Direction Of Arrival Estimation Performance Research Articles

Direction-of-arrival and power spectral density estimation using a single directional microphone and group-sparse optimization

In this paper, two approaches are proposed for estimating the direction of arrival (DOA) and power spectral density (PSD) of stationary point sources by using a single, rotating, directional microphone. These approaches are based on a method previously presented by the authors, in which point source DOAs were estimated by using a broadband signal model and solving a group-sparse optimization problem, where the number of observations made by the rotating directional microphone can be lower than the number of candidate DOAs in an angular grid. The DOA estimation is followed by the estimation of the sources’ PSDs through the solution of an overdetermined least squares problem. The first approach proposed in this paper includes the use of an additional nonnegativity constraint on the residual noise term when solving the group-sparse optimization problem and is referred to as the Group Lasso Least Squares (GL-LS) approach. The second proposed approach, in addition to the new nonnegativity constraint, employs a narrowband signal model when building the linear system of equations used for formulating the group-sparse optimization problem, where the DOAs and PSDs can be jointly estimated by iterative, group-wise reweighting. This is referred to as the Group-Lasso with l_1-reweighting (GL-L1) approach. Both proposed approaches are implemented using the alternating direction method of multipliers (ADMM), and their performance is evaluated through simulations in which different setup conditions are considered, ranging from different types of model mismatch to variations in the acoustic scene and microphone directivity pattern. The results obtained show that in a scenario involving a microphone response mismatch between observed data and the signal model used, having the additional nonnegativity constraint on the residual noise can improve the DOA estimation for the case of GL-LS and the PSD estimation for the case of GL-L1. Moreover, the GL-L1 approach can present an advantage over GL-LS in terms of DOA estimation performance in scenarios with low SNR or where multiple sources are closely located to each other. Finally, it is shown that having the least squares PSD re-estimation step is beneficial in most scenarios, such that GL-LS outperformed GL-L1 in terms of PSD estimation errors.

Assistant vehicle locating based on DOA estimation of deep unfolded network

In view of the decline in the positioning accuracy of the vehicles with small snapshots, this paper proposes a direction of arrival(DOA) estimation method based on deep unfolded network to assist the global positioning system to achieve high-precision locating. Firstly, the signal emitted from the on board unit installed on the vehicle is received by the array antenna of the road side unit(RSU), then RSU transmits the array data to cloud service platform, in which the traditional fixed point continuation algorithm is improved by using l1 norm instead of l2 norm, and the adaptive outlier point tracking algorithm is used to deal with the problem of symbol flipping caused by noise. Then we unfold the improved fixed point continuous algorithm for obtaining a neural network. In order to improve the DOA estimation performance and convergence speed, this paper uses the black widow optimization algorithm to determine the soft threshold shrinkage parameters. According to the mapping between the signal and the array manifold matrix, the DOA of the target is estimated, and its location can be evaluated from the geometry relation between vehicle and RSU. The simulation results show that the algorithm proposed in this paper has better direction finding performance and improves the vehicle positioning accuracy under small snapshots and high signal-to-noise ratio effectively.

Hole‐free sparse array for highly efficient direction of arrival estimation: Enhanced uniform difference co‐array

AbstractSparse arrays with sensors can offer number of degrees of freedom by exploiting the difference co‐array that can be obtained from the second‐order statistics of received signals. In this article, a novel sparse array with seven subarrays (SA‐7S) by carefully assembling the subarrays is proposed, and the resulting SA‐7S can generate a hole‐free uniform difference co‐array. The sensor locations of the SA‐7S array are uniquely determined by a closed‐form expression and the number of achievable degrees of freedom is analytically presented as well. Theoretical analysis shows that the SA‐7S can provide a higher number of degrees of freedom than most sparse linear arrays. Simulations are performed to validate the advantage of the proposed array in terms of uDOFs, mutual coupling and direction of arrival estimation performance.

