[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (425)

Search Parameters:
Keywords = angle-of-arrival

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
16 pages, 3949 KiB  
Technical Note
Precision Analysis of Multi-Parameter Multi-Epoch Emitter Localization Radar in Three-Satellite Formation
by Yiming Lian, Yuxuan Wu, Yaowen Chen, Xian Liu and Liming Jiang
Remote Sens. 2025, 17(1), 96; https://doi.org/10.3390/rs17010096 - 30 Dec 2024
Viewed by 251
Abstract
Emitter localization offers significant advantages such as high concealment, long detection range, and low cost, making it indispensable in target positioning. The utilization of low earth orbit satellite formation with AOA (Angle of Arrival) and TDOA (Time Difference of Arrival) measurements is a [...] Read more.
Emitter localization offers significant advantages such as high concealment, long detection range, and low cost, making it indispensable in target positioning. The utilization of low earth orbit satellite formation with AOA (Angle of Arrival) and TDOA (Time Difference of Arrival) measurements is a key technology for achieving emitter localization. To address the issues of requiring numerous cooperative platforms and the poor accuracy of single-epoch solutions with single-parameter closed-form algorithms, this paper proposes a multi-parameter multi-epoch positioning method based on a three-satellite formation. Simulation data are used to analyze the positioning accuracy under various epochs and different TDOA and AOA noise conditions. The experimental results demonstrate that, compared to the traditional single-parameter single-epoch localization method, utilizing a three-satellite formation with combined AOA and TDOA parameters, along with a multi-epoch solution approach, significantly improves localization accuracy to within an order of ten meters. This method enhances robustness and provides a viable strategy for addressing localization challenges caused by underdetermined systems of equations. Additionally, the results verify that an accumulated almanac element duration of 20 s ensures high positioning accuracy while maintaining a low computational cost. The combined multi-parameter multi-epoch method shows substantial advantages in improving both accuracy and robustness, providing valuable insights for future satellite-based emitter localization technologies. Full article
(This article belongs to the Special Issue Advances in Applications of Remote Sensing GIS and GNSS)
Show Figures

Figure 1

Figure 1
<p>AOA measurements of azimuth and elevation angles.</p>
Full article ">Figure 2
<p>Time difference hyperbola. (The red arrow in the figure is labeled as <span class="html-italic">r<sub>i</sub></span>).</p>
Full article ">Figure 3
<p>Three-satellite formation satellite configuration. (S1, S2, and S3 as sun-synchronous orbit satellites).</p>
Full article ">Figure 4
<p>Impact of different epoch accumulation durations on localization results with TDOA noise levels of 1.2–3 m.</p>
Full article ">Figure 5
<p>Impact of TDOA noise on localization results across different epoch accumulations.</p>
Full article ">Figure 6
<p>Runtime of AOA/TDOA combined algorithm for different epoch accumulation durations.</p>
Full article ">Figure 7
<p>Impact of different epoch accumulation durations on localization results with AOA noise levels of 0.1–1°.</p>
Full article ">Figure 8
<p>Impact of AOA noise on localization results across different epoch accumulations.</p>
Full article ">Figure 9
<p>Impact of AOA noise on localization results across different epoch accumulations. (The AOA noise of the left image (<b>a</b>) is 0.5° and that the right image (<b>b</b>) is 1°).</p>
Full article ">
20 pages, 5738 KiB  
Article
Time-of-Arrival and Angle-of-Arrival Measurement-Assisted 3D Inter-Unmanned Aerial Vehicle Relative Localization Under Distance-Dependent Noise Model
by Jiawei Tang, Tian Chang, Qinglong Jiang, Xuhui Ding and Dekang Liu
Electronics 2025, 14(1), 90; https://doi.org/10.3390/electronics14010090 - 28 Dec 2024
Viewed by 234
Abstract
This paper addresses the 3D relative localization problem for two unmanned aerial vehicles (UAVs) using a combination of time-of-arrival (TOA) and angle-of-arrival (AOA) measurements across varied flight trajectories. We commenced by examining the problem of relative attitude estimation using only time-of-arrival (TOA) measurements, [...] Read more.
This paper addresses the 3D relative localization problem for two unmanned aerial vehicles (UAVs) using a combination of time-of-arrival (TOA) and angle-of-arrival (AOA) measurements across varied flight trajectories. We commenced by examining the problem of relative attitude estimation using only time-of-arrival (TOA) measurements, taking into account a distance-dependent noise model. To address this issue, we constructed a constrained weighted least squares (CWLS) problem and applied semidefinite relaxation (SDR) techniques for its resolution. Furthermore, we extended our analysis to incorporate AOA measurements and scrutinize the Cramer–Rao Lower Bound (CRLB) to illustrate enhanced localization accuracy through TOA-AOA integration compared to TOA alone under stable trajectory conditions. Ultimately, numerical simulations substantiate the efficacy of the proposed methodologies. Full article
Show Figures

