Arrival Estimation Research Articles

Direction of Arrival Estimation of Meteors Echoes using Array Radio Antennas

Array antennas have an interesting role in the radio astronomy field. The array antennas allow astronomers to obtain high-resolution signals with high sensitivity to weak signals. This paper estimates the meteors' positions entering the Earth's atmosphere and develops a simulation for array antenna radar to analyze the meteor's echoes. The GNU radio software was used to process the echoes, which is a free open-source software development toolkit that provides signal processing blocks to implement in radio projects. Then, the simulation determines the azimuth and elevation of the meteors. An improved Multiple Signal Classification (MUSIC) algorithm has been suggested to analyze these echoes. The detected power of each meteor echo has a Doppler frequency shift due to the high speed of the meteors, which impacts the accuracy of the Direction of Arrival (DOA) estimation. The Doppler shift was considered in this simulation, and the results showed that the suggested method has low complexity and high resolution and can estimate the meteors' position with the minimum error.

A New Method for Joint Sparse DOA Estimation

To tackle the issue of poor accuracy in single-snapshot data processing for Direction of Arrival (DOA) estimation in passive radar systems, this paper introduces a method for judiciously leveraging multi-snapshot data. This approach effectively enhances the accuracy of DOA estimation and spatial angle resolution in passive radar systems. Additionally, in response to the non-convex nature of the mixed norm, we propose a hyperbolic tangent model as a replacement, transforming the problem into a directly solvable convex optimization problem. The rationality of this substitution is thoroughly demonstrated. Lastly, through a comparative analysis with existing discrete grid DOA estimation methods, we illustrate the superiority of the proposed approach, particularly under conditions of medium signal-to-noise ratio, varying numbers of snapshots, and close target angles. This method is less affected by the number of array elements, and is more usable in practices verified in real-world scenarios.

Integrating arrival time estimation in truck scheduling: an explorative study in grocery retailing

ABSTRACT This paper studies a new managerial approach that integrates predictive trucks’ estimated time of arrival (ETA) into truck scheduling to deal with the truck arrival time uncertainty. The approach exploits ETA to reschedule trucks by the up-to-date information and aims to minimize the trucks’ waiting time. The approach was applied in a real case. Results quantified the impact of adopting ETA for truck scheduling, also showing how the ETA accuracy and peak truck arrival rate affect the total trucks’ waiting time. The paper enriches both truck scheduling literature, investigating a new managerial approach to deal with truck arrival time uncertainty, which greatly threatens the synchronization of logistics flows, and Industry 4.0 literature, showing how real-time data availability can change traditional decision-making processes. Insights for the approach application are discussed, together with the economic, environmental, and social benefits by supply chain actors (i.e. carriers, warehouse managers, and drivers).

A novel damage localization method of Circular Phased Array using Minimum Variance Distortionless Response Beamforming with Autocorrelation Matrix Diagonal Loading

Damage localization methods based on Acoustic Emission (AE) can be classified into time-based and waveform-based. However, the former requires a large number of sensors while the latter is limited to 2D plane localization. In order to address the challenge of achieving more accurate 3D localization using a reduced number of sensors, this paper proposes a Circular Phased Array using Minimum Variance Distortionless Response (MVDR) Beamforming with Autocorrelation Matrix Diagonal Loading (AMDL) method. Firstly, a sparse circular array is utilized to form multiple beamforming for coherent shear wave signals, decomposing the original 3D localization problem into Direction Of Arrival (DOA) estimation. Secondly, azimuth angle, elevation angle and autocorrelation matrix diagonal loading methods are introduced, working in conjunction with the MVDR beamforming algorithm. Finally, spatial integration is performed through matrix decomposition to solve geometric overdetermined equations. The effectiveness of the proposed method is validated through numerical simulations and experimental verifications under various damage conditions. Results indicate that estimation errors for azimuth and elevation angles are both less than 2 %, while 3D damage source localization errors remain within a range of less than 3 %. This proposed method extends beamforming technology from 2D plane localization to 3D localization, significantly reducing the complexity of sensor arrangement and lowering the cost of structural health monitoring systems by utilizing a small number of sensors.

