc array for 2D DOA estimation

This paper exploits a sparse array representation, a novel nested arc array, to generate a virtual non-uniform circular arrays that have been presented and investigated. To increase the array aperture, the virtual array has been developed using higher-order statistics, namely, the Forth-Order Cumulants (FOC). The extended array contains a combination of physical as well as virtual sensors. The increased degrees of freedom (DOFs) in the resultant virtual array make it suitable for over-and under-determined direction of arrival (DOA) estimation. The Cramer-Rao bound (CRB) and the (DOA) estimation for such an array are developed and investigated for various arrays. The proposed array performance is superior to that of the uniform one. Further, the offered array is suitable for two-dimensional (2D) DOA estimation problems.

DOA estimation for uniform circular array without the source number based on beamspace transform and higher-order cumulant

Fourth-order cumulant is one of most widely used high-order cumulant for direction of arrival (DOA) estimation due to its ability of expanding the virtual array aperture as well as suppressing Gaussian noise. To address the two-dimensional (2D) DOA estimation problem, we propose a modified MUSIC scheme for uniform circular array (UCA) in this paper. Firstly, the fourth-order cumulant of UCA is considered to construct a new propagator, resulting in the elimination of a priori knowledge of the number of signals. Secondly, the UCA is transformed by beamspace transformation, reducing the time computational complexity of the algorithm since the two-dimensional grid search and singular value decomposition are avoided. And finally a low-rank recovery algorithm is adopted to improve the accuracy regarding the limited snapshots scenario. The numerical simulations validate the superiority of the proposed method.

Improved block sparse Bayesian learning based DOA estimation for massive MIMO systems

Direction-of-arrival (DOA) estimation is crucial for suppressing inter-cell interference in massive multiple-input multiple-output (MIMO) systems. However, conventional algorithms are unsuitable for low signal-to-noise ratio (SNR) and a small number of snapshots. Consequently, in an attempt to achieve fast reconstruction speed while ensuring high accuracy, this study proposes an improved block sparse Bayesian learning-based DOA estimation algorithm for two-dimension massive MIMO systems. Using the sparse characteristics and inherent structure of the signal, the DOA estimation problem is transformed to a joint task of sparse signal reconstruction and parameter optimization. Subsequently, the estimation accuracy is improved through complete excavation and learning of the signal temporal structure. In addition, to avoid the direct solution of the posterior probability distribution, reduce the number of iterations and increase the reconstruction speed, variational inference is used to approximate the Bayesian model and solve the joint problem through parameter learning. Moreover, the auxiliary angle is introduced to avoid extra angle matching, which further reduces the complexity. Simulations are performed to verify the proposed method and the results prove its superiority when applied to massive MIMO systems compared with some existing DOA estimation algorithms.

Direction of arrival estimation of unknown emitter by deep neural networks with array imperfections

AbstractIn array signal processing, high‐resolution direction‐of‐arrival (DOA) estimation by eigendecomposition method requires knowledge of the array covariance matrix and an exact characterisation of the array. The dependence of most such methods on the array manifold substantially degrades their array performance when the actual sensors deviate from their assumed nominal values. This article aims at formulating a deep neural network framework for DOA estimation with feasible computational complexity. The two‐stage algorithm is composed of a detection network and a series of parallel DOA estimation networks: the multilayer perceptron is trained to detect the presence of one or more sources in an angular sector at the first stage, the DOA estimation networks then estimate their respective DOAs at the second stage. When a single type of array imperfection is considered, numerical results reveal that the DNN‐based method can obtain DOA estimates with much higher precision than the existing techniques for significant location errors and gain/phase perturbations, they also illustrate the potential usefulness of the proposed algorithm towards better DOA estimation accuracy for mutual coupling as the mutual coupling matrix is not simplified. Moreover, the proposed method is finally extended to deal with the DOA estimation problem when multiple types of array perturbations coexist.