Figure 1

Figure 1
<p>Scenario of UAV relative localization estimation.</p>
Full article ">Figure 2
<p>Four trajectories of two UAVs.</p>
Full article ">Figure 3
<p>Acomparison of the influence of noise level on the SDP under different flight trajectories.</p>
Full article ">Figure 3 Cont.
<p>Acomparison of the influence of noise level on the SDP under different flight trajectories.</p>
Full article ">Figure 4
<p>A comparison of the influence of noise levels on the SDR TOA and TOA-AOA methods under four different flight trajectories.</p>
Full article ">Figure 5
<p>A comparison of the influence of number of measurements on the SDR TOA and TOA-AOA methods under four different flight trajectories.</p>
Full article ">
21 pages, 7791 KiB  
Article
Simulation Study on Detection and Localization of a Moving Target Under Reverberation in Deep Water
by Jincong Dun, Shihong Zhou, Yubo Qi and Changpeng Liu
J. Mar. Sci. Eng. 2024, 12(12), 2360; https://doi.org/10.3390/jmse12122360 - 22 Dec 2024
Viewed by 350
Abstract
Deep-water reverberation caused by multiple reflections from the seafloor and sea surface can affect the performance of active sonars. To detect a moving target under reverberation conditions, a reverberation suppression method using multipath Doppler shift in deep water and wideband ambiguity function (WAF) [...] Read more.
Deep-water reverberation caused by multiple reflections from the seafloor and sea surface can affect the performance of active sonars. To detect a moving target under reverberation conditions, a reverberation suppression method using multipath Doppler shift in deep water and wideband ambiguity function (WAF) is proposed. Firstly, the multipath Doppler factors in the deep-water direct zone are analyzed, and they are introduced into the target scattered sound field to obtain the echo of the moving target. The mesh method is used to simulate the deep-water reverberation waveform in time domain. Then, a simulation model for an active sonar based on the source and short vertical line array is established. Reverberation and target echo in the received signal can be separated in the Doppler shift domain of the WAF. The multipath Doppler shifts in the echo are used to estimate the multipath arrival angles, which can be used for target localization. The simulation model and the reverberation suppression detection method can provide theoretical support and a technical reference for the active detection of moving targets in deep water. Full article
(This article belongs to the Section Ocean Engineering)
Show Figures

Figure 1

Figure 1
<p>Transmission and reception models for the edges of the transmitted pulse. (<b>a</b>) The front edge. (<b>b</b>) The back edge.</p>
Full article ">Figure 2
<p>Schematic of the simplified calculation.</p>
Full article ">Figure 3
<p>Theoretical and calculated values of Doppler factors for different paths as a function of the horizontal distance between the sonar and the target. (<b>a</b>) DD. (<b>b</b>) DSR. (<b>c</b>) SRSR.</p>
Full article ">Figure 4
<p>Schematic of the mesh method.</p>
Full article ">Figure 5
<p>Flowchart of the detection and localization algorithm for moving targets in deep water.</p>
Full article ">Figure 6
<p>WAF of the transmitted signal.</p>
Full article ">Figure 7
<p>Schematic of the sound field.</p>
Full article ">Figure 8
<p>Waveform of the received signal.</p>
Full article ">Figure 9
<p>WAF of the received signal.</p>
Full article ">Figure 10
<p>WAF as a function of time delay and Doppler shift. (<b>a</b>) A 2D pseudo-color map. (<b>b</b>) A color plot zooming in the echoes.</p>
Full article ">Figure 11
<p>Image of the analytical signal <math display="inline"><semantics> <mrow> <mi>y</mi> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>,</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p>The contour plots of (<b>a</b>) the difference in time delay between the target echoes of the DD path and the DSR path, and (<b>b</b>) the arrival angle of echoes of the DD path.</p>
Full article ">Figure 13
<p>Cost function for the joint estimation of the target’s depth and range. The label “∗” indicates the true target position.</p>
Full article ">Figure 14
<p>(<b>a</b>) RERE and (<b>b</b>) REDE as functions of the target depth. The red lines represent the zero-error lines, while the dots lines denote the error curves.</p>
Full article ">Figure 15
<p>(<b>a</b>) RERE and (<b>b</b>) REDE as functions of the target range. The red lines represent the zero-error lines, while the dots lines denote the error curves.</p>
Full article ">Figure 16
<p>(<b>a</b>) RERE and (<b>b</b>) REDE as functions of the target velocity. The red lines represent the zero-error lines, while the dots lines denote the error curves.</p>
Full article ">Figure 17
<p>PCL as a function of SRR.</p>
Full article ">
13 pages, 4861 KiB  
Technical Note
Research on 2-D Direction of Arrival (DOA) Estimation for an L-Shaped Array
by Kun Ye, Lang Zhou, Shaohua Hong, Xuebo Zhang and Haixin Sun
Remote Sens. 2024, 16(24), 4787; https://doi.org/10.3390/rs16244787 - 22 Dec 2024
Viewed by 300
Abstract
Lately, there has been a significant increase in interest in coprime array configurations, as they offer the advantage of generating more extensive array apertures and enhanced degrees of freedom when contrasted with standard linear arrays. This document introduces an innovative two-dimensional direction-of-arrival (2-D [...] Read more.
Lately, there has been a significant increase in interest in coprime array configurations, as they offer the advantage of generating more extensive array apertures and enhanced degrees of freedom when contrasted with standard linear arrays. This document introduces an innovative two-dimensional direction-of-arrival (2-D DOA) estimation technique founded on the zero-completion principle. In particular, our initial step involves interpolating the synthetic co-array signals to achieve completion, followed by the regeneration of the covariance matrix utilizing the interpolated synthetic signals. Then, the 2-D angle estimation is realized based on the complemented matrix using the auto-pairing method. The computational modeling outcomes indicate that the suggested method demonstrates superior angular discriminability. Moreover, this method excels in estimation accuracy when contrasted with its algorithmic counterparts. Full article
(This article belongs to the Special Issue Ocean Remote Sensing Based on Radar, Sonar and Optical Techniques)
Show Figures