Low-Rank and Row-Sparse Decomposition for Joint DOA Estimation and Distorted Sensor Detection

Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. We consider an array model within which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array model, the problem of joint direction-of-arrival (DOA) estimation and distorted sensor detection is formulated under the framework of low-rank and row-sparse decomposition. We derive an iteratively reweighted least squares (IRLS) algorithm to solve the resulting problem. The convergence property of the IRLS algorithm is analyzed by means of the monotonicity and boundedness of the objective function. Extensive simulations are conducted regarding parameter selection, convergence speed, computational complexity, and performances of DOA estimation as well as distorted sensor detection. Even though the IRLS algorithm is slightly worse than the alternating direction method of multipliers in detecting the distorted sensors, the results show that our approach outperforms several state-of-the-art techniques in terms of convergence speed, computational cost, and DOA estimation performance.

Deep learning-based Direction-of-arrival estimation for far-field sources under correlated near-field interferences

This paper proposes a deep learning-based Direction-of-arrival (DOA) estimation to detect interfered far-field sources. The proposed method consists of a near-field interference rejection network (NFIRnet) and a DOA estimation network (DOAnet). The NFIRnet calculates the near-field components of the covariance matrix by convolutional neural networks with the proposed complex mapper. The near-field components are rejected from the covariance matrix. The DOAnet removes the residuals of the interferences by the proposed self-spatial attention network and estimates the DOAs of the interfered far-field sources. Computer simulations demonstrated that the proposed method had better DOA estimation performance than the conventional methods.

New Array Designs for DoA Estimation of Non-Circular Signals With Reduced Mutual Coupling

Recently, many sparse arrays are proposed to achieve increased uniform degrees of freedom (uDoFs) for the direction of arrival (DoA) estimation of non-circular sources. In light of this recent attention, the high number of uDoFs is the primary motivation for designing those sparse array structures. Although both the number of uDoF and mutual coupling can influence the DoA estimation performance. However, mutual coupling is not considered in many of those sparse array configurations. In this paper, two optimized shifted coprime arrays with sum-difference coarrays, called OSCAwSDCa-I and OSCAwSDCa-II, are proposed to reduce mutual coupling. The OSCAwSDCa-I and OSCAwSDCa-II are obtained by rearranging actual sensors of the augmented coprime array. The proposed array designs have closed-form expressions for their sensor locations and achievable uDoFs. Additionally, it is proven that the first three weights of OSCAwSDCa-II are independent of the array size. Moreover, the number of virtual sensors co-locating at the same lag is reduced. Consequently, smaller weight values are obtained, resulting in more robustness against mutual coupling. Finally, extensive simulations show that OSCAwSDCa-I and OSCAwSDCa-II can achieve comparable uDoFs concerning the existing array structures. In the presence of strong mutual coupling, simulation results demonstrate the robustness of OSCAwSDCa-II more than other compared configurations.

Positioning and Contour Extraction of Autonomous Vehicles Based on Enhanced DOA Estimation by Large-Scale Arrays

As an important branch of internet of vehicle (IoV) systems, autonomous vehicle (AV) positioning based on direction-of-arrival (DOA) estimation has received extensive attention in recent years. In this paper, an AV positioning method under unknown mutual coupling is proposed within the framework of large-dimensional asymptotic theory (LAT). Firstly, enhanced and closed-form DOA estimation is achieved by jointly exploiting large-scale uniform linear arrays (ULAs), Toeplitz rectification and the phase transformation result associated with the sample covariance matrix; secondly, a more reliable subset/set of DOAs is constructed according to the signal-to-noise at receivers; finally, robust AV positioning is achieved with the reliable subset/set. Motivated by satisfactory DOA estimation performance, an AV contour extraction scheme is developed with the aid of two antennas installed on an AV. The proposed method shows several salient advantages compared with existing methods, including improved resolution and accuracy, reduced computational complexity, robustness to mutual coupling and unreasonable DOA estimates, as well as the ability to effectively extract AV contour information.

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.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array (ULA) radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles (UAVs). In practice, a ULA’s multi-target direction of arrival (DOA) estimation performance suffers from significant performance degradation owing to the limited number of physical elements. To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform, we propose a nonuniform linear motion sampling underdetermined DOA estimation method. Using the motion of the UAV platform, the echo signal is sampled at different positions. Then, according to the concept of difference co-array, a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom (DOFs). Through position analysis of the original and motion arrays, we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs. Under the condition of no increase in the aperture of the physical array, the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA. The results of numerical simulations conducted herein verify the superior performance of the proposed method.