Research on hydroacoustic signal processing algorithm based on B-spline and Hilbert transform

Purpose This paper aims to solve the problems of baseline drift, susceptibility to abnormal data interference during baseline drift processing, and phase inconsistency in underwater acoustic target detection and signal processing of single microelectromechanical systems (MEMS) vector hydrophone. To this end, this paper proposes a baseline drift removal algorithm based on Huber regression model with B-spline interpolation (H-BS) and a phase compensation algorithm based on the Hilbert transform. Design/methodology/approach First, the Huber regression model is innovatively introduced into the conventional B-spline interpolation (B-spline) to solve the control point vectors more accurately and to improve the anti-interference ability of the abnormal data when the B-spline interpolation fitting removes baseline drift and the baseline drift components in the signals are fitted accurately and removed by the above method. Next, the Hilbert transform is applied to the three-channel output signals of the MEMS vector hydrophone to calculate the instantaneous phase and the phase compensation is performed on the vector X/Y signals with the scalar P signal as the reference. Findings Through simulation experiments, it is found that H-BS proposed in this paper has smaller processing error and better robustness than variational modal decomposition and B-spline, but the H-BS algorithm takes slightly longer than the B-spline. In the actual lake test experiments, the H-BS algorithm can effectively remove the baseline drift component in the original signal and restore the signal waveform, and after the Hilbert transform phase compensation, the direction of arrival estimation accuracy of the signal is improved by 1°∼2°, which realizes high-precision orientation to the acoustic source target. Originality/value In this paper, the Huber regression model is introduced into B-spline interpolation fitting for the first time and applied in the specialized field of hydroacoustic signal baseline drift removal. Meanwhile, the Hilbert transform is applied to phase compensation of hydroacoustic signals. After simulation and practical experiments, these two methods are verified to be effective in processing hydroacoustic signals and perform better than similar methods. This study provides a new research direction for the signal processing of MEMS vector hydrophone, which has important practical engineering application value.

Research on underwater target signal orientation estimation based on smoothness priors approach

Purpose This paper aims to address the challenges in hydroacoustic signal detection, signal distortion and target localization caused by baseline drift. The authors propose a combined algorithm that integrates short-time Fourier transform (STFT) detection, smoothness priors approach (SPA), attitude calibration and direction of arrival (DOA) estimation for micro-electro-mechanical system vector hydrophones. Design/methodology/approach Initially, STFT method screens target signals with baseline drift in low signal-to-noise ratio environments, facilitating easier subsequent processing. Next, SPA is applied to the screened target signal, effectively removing the baseline drift, and combined with filtering to improve the signal-to-noise ratio. Then, vector channel amplitudes are corrected using attitude correction with 2D compass data. Finally, the absolute target azimuth is estimated using the minimum variance distortion-free response beamformer. Findings Simulation and experimental results demonstrate that the SPA outperforms high-pass filtering in removing baseline drift and is comparable to the effectiveness of variational mode decomposition, with significantly shorter processing times, making it more suitable for real-time applications. The detection performance of the STFT method is superior to instantaneous correlation detection and sample entropy methods. The final DOA estimation achieves an accuracy within 2°, enabling precise target azimuth estimation. Originality/value To the best of the authors’ knowledge, this study is the first to apply SPA to baseline drift removal in hydroacoustic signals, significantly enhancing the efficiency and accuracy of signal processing. It demonstrates the method’s outstanding performance in the field of underwater signal processing. In addition, it confirms the reliability and feasibility of STFT for signal detection in the presence of baseline drift.

An RD-Domain Virtual Aperture Extension Method for Shipborne HFSWR

High-frequency surface wave radar (HFSWR) is widely used for detecting sea surface or low-altitude targets due to its all-weather operation and over-the-horizon detection capability. To further enhance the maneuverability and detection range of HFSWR, shipborne HFSWR has been developed. However, compared to shore-based platforms, shipborne platforms face challenges such as a small array aperture and reduced Direction of Arrival (DOA) estimation performance due to their limited size. The traditional time–domain virtual aperture extension method, based on the principle of space-time equivalence, aims to improve the array aperture but has limitations when used for HFSWR background or multiple targets with different speeds. To address these issues, this paper proposes a range-Doppler domain (RD-domain) virtual aperture extension method for the uniform linear array, based on the uniform motion model. The contributions of this work include (1) a continuous motion model for shipborne HFSWR, (2) a virtual aperture processing flowchart for shipborne HFSWR, and (3) an RD-domain aperture extension method suitable for HFSWR background or multiple targets with varying speeds. Through simulation and experimental data, we validate the proposed method and analyze its performance.

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.

Impact of hardware impairments and BS antenna tilt on 3D drone localization and tracking

Today, GPS-free drone localization is increasingly gaining attention in various applications, but it faces significant accuracy challenges in three-dimensional (3D) space due to various impairments. This study investigates the effects of carrier frequency offset (CFO), phase noise (PN), and down-tilted base station (BS) antennas on drone positioning and tracking. Additionally, we explore the impact of inter-site distance (ISD) and BS density on drone position estimation accuracy. In our methodology, we consider a flying drone equipped with a single transmission antenna and BSs configured with 4 × 4 antennas under specific impairments. We first analyze the effects of these impairments on the signal’s covariance matrix. Then, using the MUSIC algorithm, we estimate the azimuth and elevation angles, which serve as the basis for drone localization using the Least Squares (LS) method across all BSs. Finally, the estimated positions feed into an Extended Kalman Filter (EKF) for tracking. Our results present a sequential analysis of the impact of all impairments on the off-diagonal covariance matrix, on the Angle of Arrival (AOA) estimation and 3D drone localization. We use simulations to demonstrate how hardware impairments affect 3D drone localization accuracy under varying ISD and BS densities.