Figure 1

Figure 1
<p>Array structure.</p>
Full article ">Figure 2
<p>DOA estimation results obtained by different algorithms. (<b>a</b>) DFT. (<b>b</b>) JSVD. (<b>c</b>) LCCM. (<b>d</b>) Proposed. (Red crosses indicate estimated results, while blue circles indicate actual values).</p>
Full article ">Figure 3
<p>Spatial spectrum of DOA estimation by different algorithms. (<b>a</b>) DFT. (<b>b</b>) JSVD. (<b>c</b>) LCCM. (<b>d</b>) Proposed.</p>
Full article ">Figure 4
<p>Comparison of the RMSE performance of DFT, JSVD, and LCCM and the proposed (<b>a</b>) number of snapshots. (<b>b</b>) SNR.</p>
Full article ">Figure 5
<p>Comparison of RMSE performance of the proposed algorithm under different physical sensors: (<b>a</b>) the number of snapshots. (<b>b</b>) SNR.</p>
Full article ">Figure 6
<p>RMSE performance comparison of array structures: (<b>a</b>) number of snapshots. (<b>b</b>) SNR.</p>
Full article ">Figure 7
<p>Comparison of RMSE performance at 1/Sqrt(T).</p>
Full article ">Figure 8
<p>Comparison of RMSE performance at 1/Sqrt(SNR).</p>
Full article ">
25 pages, 6743 KiB  
Article
Online Autonomous Motion Control of Communication-Relay UAV with Channel Prediction in Dynamic Urban Environments
by Cancan Tao and Bowen Liu
Drones 2024, 8(12), 771; https://doi.org/10.3390/drones8120771 - 19 Dec 2024
Viewed by 474
Abstract
In order to improve the network performance of multi-unmanned ground vehicle (UGV) systems in urban environments, this article proposes a novel online autonomous motion-control method for the relay UAV. The problem is solved by jointly considering unknown RF channel parameters, unknown multi-agent mobility, [...] Read more.
In order to improve the network performance of multi-unmanned ground vehicle (UGV) systems in urban environments, this article proposes a novel online autonomous motion-control method for the relay UAV. The problem is solved by jointly considering unknown RF channel parameters, unknown multi-agent mobility, the impact of the environments on channel characteristics, and the unavailable angle-of-arrival (AoA) information of the received signal, making the solution of the problem more practical and comprehensive. The method mainly consists of two parts: wireless channel parameter estimation and optimal relay position search. Considering that in practical applications, the radio frequency (RF) channel parameters in complex urban environments are difficult to obtain in advance and are constantly changing, an estimation algorithm based on Gaussian process learning is proposed for online evaluation of the wireless channel parameters near the current position of the UAV; for the optimal relay position search problem, in order to improve the real-time performance of the method, a line search algorithm and a general gradient-based algorithm are proposed, which are used for point-to-point communication and multi-node communication scenarios, respectively, reducing the two-dimensional search to a one-dimensional search, and the stability proof and convergence conditions of the algorithm are given. Comparative experiments and simulation results under different scenarios show that the proposed motion-control method can drive the UAV to reach or track the optimal relay position and improve the network performance, while demonstrating that it is beneficial to consider the impact of the environments on the channel characteristics. Full article
Show Figures

Figure 1

Figure 1
<p>Illustration of air-to-ground relay communication scenario in urban environments.</p>
Full article ">Figure 2
<p>Motion control framework.</p>
Full article ">Figure 3
<p>Schematic diagram of air-to-ground signal propagation.</p>
Full article ">Figure 4
<p>Flight trajectories of the UAV that supports communication for two stationary UGVs.</p>
Full article ">Figure 5
<p>Changes in communication performance when the UAV supports communication for two stationary UGVs.</p>
Full article ">Figure 6
<p>Flight trajectories of the UAV that supports communication for multiple stationary UGVs.</p>
Full article ">Figure 7
<p>Changes in communication performance when the UAV supports communication for multiple stationary UGVs.</p>
Full article ">Figure 8
<p>Flight trajectories of the UAV that supports point-to-point communication for two moving UGVs.</p>
Full article ">Figure 9
<p>Changes in communication performance when the UAV supports point-to-point communication for two moving UGVs.</p>
Full article ">Figure 10
<p>Flight trajectories of the UAV that supports multi-node communication for multiple moving UGVs.</p>
Full article ">Figure 11
<p>Changes in communication performance when the UAV supports multi-node communication for multiple moving UGVs.</p>
Full article ">Figure 12
<p>Flight trajectories of the UAV that supports point-to-point communication for two moving UGVs with unknown channel parameters.</p>
Full article ">Figure 13
<p>Changes in communication performance when the UAV supports point-to-point communication for two moving UGVs with unknown channel parameters.</p>
Full article ">Figure 14
<p>Flight trajectories of the UAV that supports multi-node communication for multiple moving UGVs with unknown channel parameters.</p>
Full article ">Figure 15
<p>Changes in communication performance when the UAV supports multi-node communication for multiple moving UGVs with unknown channel parameters.</p>
Full article ">
20 pages, 4895 KiB  
Article
A Fast Two-Dimensional Direction-of-Arrival Estimator Using Array Manifold Matrix Learning
by Jieyi Lu, Long Yang, Yixin Yang and Lu Wang
Remote Sens. 2024, 16(24), 4654; https://doi.org/10.3390/rs16244654 - 12 Dec 2024
Viewed by 369
Abstract
Sparsity-based methods for two-dimensional (2D) direction-of-arrival (DOA) estimation often suffer from high computational complexity due to the large array manifold dictionaries. This paper proposes a fast 2D DOA estimator using array manifold matrix learning, where source-associated grid points are progressively selected from the [...] Read more.
Sparsity-based methods for two-dimensional (2D) direction-of-arrival (DOA) estimation often suffer from high computational complexity due to the large array manifold dictionaries. This paper proposes a fast 2D DOA estimator using array manifold matrix learning, where source-associated grid points are progressively selected from the set of predefined angular grids based on marginal likelihood maximization in the sparse Bayesian learning framework. This grid selection reduces the size of the manifold dictionary matrix, avoiding large-scale matrix inversion and resulting in reduced complexity. To overcome grid mismatch errors, grid optimization is established based on the marginal likelihood, with a dichotomizing-based solver provided that is applicable to arbitrary planar arrays. For uniform rectangular arrays, we present a 2D zoom fast Fourier transform as an alternative to the dichotomizing-based solver by transforming the manifold vector in a specific form, thus accelerating the computation without compromising accuracy. Simulation results verify the superior performance of the proposed methods in terms of estimation accuracy, computational efficiency, and angle resolution compared to state-of-the-art methods for 2D DOA estimation. Full article
(This article belongs to the Special Issue Ocean Remote Sensing Based on Radar, Sonar and Optical Techniques)
Show Figures