Joint Model-Order and Robust DoA Estimation for Underwater Sensor Arrays

The direction-of-arrival (DoA) estimation algorithms have a fundamental role in target bearing estimation by sensor array systems. Recently, compressive sensing (CS)-based sparse reconstruction techniques have been investigated for DoA estimation due to their superior performance relative to the conventional DoA estimation methods, for a limited number of measurement snapshots. In many underwater deployment scenarios, the acoustic sensor arrays must perform DoA estimation in the presence of several practical problems such as unknown source number, faulty sensors, low values of the received signal-to-noise ratio (SNR), and access to a limited number of measurement snapshots. In the literature, CS-based DoA estimation has been investigated for the individual occurrence of some of these errors but the estimation under joint occurrence of these errors has not been studied. This work investigates the CS-based robust DoA estimation to account for the joint impact of faulty sensors and low SNR conditions experienced by a uniform linear array of underwater acoustic sensors. Most importantly, the proposed CS-based DoA estimation technique does not require a priori knowledge of the source order, which is replaced in the modified stopping criterion of the reconstruction algorithm by taking into account the faulty sensors and the received SNR. Using Monte Carlo techniques, the DoA estimation performance of the proposed method is comprehensively evaluated in relation to other techniques.

Direction-of-Arrival (DoA) Estimation Performance for Satellite Applications in a Multipath Environment with Rician Fading and Spatial Correlation

Direction-of-arrival (DoA) estimation methods are highly versatile and find extensive applications in satellite communication. DoA methods are employed across a range of orbits, from low Earth orbits (LEO) to geostationary Earth orbits (GEO). They serve multiple applications, including altitude determination, geolocation and estimation accuracy, target localization, and relative and collaborative positioning. This paper provides a framework for modeling the DoA angle in satellite communications with respect to the elevation angle. The proposed approach employs a closed-form expression that incorporates various factors, such as the antenna boresight angle, satellite and Earth station positions, and the altitude parameters of the satellite stations. By leveraging this formulation, the work accurately calculates the Earth station’s elevation angle and effectively models the DoA angle. To the authors’ knowledge, this contribution is unique and has not been previously addressed in the available literature. Furthermore, this paper studies the impact of spatial correlation in the channel on well-known DoA estimation techniques. As a significant part of this contribution, the authors introduce a signal model incorporating correlation in satellite communication. Although selected studies have presented spatial signal correlation models in satellite communications to analyze the performance metrics, such as the bit error or symbol error probability, outage probability, and ergodic capacity, this work stands out by presenting and adapting a correlation model in the signal specifically for studying DoA estimations. Accordingly, this paper evaluates DoA estimation performance using root mean square error (RMSE) measurements for different satellite communication link conditions (uplink and downlink) through extensive Monte Carlo simulations. The simulation’s performance is evaluated by comparing it with the Cramer–Rao lower bound (CRLB) performance metric under additive white Gaussian noise (AWGN) conditions, i.e., thermal noise. The simulation results demonstrate that incorporating a spatial signal correlation model for DoA estimations significantly improves RMSE performance in satellite systems.

Direction finding method via acoustic vector sensor array with fluctuating misorientation

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

An Optimal Shaped Sensor Array Derivation.

In Structural Health Monitoring (SHM) applications, the Direction of Arrival (DoA) estimation of Guided Waves (GW) on sensor arrays is often used as a fundamental means to locate Acoustic Sources (AS) generated by damages growth or undesired impacts in thin-wall structures (e.g., plates or shells). In this paper, we consider the problem of designing the arrangement and shape of piezo-sensors in planar clusters in order to optimize the DoA estimation performance in noise-affected measurements. We assume that: (i) the wave propagation velocity is unknown, (ii) the DoA is estimated via the time delays of wavefronts between sensors, and (iii) the maximum value of the time delays is limited. The optimality criterion is derived basing on the Theory of Measurements. The sensor array design is so that the DoA variance is minimized in an average sense by exploiting the Calculus of Variations. In this way, considering a three-sensor cluster and a monitored angles sector of 90°, the optimal time delays-DoA relations are derived. A suitable re-shaping procedure is used to impose such relations and, at the same time, to induce the same spatial filtering effect between sensors so that the sensor acquired signals are equal except for a time-shift. In order to achieve the last aim, the sensors shape is realized by exploiting a technique called Error Diffusion, which is able to emulate piezo-load functions with continuously modulated values. In this way, the Shaped Sensors Optimal Cluster (SS-OC) is derived. A numerical assessment via Green's functions simulations shows improved performance in DoA estimation by means of the SS-OC when compared to clusters realized with conventional piezo-disk transducers.