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.

DOA Estimation Method for Vector Hydrophones Based on Sparse Bayesian Learning.

Through extensive literature review, it has been found that sparse Bayesian learning (SBL) is mainly applied to traditional scalar hydrophones and is rarely applied to vector hydrophones. This article proposes a direction of arrival (DOA) estimation method for vector hydrophones based on SBL (Vector-SBL). Firstly, vector hydrophones capture both sound pressure and particle velocity, enabling the acquisition of multidimensional sound field information. Secondly, SBL accurately reconstructs the received vector signal, addressing challenges like low signal-to-noise ratio (SNR), limited snapshots, and coherent sources. Finally, precise DOA estimation is achieved for multiple sources without prior knowledge of their number. Simulation experiments have shown that compared with the OMP, MUSIC, and CBF algorithms, the proposed method exhibits higher DOA estimation accuracy under conditions of low SNR, small snapshots, multiple sources, and coherent sources. Furthermore, it demonstrates superior resolution when dealing with closely spaced signal sources.

Multi-microphone simultaneous speakers detection and localization of multi-sources for separation and noise reduction

This paper addresses the challenge of online blind speaker separation in a multi-microphone setting. The linearly constrained minimum variance (LCMV) beamformer is selected as the backbone of the separation algorithm due to its distortionless response and capacity to create a null towards interfering sources. A specific instance of the LCMV beamformer that considers acoustic propagation is implemented. In this variant, the relative transfer functions (RTFs) associated with each speaker of interest are utilized as the steering vectors of the beamformer. A control mechanism is devised to ensure robust estimation of the beamformer’s building blocks, comprising speaker activity detectors and direction of arrival (DOA) estimation branches. This control mechanism is implemented as a multi-task deep neural network (DNN). The primary task classifies each time frame based on speaker activity: no active speaker, single active speaker, or multiple active speakers. The secondary task is DOA estimation. It is implemented as a classification task, executed only for frames classified as single-speaker frames by the primary branch. The direction of the active speaker is classified into one of the multiple ranges of angles. These frames are also leveraged to estimate the RTFs using subspace estimation methods. A library of RTFs associated with these DOA ranges is then constructed, facilitating rapid acquisition of new speakers and efficient tracking of existing speakers. The proposed scheme is evaluated in both simulated and real-life recordings, encompassing static and dynamic scenarios. The benefits of the multi-task approach are showcased, and significant improvements are evident, even when the control mechanism is trained with simulated data and tested with real-life data. A comparison between the proposed scheme and the independent low-rank matrix analysis (ILRMA) algorithm reveals significant improvements in static scenarios. Furthermore, the tracking capabilities of the proposed scheme are highlighted in dynamic scenarios.

Multifunctional Intelligent Reconfigurable Metasurface.

The emergent reconfigurable metasurfaces (RMs) have attracted a lot of attention due to their potential in broad applications. As a general platform, RMs are able to control the reflection (or refraction) of incident waves with predefined functionalities. Nevertheless, the operation of RMs is highly dependent on the arrival direction of incidence. The self-adaptive design of an RM, so that it can respond to varied incident waves automatically, is highly requested in practical implementation, which is actually challenging. This study reports the realization of an intelligent RM (IRM) system, which can detect the arrival direction of impinging waves and respond to the incidence with a predefined functionality accordingly. This IRM system is constructed by integrating a direction of the arrival estimation module, a frontend by the varactor-based metasurface, and a central control unit. In experiments, an IRM system designed for TM polarization is demonstrated to perform various functions, i.e., retroreflection, directional reflection, and fixed-point energy focusing, which are highly requested by edge communication and sensing. The measured results imply that this IRM system responds quite well within a wide incident range from -60° to 60° in a frequency range from 9 to 9.5 GHz. The proposed IRM can be a good candidate for boosting 5G communication and Internet of Things applications, including beam shaping/steering, RCS manipulation, object imaging, and sensor recharging.

A high-resolution method for direction of arrival estimation based on an improved self-attention module.