Figure 1

Figure 1
<p>Configuration of the planar array: (<b>a</b>) arbitrary planar array; (<b>b</b>) URA. Blue dots represent array sensors; red dots represent the source position; <span class="html-italic">B</span> represents the projection of the source position onto the <span class="html-italic">x</span>–<span class="html-italic">y</span> plane.</p>
Full article ">Figure 2
<p>Diagram of the dichotomizing method: (<b>a</b>) initialization; (<b>b</b>) the first iteration.</p>
Full article ">Figure 3
<p>RMSE performance versus SNR, where a URA is utilized, and <span class="html-italic">L</span> is 50: (<b>a</b>) azimuth; (<b>b</b>) elevation.</p>
Full article ">Figure 4
<p>Average runtime versus SNR, where a URA is utilized, and <span class="html-italic">L</span> is 50.</p>
Full article ">Figure 5
<p>RMSE performance versus snapshots, where a URA is utilized, and SNR is 10 dB: (<b>a</b>) azimuth; (<b>b</b>) elevation.</p>
Full article ">Figure 6
<p>Average runtime versus snapshots, where a URA is utilized, and SNR is 10 dB.</p>
Full article ">Figure 7
<p>Probability of source resolution versus angular separation, where a URA is utilized, SNR is 10 dB, and <span class="html-italic">L</span> is 50: (<b>a</b>) azimuth; (<b>b</b>) elevation.</p>
Full article ">Figure 8
<p>RMSE performance versus GI, where a URA is utilized, SNR is 10 dB, and <span class="html-italic">L</span> is 50: (<b>a</b>) azimuth; (<b>b</b>) elevation.</p>
Full article ">Figure 9
<p>Average runtime versus GI, where a URA is utilized, SNR is 10 dB, and <span class="html-italic">L</span> is 50.</p>
Full article ">Figure 10
<p>Result of 2D DOA estimation using an arbitrary planar array, where SNR is 0 dB, and <span class="html-italic">L</span> is 50: (<b>a</b>) array configuration; (<b>b</b>) 2D DOA estimates.</p>
Full article ">
31 pages, 22621 KiB  
Article
A Ray-Tracing-Based Single-Site Localization Method for Non-Line-of-Sight Environments
by Shuo Hu, Lixin Guo and Zhongyu Liu
Sensors 2024, 24(24), 7925; https://doi.org/10.3390/s24247925 - 11 Dec 2024
Viewed by 408
Abstract
Localization accuracy in non-line-of-sight (NLOS) scenarios is often hindered by the complex nature of multipath propagation. Traditional approaches typically focus on NLOS node identification and error mitigation techniques. However, the intricacies of NLOS localization are intrinsically tied to propagation challenges. In this paper, [...] Read more.
Localization accuracy in non-line-of-sight (NLOS) scenarios is often hindered by the complex nature of multipath propagation. Traditional approaches typically focus on NLOS node identification and error mitigation techniques. However, the intricacies of NLOS localization are intrinsically tied to propagation challenges. In this paper, we propose a novel single-site localization method tailored for complex multipath NLOS environments, leveraging only angle-of-arrival (AOA) estimates in conjunction with a ray-tracing (RT) algorithm. The method transforms NLOS paths into equivalent line-of-sight (LOS) paths through the generation of generalized sources (GSs) via ray tracing. A novel weighting mechanism for GSs is introduced, which, when combined with an iteratively reweighted least squares (IRLS) estimator, significantly improves the localization accuracy of non-cooperative target sources. Furthermore, a multipath similarity displacement matrix (MSDM) is incorporated to enhance accuracy in regions with pronounced multipath fluctuations. Simulation results validate the efficacy of the proposed algorithm, achieving localization performance that approaches the Cramér–Rao lower bound (CRLB), even in challenging NLOS scenarios. Full article
Show Figures