Robust DOA Estimation Based on an Exponential Hyperbolic Cosine Adaptive Algorithm

Direction-of-arrival (DOA) estimation methods based on conventional adaptive signal processing are not robust to outliers. A robust DOA estimation technique based on an exponential hyperbolic cosine function (EHCF) under such situations is proposed in this letter. To further enhance the performance of the proposed approach, a variable scale parameter strategy has been incorporated into the proposed scheme. The new methods have been shown to offer improved and robust DOA estimation performance.

Uncertainty quantification of deep learning based direction-of-arrival estimation with conformal prediction

Direction-of-arrival (DOA) estimation is an important task in array signal processing with applications in underwater acoustics, biomedicine, geophysics, and robotics. The signals recorded on a spatially distributed array along with an analytical model of wave propagation, are used to estimate the unknown DOA. Recently, end-to-end deep learning-based methods have been proposed for improving DOA estimation performance. Yet, real-time DOA estimation has a number of challenges such as sensor noise, reverberant surroundings, uncertainty in sensor locations and environment. In this work, we propose to use conformal prediction for uncertainty quantification in DOA estimation. Conformal prediction is a statistically rigorous method to provide confidence intervals for an estimated quantity without making distributional assumptions. With conformal prediction, confidence intervals are computed via quantiles of user-defined score values. This easy-to-use method can be applied to any trained classification/regression model as long as an appropriate score function is chosen. The proposed approach shows potential to enhance the real-time applicability of deep learning methods for DOA estimation. We illustrate the advantages of conformal prediction for different deep-learning methods for DOA estimation. To the best of our knowledge, this is the first analysis of using conformal prediction for uncertainty quantification of deep learning methods for acoustic estimation.

DOA Estimation Using Deep Neural Network with Angular Sliding Window

Deep neural network (DNN) has shown great potential in direction-of-arrival (DOA) estimation. In high dynamic signal-to-noise (SNR) scenarios, the estimation accuracy of the weaker sources may degrade significantly due to insufficient training samples. This paper proposes a deep neural network framework with sliding window operation. The whole field-of-view (FOV) is divided into a series of sub-regions via sliding windows. Each sub-region is assumed to contain one source at most. Thus, the single-source data can be used to train all the networks, alleviating the need for the training samples and the prior information on the number of sources. A detector network and an estimator network are followed for each sub-region, enabling high estimation accuracy and the number of sources. Simulation and real data experiment results show that the proposed method can achieve excellent DOA and source number estimation performance. Specifically, in the real data experiment, the results show that the RMSE of the proposed method reaches 0.071, which is at least 0.03 lower than FFT, MUSIC, ESPRIT, and a deep learning method namely deep convolutional network (DCN), cannot estimate the lower SNR source in high dynamic SNR scenarios.

An efficient sparse method for direction-of-arrival estimation in the presence of strong interference.

Target direction-of-arrival (DOA) estimation is often difficult in the presence of strong interference-especially when the target DOA is very close to the interference DOA-since the strong interference signal can mask the weak target signal and make the DOA estimation hard. To address this problem, an efficient sparse method for DOA estimation is proposed in this paper, in which the effect of strong interference on the target DOA estimation is significantly reduced. An on-grid version of the grid evolution technique is then developed to nonuniformly refine the grid, thereby reducing the computational complexity while retaining reasonable accuracy. Numerical simulations and experimental results demonstrate that, compared to state-of-art methods, the proposed method achieves higher efficiency and better DOA estimation performance in the presence of strong interference.