The high-resolution direction of arrival (DOA) estimation is a prominent research issue in underwater acoustics. The existing high-resolution methods include subspace methods and sparse representation methods. However, the performance of subspace methods suffers from low signal-to-noise ratio (SNR) and limited snapshots conditions, and the computational complexity of sparse representation methods is too high. The neural network methods are emerging high-resolution methods. However, insufficient support for big data is frequently observed in underwater acoustics, and conventional network structures present challenges in further enhancing performance. To address the aforementioned problems, we propose a neural network method based on an improved self-attention module to achieve high accuracy and robust DOA estimation. First, we design a multi-head self-attention module with large-scale convolutional kernels and residual structures to improve the estimated accuracy. Second, we propose an improved input feature to enhance the robustness to non-uniform noise and unequal-intensity targets. The simulations demonstrate that the proposed method exhibits superior angle resolution compared to sparse representation methods under the same simulation conditions. The proposed method demonstrates exceptional accuracy and robustness in DOA estimation under challenging conditions of low SNR, limited snapshots, and unequal-intensity targets. The experimental results further prove the effectiveness of the proposed method.

Reliable underwater multi-target direction of arrival estimation with optimal transport using deep models.

Multi-target direction of arrival (DoA) estimation is an important and challenging task for sonar signal processing. In this study, we propose a method called learning direction of arrival with optimal transport (LOT) to accurately estimate the DoAs of multiple sources with a single deep model. We model the DoA estimation problem as a multi-label classification task and introduce an optimal transport (OT) loss based on the OT theory to capture the intrinsic continuity within the angular categories. We design a cost matrix for the OT loss in LOT approach to characterize the order and periodicity of the angular grid. The LOT approach encourages reliable predictions closer to the ground truth and suppresses spurious targets. We also propose a lightweight channel mask data augmentation module for deep models that use items related to the covariance matrix as input. The proposed methods can be seamlessly integrated with different model architectures and we indicate the portability with experiments on several typical network backbones. Experiments across various scenarios using different measurements show the effectiveness and robustness of our approaches. Results on SwellEx-96 experimental data demonstrate the practicality in real applications.

MDTCNet: Multi-Task Classifications Network and TCNN for Direction of Arrival Estimation

MDTCNet: Multi-Task Classifications Network and TCNN for Direction of Arrival Estimation

Robust Indoor Positioning with Smartphone by Utilizing Encoded Chirp Acoustic Signal.

Recently, indoor positioning has been one of the hot topics in the field of navigation and positioning. Among different solutions on indoor positioning, positioning with acoustic signals has its promise due to its relatively high accuracy in the line of sight scenarios, low cost, and ease of being implemented in smartphones. In this work, a novel acoustic positioning method, called RATBILS, is proposed, in which encoded chirp acoustic signals are modulated and transmitted by different acoustic base stations. The smartphones receive the signals and perform the following three steps: (1) preprocessing; (2) time of arrival (TOA) estimation; and (3) time difference of arrival (TDOA) calculation and location estimation. In the preprocessing stage, we use band pass filters to filter out low-frequency noise from the environment. At the same time, we perform a signal decoding function in order to lock onto the positioning source. In the TOA estimation stage, we conduct both coarse and fine detection to enhance the accuracy and robustness of TOA estimation. The primary goal of coarse detection is to establish a noise range for fine detection. The main objective of fine detection is to emphasize the intensity of the first arrival diameter and resistance with multipath and non-line-of-sight (NLOS) caused by human body obstruction. In the TDOA calculation and location estimation stage, we estimate the TDOA based on the TOA estimation and then use the TDOA results for position estimation. In order to evaluate the performance of the proposed RATBILS system, two indoor field tests are carried out. The test results show that the RATBILS system achieves a positioning error of 0.23 m at 92% in region 1 of scene 1 and is superior to the traditional threshold method. The RATBILS system achieves a positioning error of 0.56 m at 92% in region 2 of scene 1 and is superior to the traditional threshold method. In scene 2, the maximum average positioning error was 1.26 m, which is better than the 3.33 m and 3.87 m of the two traditional threshold methods.

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.

Robust Underwater Direction-of-Arrival Estimation Method Using Acoustic Sensor Array under Unknown Swing Deviation Elements

This paper presents a strategy called the alternating iterative minimization method (AIMM), aimed at enhancing the precision of direction of arrival (DOA) estimation when utilizing an acoustic vector sensor array (AVSA) with unknown swing deviation elements (SDEs). The AVSA model with unknown SDEs is formulated by incorporating the swing deviation parameter. Later, to estimate the swing deviation matrix (SDM) and the sparse signal power by using the alternating iteration method, the auxiliary cost functions with respect to SDM and the sparse signal power are formulated based on the regularized weighted least squares (RWLS) and regularized covariance matrix fitting (RCMF) criteria. Furthermore, their analytical expressions have also been quantified. In order to mitigate the effect of unknown SDEs on the accuracy of DOA estimation, any sub-time segment (STS) in the dataset is selected as the reference to convert the received data of different STS into the reference STS using the estimated SDM. The simulation and experimental outcomes conclusively represent the effectiveness of the suggested TSIM approach using AVSA in handling unknown SDEs.

An Improved Unfolded Coprime Linear Array Design for DOA Estimation with No Phase Ambiguity

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method.