Figure 1

Figure 1
<p>A flowchart of the proposed RT algorithm.</p>
Full article ">Figure 2
<p>Binary tree structure of ray nodes.</p>
Full article ">Figure 3
<p>Schematic diagram of ray-splitting structure. Red nodes indicate split nodes that will be deleted, while blue nodes represent newly generated split nodes.</p>
Full article ">Figure 4
<p>Schematic diagram of ray tube determination and reception. Red lines represent virtual ray tubes, while blue lines indicate the edge rays of the ray tube.</p>
Full article ">Figure 5
<p>An overview of the overall technical roadmap of the RT-LBS algorithm.</p>
Full article ">Figure 6
<p>Power measurement system architecture and key equipment. The <b>upper half</b> of the figure is the block diagram of the channel sounder used in this paper. The <b>lower half</b> is the key equipment of the sounder, including the signal generator, power amplifier, spectrum analyzer, power supplier, RTK, and antennas.</p>
Full article ">Figure 7
<p>Localization test system architecture and key equipment. The <b>upper half</b> of the figure is the block diagram of the localization test system used in this paper. The <b>lower half</b> is the key equipment in the signal transmitter system, UCA direction-finding equipment, the Rx antenna array, and the RF processing circuit.</p>
Full article ">Figure 8
<p>Measurement scenario. (<b>a</b>) The raw point cloud image of the measurement scenario. (<b>b</b>) The geometric building model extracted from the point cloud.</p>
Full article ">Figure 9
<p>Measurement path and power distribution at (<b>a</b>) 3 GHz frequency, (<b>b</b>) 3.6 GHz frequency, (<b>c</b>) 4 GHz frequency, (<b>d</b>) 5 GHz frequency, and (<b>e</b>) 5.9 GHz frequency.</p>
Full article ">Figure 10
<p>Raw power measurement data and power measurement data after applying the sliding filter at (<b>a</b>) 3 GHz frequency, (<b>b</b>) 3.6 GHz frequency, (<b>c</b>) 4 GHz frequency, (<b>d</b>) 5 GHz frequency, and (<b>e</b>) 5.9 GHz frequency.</p>
Full article ">Figure 11
<p>RSS predictions and measurements in the scenario at (<b>a</b>) 3 GHz frequency, (<b>b</b>) 3.6 GHz frequency, (<b>c</b>) 4 GHz frequency, (<b>d</b>) 5 GHz frequency, and (<b>e</b>) 5.9 GHz frequency. The basic RT method refers to the approach presented in [<a href="#B39-sensors-24-07925" class="html-bibr">39</a>].</p>
Full article ">Figure 12
<p>The angle measurement scenario and the positions of the NCTS (denoted by T1, T2, and T3) and sensor (denoted by R).</p>
Full article ">Figure 13
<p>The AOA spectrum measured for the source located at T1.</p>
Full article ">Figure 14
<p>The AOA spectrum measured for the source located at T2.</p>
Full article ">Figure 15
<p>The AOA spectrum measured for the source located at T3.</p>
Full article ">Figure 16
<p>Comparison between measured AS and simulated multipath at (<b>a</b>) T1 position, (<b>b</b>) T2 position, and (<b>c</b>) T3 position.</p>
Full article ">Figure 17
<p>NCTS and sensor positions and a geometrical map of the scenario. The line segments represent the multipath between the source and the sensor, distinguished using different colors.</p>
Full article ">Figure 18
<p>A comparison of the proposed localization algorithm’s accuracy with the CRLB. (<b>a</b>) The source at location A; (<b>b</b>) the source at location B; (<b>c</b>) the source at location C.</p>
Full article ">Figure 19
<p>Localization error at point A with different AOA and RSSD errors.</p>
Full article ">Figure 20
<p>Localization error at point B with different AOA and RSSD errors.</p>
Full article ">Figure 21
<p>Localization error at point C with different AOA and RSSD errors.</p>
Full article ">Figure 22
<p>MSD distribution at (<b>a</b>) 0.1° AOA error, (<b>b</b>) 0.5°AOA error, (<b>c</b>) 1°AOA error, (<b>d</b>) 2°AOA error, (<b>e</b>) 4°AOA error, and (<b>f</b>) 6°AOA error.</p>
Full article ">Figure 22 Cont.
<p>MSD distribution at (<b>a</b>) 0.1° AOA error, (<b>b</b>) 0.5°AOA error, (<b>c</b>) 1°AOA error, (<b>d</b>) 2°AOA error, (<b>e</b>) 4°AOA error, and (<b>f</b>) 6°AOA error.</p>
Full article ">Figure 23
<p>Schematic diagram of displacement compensation expansion method.</p>
Full article ">Figure 24
<p>Planar Localization Error Distribution with 0.1° AOA error. (<b>a</b>) Original localization algorithm; (<b>b</b>) localization algorithm with MSDM.</p>
Full article ">Figure 25
<p>Planar Localization Error Distribution with 0.5° AOA error. (<b>a</b>) Original localization algorithm; (<b>b</b>) localization algorithm with MSDM.</p>
Full article ">Figure 26
<p>Planar Localization Error Distribution with 1° AOA error. (<b>a</b>) Original localization algorithm; (<b>b</b>) localization algorithm with MSDM.</p>
Full article ">Figure 27
<p>Planar Localization Error Distribution with 2° AOA error. (<b>a</b>) Original localization algorithm; (<b>b</b>) localization algorithm with MSDM.</p>
Full article ">Figure 28
<p>Planar Localization Error Distribution with 4° AOA error. (<b>a</b>) Original localization algorithm; (<b>b</b>) localization algorithm with MSDM.</p>
Full article ">Figure 29
<p>Planar Localization Error Distribution with 6° AOA error. (<b>a</b>) Original localization algorithm; (<b>b</b>) localization algorithm with MSDM.</p>
Full article ">Figure 30
<p>Schematic diagram of GPU acceleration algorithm.</p>
Full article ">Figure 31
<p>Power coverage map.</p>
Full article ">Figure 32
<p>Efficiency comparison of different acceleration methods.</p>
Full article ">
20 pages, 2178 KiB  
Article
Performance Analysis of Cardioid and Omnidirectional Microphones in Spherical Sector Arrays for Coherent Source Localization
by Chibuzo Joseph Nnonyelu, Meng Jiang, Marianthi Adamopoulou and Jan Lundgren
Sensors 2024, 24(23), 7572; https://doi.org/10.3390/s24237572 - 27 Nov 2024
Viewed by 440
Abstract
Traditional spherical sector microphone arrays using omnidirectional microphones face limitations in modal strength and spatial resolution, especially within spherical sector configurations. This study aims to enhance array performance by developing a spherical sector array employing first-order cardioid microphones. A model based on spherical [...] Read more.
Traditional spherical sector microphone arrays using omnidirectional microphones face limitations in modal strength and spatial resolution, especially within spherical sector configurations. This study aims to enhance array performance by developing a spherical sector array employing first-order cardioid microphones. A model based on spherical sector harmonic (SSH) functions is introduced to extend the benefits of spherical harmonics to sector arrays. Modal strength analysis demonstrates that cardioid microphones in open spherical sectors enhance nonzero-order strengths and eliminate the nulls associated with spherical Bessel functions. We find that the spatial resolution of spherical cap arrays depends on the array’s maximum order and the limiting polar angle, but is independent of the microphone gain pattern. We assess direction-of-arrival (DOA) estimation performance for coherent wideband sources using the array manifold interpolation method, and compare cardioid and omnidirectional arrays through simulations in both open and rigid hemispherical configurations. The results indicate that cardioid arrays outperform omnidirectional ones on DOA estimation tasks, with performance improving alongside increased microphone directivity in the open hemispherical configuration. Specifically, hypercardioid microphones yielded the best results in the open configuration, while subcardioid microphones (without nulls) were optimal in rigid configurations. These findings demonstrate that spherical sector arrays of first-order cardioid microphones offer improved modal strength and DOA estimation capabilities over traditional omnidirectional arrays, providing significantly enhancing performance in spherical sector array processing. Full article
(This article belongs to the Section Physical Sensors)
Show Figures