Gridless DOA Estimation With Multiple Frequencies

Direction-of-arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this paper, the continuous (gridless) DOA estimation problem with multiple frequencies is considered. This problem is formulated as an atomic norm minimization (ANM) problem. The ANM problem is equivalent to a semi-definite program (SDP) which can be solved by an off-the-shelf SDP solver. The dual certificate condition is provided to certify the optimality of the SDP solution so that the sources can be localized by finding the roots of a polynomial. We also construct the dual polynomial to satisfy the dual certificate condition and show that such a construction exists when the source amplitude has a uniform magnitude. In multi-frequency ANM, spatial aliasing of DOAs at higher frequencies can cause challenges. We discuss this issue extensively and propose a robust solution to combat aliasing. Numerical results support our theoretical findings and demonstrate the effectiveness of the proposed method.

MCRB on DOA Estimation for Automotive MIMO Radar in the Presence of Multipath

Autonomous driving and advanced active safety features require accurate high-resolution sensing capabilities. Automotive radars are the key component of the vehicle sensing suit. However, when these radars operate in proximity to flat surfaces, such as roads and guardrails, they experience a multipath phenomenon that can degrade the accuracy of the direction-of-arrival (DOA) estimation. Presence of multipath leads to misspecification in the radar data model, resulting in estimation performance degradation, which cannot be reliably predicted by conventional performance bounds. In this paper, the misspecified Cramér-Rao bound (MCRB), which accounts for model misspecification, is derived for the problem of DOA estimation in the presence of multipath which is ignored by the estimator. Analytical relations between the MCRB and the Cramér-Rao bound are established, and the DOA estimation performance degradation due to multipath is investigated. The results show that the MCRB reliably predicts the asymptotic performance of the misspecified maximum-likelihood estimator and therefore, can serve as an efficient tool for automotive radar performance evaluation and system design.

A Novel DOA Estimation for Low-Elevation Target Method Based on Multiscattering Center Equivalent Model

The multipath in very high-frequency (VHF)radar will reduce the direction-of-arrival (DOA) estimation accuracy for the low-angle target following. Since the target and multipath signals have strong coherence in the spatial domain, it is challenging to distinguish them accurately. Especially in some terrain complex regions, various scattering media cause the multipath echo exhibit the multi-channel and nonuniform energy distribution features. Therefore, the single multipath DOA estimation methods will mismatch the actual signal, resulting in inaccurate DOA estimation. The current letter presents a new DOA estimation approach using a multiple scattering center model in complex terrain to solve the mentioned issue. In the presented method, multiple multipath is analogous to a single one based on the multipath signal’s spatial coherence. The equivalent model represents the DOA estimation problem with a parametric optimization problem, and the accurate estimation results can be attained using the Newton optimization approach. Compared with the conventional sparse reconstruction method, the presented method is not restricted by the Restricted Isometry Property (RIP), and employs a robust parameter estimation method to solve the angle super-resolution problem under the low signal-to-noise ratio (SNR). The experimental results reflect that the presented model and approach can efficiently promote the DOA estimation precision and calculational performance compared to conventional DOA estimation approaches.

DOA Estimation for Massive MIMO Systems with Unknown Mutual Coupling Based on Block Sparse Bayesian Learning.

Obtaining accurate angle parameters using direction-of-arrival (DOA) estimation algorithms is crucial for acquiring channel state information (CSI) in massive multiple-input multiple-output (MIMO) systems. However, the performance of the existing algorithms deteriorates severely due to mutual coupling between antenna elements in practical engineering. Therefore, for solving the array mutual coupling, the array output signal vector is modeled by mutual coupling coefficients and the DOA estimation problem is transformed into block sparse signal reconstruction and parameter optimization in this paper. Then, a novel sparse Bayesian learning (SBL)-based algorithm is proposed, in which the expectation-maximum (EM) algorithm is used to estimate the unknown parameters iteratively, and the convergence speed of the algorithm is enhanced by utilizing the approximate approximation. Moreover, considering the off-grid error caused by discretization processes, the grid refinement is carried out using the polynomial roots to realize the dynamic update of the grid points, so as to improve the DOA estimation accuracy. Simulation results show that compared with the existing algorithms, the proposed algorithm is more robust to mutual coupling and off-grid error and can obtain better estimation performance.