A new array extension configuration method based on nesting and minimum redundancy

AbstractWhile the uniform linear array (ULA) is a well‐known array configuration being widely used in various practical application scenarios, it also encounters numerous challenges in the field of direction‐of‐arrival (DOA) estimation. Specifically, it is difficult for the ULA to achieve a satisfactory DOA estimation accuracy, especially in the case of closely spaced sources. That is because that the resolvability of ULA is severely restricted by its limited DOA. To circumvent this issue and further improve the DOA estimation performance, a new array geometry is designed. Inspired by the fact that some linear sparse co‐arrays can yield higher DOFs and larger array apertures, the proposed array configuration is developed by nesting two or more minimum‐redundant arrays in a dedicated way. The simulation results indicate that the proposed array configuration can significantly increase the DOFs and the length of virtual array apertures, and an improved estimation accuracy can be accepted.

BSBL-Based Auxiliary Vehicle Position Analysis in Smart City Using Distributed MEC and UAV-Deployed IoT

Smart city enters the new 3.0 era, and Internet of Things (IoT) perform as the urban neural network in smart city. In the industrial areas of smart city, the IoT focuses on industrial applications, such as logistics and environmental monitoring. In this work, an auxiliary position analysis framework composed of IoT and distributed mobile-edge computing (MEC) is proposed to analyze the position of vehicles in the industrial areas of smart city. In the proposed framework, IoT are deployed by multiple unmanned aerial vehicles (UAVs) equipped with uniform linear array (ULA), which receives the signal emitted by vehicles for obtaining the direction of arrival (DOA), and the distributed MEC provides computing and synchronization services to auxiliary positioning. The DOA estimation is a key issue for auxiliary positioning in the proposed framework. To realize DOA estimation with unknown mutual coupling (MC) existing in IoT nodes, a novel block sparse Bayesian learning (SBL) algorithm is developed. In the developed algorithm, the unknown MC existing between sensors in each IoT nodes is first fused with the signal by parameterizing steering vector. Then, a block SBL (BSBL) procedure is presented to perform DOA estimation by using the inherent block sparse structure in the equivalent signal obtained after fusion. Benefiting from the fusion of MC and signal, the developed DOA estimation algorithm does not require a separate estimation of the unknown MC and also does not cause the loss of the array aperture. Based on the DOA estimation information, the position of vehicles in the industrial environment is effectively analyzed through weighted multiple cross-locations. Synthetic data set simulation is carried out to verify that the vehicle positions in smart city can be efficiently analyzed and estimated based on the presented framework and algorithm.

DOA Estimation of Indoor Sound Sources Based on Spherical Harmonic Domain Beam-Space MUSIC

The Multiple Signal Classification (MUSIC) algorithm has become one of the most popular algorithms for estimating the direction-of-arrival (DOA) of multiple sources due to its simplicity and ease of implementation. Spherical microphone arrays can capture more sound field information than planar arrays. The collected multichannel speech signals can be transformed from the space domain to the spherical harmonic domain (SHD) for processing through spherical modal decomposition. The spherical harmonic domain MUSIC (SHD-MUSIC) algorithm reduces the dimensionality of the covariance matrix and achieves better DOA estimation performance than the conventional MUSIC algorithm. However, the SHD-MUSIC algorithm is prone to failure in low signal-to-noise ratio (SNR), high reverberation time (RT), and other multi-source environments. To address these challenges, we propose a novel joint spherical harmonic domain beam-space MUSIC (SHD-BMUSIC) algorithm in this paper. The advantage of decoupling the signal frequency and angle information in the SHD is exploited to improve the anti-reverberation property of the DOA estimation. In the SHD, the broadband beamforming matrix converts the SHD sound pressure to the beam domain output. Beamforming enhances the incoming signal in the desired direction and reduces the SNR threshold as well as the dimension of the signal covariance matrix. In addition, the 3D beam of the spherical array has rotational symmetry and its beam steering is decoupled from the beam shape. Therefore, the broadband beamforming constructed in this paper allows for the arbitrary adjustment of beam steering without the need to redesign the beam shape. Both simulation experiments and practical tests are conducted to verify that the proposed SHD-BMUSIC algorithm has a more robust adjacent source discrimination capability than the SHD-MUSIC algorithm.