Figure 1

Figure 1
<p>Hemispherical microphone array showing positions of nearly-uniformly sampled microphone locations.</p>
Full article ">Figure 2
<p>Mode strength variation with mode <math display="inline"><semantics> <mrow> <mi>k</mi> <mi>r</mi> </mrow> </semantics></math> for different degrees of <span class="html-italic">n</span> and (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> (standard cardioid), (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> (subcardioid), and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (omnidirectional) for a open hemisphere of radius <math display="inline"><semantics> <mrow> <mn>8</mn> <mspace width="0.166667em"/> <mi>cm</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>Mode strength variation with mode <math display="inline"><semantics> <mrow> <mi>k</mi> <mi>r</mi> </mrow> </semantics></math> for different degrees of <span class="html-italic">n</span> and (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> (hypercardioid), (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> (subcardioid), and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (omnidirectional) for a rigid hemisphere of radius <math display="inline"><semantics> <mrow> <mn>8</mn> <mspace width="0.166667em"/> <mi>cm</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Plot of the normalized directivity function <math display="inline"><semantics> <mrow> <msub> <mi>w</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mo>Θ</mo> <mo>)</mo> </mrow> </mrow> </semantics></math> versus the angle between the source direction and look direction <math display="inline"><semantics> <mo>Θ</mo> </semantics></math> using a hemisphere for various orders <span class="html-italic">N</span>.</p>
Full article ">Figure 5
<p>Plot of the spatial resolution <math display="inline"><semantics> <msub> <mo>Θ</mo> <mn>0</mn> </msub> </semantics></math> versus order <span class="html-italic">N</span> and fitting to a rational function <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>a</mi> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mstyle> </semantics></math> for different values of <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>.</p>
Full article ">Figure 6
<p>Plots of the beampattern magnitude versus the polar angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> and azimuthal angle <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> for four incident coherent sources from <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mo>(</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <msup> <mn>30</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>150</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <msup> <mn>80</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>220</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <msup> <mn>30</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>300</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </mrow> </semantics></math> using an open hemisphere of (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> (hypercardioid), (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> (standard cardioid), (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> (subcardioid), and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (omnidirectional).</p>
Full article ">Figure 7
<p>Plots of the beampattern magnitude versus the polar angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> and azimuthal angle <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> for four incident coherent sources from <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mo>(</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <msup> <mn>30</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>150</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <msup> <mn>80</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>220</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <msup> <mn>30</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>300</mn> <mo>°</mo> </msup> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </mrow> </semantics></math> using a rigid hemisphere of (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> (hypercardioid), (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> (subcardioid), and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (omnidirectional).</p>
Full article ">Figure 8
<p>Plots of the cumulative mean error <math display="inline"><semantics> <msub> <mi>CME</mi> <mrow> <mi>θ</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </msub> </semantics></math> versus the signal-to-noise ratio (SNR) for various <math display="inline"><semantics> <mi>α</mi> </semantics></math> in (<b>a</b>) open hemisphere and (<b>b</b>) rigid hemisphere.</p>
Full article ">Figure 9
<p>Plots of the root mean square error (RMSE) versus the signal-to-noise ratio (SNR) of an open hemisphere with various <math display="inline"><semantics> <mi>α</mi> </semantics></math> for (<b>a</b>) the polar angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> and (<b>b</b>) the azimuthal angle <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>.</p>
Full article ">Figure 10
<p>Plots of the root mean square error (RMSE) versus the signal-to-noise ratio (SNR) of a rigid hemisphere with various <math display="inline"><semantics> <mi>α</mi> </semantics></math>: (<b>a</b>) the polar angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> and (<b>b</b>) the azimuthal angle <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>.</p>
Full article ">Figure 11
<p>Plots of the average <math display="inline"><semantics> <mi>RMSE</mi> </semantics></math> and minimum and maximum RMSE of the polar and azimuthal angles versus the cardioid type <math display="inline"><semantics> <mi>α</mi> </semantics></math> for (<b>a</b>) an open hemisphere and (<b>b</b>) a rigid hemisphere for an SNR of 10 dB.</p>
Full article ">Figure 12
<p>Plots of the average <math display="inline"><semantics> <mi>RMSE</mi> </semantics></math> and minimum and maximum RMSE of the polar and azimuthal angles versus the cardioid type <math display="inline"><semantics> <mi>α</mi> </semantics></math> for (<b>a</b>) an open hemisphere and (<b>b</b>) a rigid hemisphere for an SNR of 50 dB.</p>
Full article ">
9 pages, 4164 KiB  
Proceeding Paper
Direction-of-Arrival (DOA) Estimation Based on Real Field Measurements and Modified Linear Regression
by Luis Antonio Flores, Ismael Lomas, Lenin Guachalá, Pablo Lupera-Morillo, Robin Álvarez and Ricardo Llugsi
Eng. Proc. 2024, 77(1), 11; https://doi.org/10.3390/engproc2024077011 - 18 Nov 2024
Viewed by 320
Abstract
This study applied modified linear regression in machine learning (ML) to predict the direction of arrival (DoA) in cellular networks using field measurements and radiofrequency parameters. Models were developed from base station data, with preprocessing for pattern identification and formula adjustments to improve [...] Read more.
This study applied modified linear regression in machine learning (ML) to predict the direction of arrival (DoA) in cellular networks using field measurements and radiofrequency parameters. Models were developed from base station data, with preprocessing for pattern identification and formula adjustments to improve the accuracy across angle ranges. Machine learning, tested here as an additional method to traditional techniques, achieved a root mean square error (RMSE) of 3.63 to 17.93, demonstrating enhanced adaptability. While requiring substantial data and computational resources, this approach highlights machine learning’s potential as a valuable tool for DoA estimation in cellular networks. Full article
(This article belongs to the Proceedings of The XXXII Conference on Electrical and Electronic Engineering)
Show Figures