A low-complexity two-dimensional DOA estimation algorithm based on an L-shaped sensor array

In this paper, a derivative-based MUSIC (multiple signal classification) algorithm for a mixture of circular and noncircular signals (DB-MUSIC-M) is proposed for two-dimensional (2D) direction of arrival (DOA) estimation employing an L-shaped uniform array. The DB-MUSIC-M transforms the 2D DOA estimation problem into a single one-dimensional (1D) estimation by finding the derivative of the objective function of the 2D improved MUSIC (I-MUSIC) algorithm, which greatly reduces its computational complexity. As it utilizes both the pseudo covariance matrix and the covariance matrix of the array data, the maximum number of signals that can be estimated is much higher than the total number of sensors. As a special case, the derivative-based MUSIC (DB-MUSIC) for circular signals is also proposed. There is no need for angle pairing for the proposed algorithms and they can handle the angle ambiguity problem effectively. As shown by simulation results, the proposed DB-MUSIC-M algorithm outperforms existing algorithms, with significantly reduced complexity compared to a direct 2D search method. Moreover, the proposed approach can be applied to some other array structures such as the uniform planar array.

Low-Complexity One-Bit DOA Estimation for Massive ULA with a Single Snapshot

Existing one-bit direction of arrival (DOA) estimate methods based on sparse recovery or subspace have issues when used for massive uniform linear arrays (MULAs), such as high computing cost, estimation accuracy depending on grid size, or high snapshot-number requirements. This paper considers the low-complexity one-bit DOA estimation problems for MULA with a single snapshot. Theoretical study and simulation results demonstrate that discrete Fourier transform (DFT) can be applied to MULA for reliable initial DOA estimation even when the received data are quantized by one-bit methods. A precise estimate is then obtained by searching within a tiny area. The resulting method is called one-bit DFT. This method is straightforward and simple to implement. High-precision DOA estimates of MULA can be obtained with a single snapshot, and the computational complexity is significantly less than that of existing one-bit DOA estimation methods. Moreover, the suggested method is easily extensible to multiple snapshot scenarios, and increasing the number of snapshots can further improve estimation precision. Simulation results show the effectiveness of the one-bit DFT method.

Direction of arrival estimation under Class A modelled noise in shallow water using variational Bayesian inference method

The shallow water noise shows obvious impulsive property, which greatly degrades the direction of arrival (DOA) performance due to the conventional design concept based on the Gaussian assumption. In this paper, DOA estimator in presence of impulsive noise utilising variational Bayesian inference is proposed. The Middleton's Class A noise model is considered as a typical underwater noise model to analyse the performance of DOA estimation. The DOA estimation problem is modelled as the sparse signal recovery problem, and the hierarchical Bayesian learning framework is formulated by considering the common sparsity of signal and the element-wise sparsity of the impulsive noise. The variational Bayesian inference realises the posterior estimation of signal and impulsive noise components. To mitigate the basis mismatches, the root sparse Bayesian learning method is applied to refine the steering vectors. Simulations verify the advantages of the proposed DOA method in terms of spatial resolution, root mean square error, accuracy, and robustness compared with the state-of-the-art benchmarks in the presence of Middleton's Class A noise.

Robust high-resolution direction-of-arrival estimation method using DenseBlock-based U-net.

Direction-of-arrival (DOA) estimation is widely used in underwater detection and localization. To address the high-resolution DOA estimation problem, a DenseBlock-based U-net structure is proposed in this paper. U-net is a U-shaped fully convolutional neural network, which yields a two-dimensional image. DenseBlock is a more efficient structure than typical convolutional layers. The proposed network replaces the concatenated convolutional layers in the original U-net with DenseBlocks. Through training, the network can remove the interference of sidelobes and noise in a conventional beam forming bearing-time record (BTR) and get a clean BTR; hence, this method has narrow beam width and few sidelobes. In addition, the network can be trained by simulation data and applied in actual data when the simulated and actual data are similar in BTR features, so the method has high generalization. For a multi-target problem, the network does not need to be trained on all cases with different target quantities and therefore can reduce the training set size. As a data-driven method, it does not rely on prior assumptions of the array model and possesses better robustness to array imperfections than typical model-based DOA algorithms. Simulations and experiments verify the advantages of the proposed method.