Figure 1

Figure 1
<p>Process flow diagram of DoA Estimation.</p>
Full article ">Figure 2
<p>(<b>a</b>) Map of the final radial and circular routes for measurements in Coverage Area 1. (<b>b</b>) Map showing the final radial and circular routes for measurements in Coverage Area 2 (Google Maps).</p>
Full article ">Figure 3
<p>The reference system was positioned at the analyzed BS.</p>
Full article ">Figure 4
<p>(<b>a</b>) Coverage Area 1 and antenna orientation. (<b>b</b>) Coverage Area 2 and antenna orientation.</p>
Full article ">Figure 5
<p>(<b>a</b>) RSSI dispersion for different DoAs as a function of the distance. (<b>b</b>) RSRQ for three DoA ranges as a function of the distance in Coverage Area 1.</p>
Full article ">Figure 6
<p>(<b>a</b>) General correlation matrix in Coverage Area 1. (<b>b</b>) Correlation matrix in a 340–360 degree range within Coverage Area 1. The more asterisks, the more significant the result.</p>
Full article ">Figure 7
<p>(<b>a</b>) RSSI dispersion for different DoAs as a function of the distance. (<b>b</b>) Scatter plot of RSRQ for different DoAs as a function of the distance in Coverage Area 2.</p>
Full article ">Figure 8
<p>(<b>a</b>) General correlation matrix in Coverage Area 2. (<b>b</b>) Correlation matrix in a 340–360 degree range within Coverage Area 2. The more asterisks, the more significant the result.</p>
Full article ">
19 pages, 5613 KiB  
Article
A New Method for Joint Sparse DOA Estimation
by Jinyong Hou, Changlong Wang, Zixuan Zhao, Feng Zhou and Huaji Zhou
Sensors 2024, 24(22), 7216; https://doi.org/10.3390/s24227216 - 12 Nov 2024
Viewed by 577
Abstract
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 [...] Read more.
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. Full article
Show Figures

Figure 1

Figure 1
<p>Passive radar system model.</p>
Full article ">Figure 2
<p>Uniform array antenna model.</p>
Full article ">Figure 3
<p>Hyperbolic tangent functions with different parameters.</p>
Full article ">Figure 4
<p>Digital TV signal simulation.</p>
Full article ">Figure 5
<p>Single array antenna pattern.</p>
Full article ">Figure 6
<p>Single target effect experiment.</p>
Full article ">Figure 7
<p>Three-objective effect experiment.</p>
Full article ">Figure 8
<p>Eight matrix DOA estimation results.</p>
Full article ">Figure 9
<p>DOA estimation results of four array elements.</p>
Full article ">Figure 10
<p>Results of 60 iterations.</p>
Full article ">Figure 11
<p>Simulation analysis similar to the real environment.</p>
Full article ">Figure 12
<p>Relationship between direction finding error and SNR.</p>
Full article ">Figure 13
<p>Relationship between direction finding error and angular interval.</p>
Full article ">Figure 14
<p>Algorithm performance versus number of snapshots.</p>
Full article ">Figure 15
<p>Algorithm performance versus number of array elements.</p>
Full article ">Figure 16
<p>Antennas and map used in the experiment.</p>
Full article ">Figure 17
<p>Experimental results of the measured data.</p>
Full article ">
16 pages, 2929 KiB  
Article
TDOA-AOA Localization Algorithm for 5G Intelligent Reflecting Surfaces
by Yuexia Zhang, Changbao Liu, Yuanshuo Gang and Yu Wang
Electronics 2024, 13(22), 4347; https://doi.org/10.3390/electronics13224347 - 6 Nov 2024
Viewed by 655
Abstract
5G positioning technology has become deeply integrated into daily life. However, in wireless signal propagation environments, there may exist non-line-of-sight (NLOS) conditions, which lead to signal blockage and subsequently hinder the provision of positioning services. To address this issue, this paper proposes an [...] Read more.
5G positioning technology has become deeply integrated into daily life. However, in wireless signal propagation environments, there may exist non-line-of-sight (NLOS) conditions, which lead to signal blockage and subsequently hinder the provision of positioning services. To address this issue, this paper proposes an intelligent reflecting surface (IRS) NLOS time difference of arrival–angle of arrival (TDOA-AOA) localization (INTAL) algorithm. First, the algorithm constructs a system model for 5G IRS localization, effectively overcoming the challenges of positioning in NLOS paths. Then, by applying the multiple signal classification algorithm to estimate the time delay and angle, and using the Chan algorithm to obtain the user’s estimated coordinates, an optimization problem is formulated to minimize the distance between the estimated and actual coordinates. The tent–snake optimization algorithm is employed to solve this optimization problem, thereby reducing localization errors. Finally, simulations demonstrate that the INTAL algorithm outperforms the snake optimization (SO) algorithm and the gray wolf optimization (GWO) algorithm under the same conditions, reducing the localization error by 56% and 60% on average, respectively. Additionally, when the signal-to-noise ratio is 30 dB, the localization error of the INTAL algorithm is only 0.2968 m, while the errors for the SO and GWO algorithms are 0.6733 m and 0.7398 m, respectively. This further proves the significant improvement of the algorithm in terms of localization accuracy. Full article
(This article belongs to the Special Issue New Advances in Navigation and Positioning Systems)
Show Figures

Figure 1

Figure 1
<p>Illustration of GIL system model.</p>
Full article ">Figure 2
<p>Illustration of US-IRS signal propagation.</p>
Full article ">Figure 3
<p>Illustration of the pitch angle relationship between US and IRS.</p>
Full article ">Figure 4
<p>Flowchart of the tent–SO algorithm.</p>
Full article ">Figure 5
<p>Variation in fitness with iterations.</p>
Full article ">Figure 6
<p>Three-dimensional localization results.</p>
Full article ">Figure 7
<p>IRS position and positioning error analysis.</p>
Full article ">Figure 8
<p>Positioning error under different numbers of snapshots and varying SNRs.</p>
Full article ">Figure 9
<p>Analysis of positioning errors for different algorithms under varying SNRs.</p>
Full article ">Figure 10
<p>Positioning error with different numbers of IRSs under varying SNRs.</p>
Full article ">
16 pages, 2967 KiB  
Technical Note
Field Programmable Gate Array (FPGA) Implementation of Parallel Jacobi for Eigen-Decomposition in Direction of Arrival (DOA) Estimation Algorithm
by Shuang Zhou and Li Zhou
Remote Sens. 2024, 16(20), 3892; https://doi.org/10.3390/rs16203892 - 19 Oct 2024
Viewed by 880
Abstract
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 [...] Read more.
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. Full article
Show Figures

Figure 1

Figure 1
<p>Systolic array structure of an 8-order covariance matrix.</p>
Full article ">Figure 2
<p>(<b>a</b>) First rotational partition diagram. (<b>b</b>) Second rotational partition diagram.</p>
Full article ">Figure 3
<p>The steps of module operation.</p>
Full article ">Figure 4
<p>Block diagram of the MUSIC algorithm.</p>
Full article ">Figure 5
<p>Simulation results of eigen-decomposition iteration for (<b>a</b>) 21 times and (<b>b</b>) 28 times.</p>
Full article ">Figure 5 Cont.
<p>Simulation results of eigen-decomposition iteration for (<b>a</b>) 21 times and (<b>b</b>) 28 times.</p>
Full article ">Figure 6
<p>Illustration of the direction-finding results on the UV plane in MATLAB and FPGA.</p>
Full article ">
17 pages, 6007 KiB  
Article
An Improved Unfolded Coprime Linear Array Design for DOA Estimation with No Phase Ambiguity
by Pan Gong and Xiaofei Zhang
Sensors 2024, 24(19), 6205; https://doi.org/10.3390/s24196205 - 25 Sep 2024
Viewed by 648
Abstract
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 [...] Read more.
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. Full article
Show Figures

Figure 1

Figure 1
<p>Unfolded coprime linear array (UCLA).</p>
Full article ">Figure 2
<p>The relationship between the phase ambiguity problem and the inter-element spacing.</p>
Full article ">Figure 3
<p>No ambiguous angle arises with two source signals, where <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mo>°</mo> <mo>,</mo> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>37</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>No ambiguous angle arises with the three given source signals, where <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mo>°</mo> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>20</mn> <mo>°</mo> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>With the method in [<a href="#B33-sensors-24-06205" class="html-bibr">33</a>], the ambiguous angle arises with three source signals that satisfy Equation (10).</p>
Full article ">Figure 6
<p>Using the method in [<a href="#B34-sensors-24-06205" class="html-bibr">34</a>] for the beamforming technique sometimes is not effective.</p>
Full article ">Figure 7
<p>(<b>a</b>) The unfolded coprime linear array. (<b>b</b>) The designed and improved unfolded coprime linear array.</p>
Full article ">Figure 8
<p>The reconstructed array configuration can achieve the full DOFs of three source signals.</p>
Full article ">Figure 9
<p>The reconstructed array configuration can achieve the full DOFs of seven source signals.</p>
Full article ">Figure 10
<p>The complexity versus the number of sensors [<a href="#B33-sensors-24-06205" class="html-bibr">33</a>,<a href="#B34-sensors-24-06205" class="html-bibr">34</a>].</p>
Full article ">Figure 11
<p>(<b>a</b>) Comparison of the proposed method to the method in [<a href="#B33-sensors-24-06205" class="html-bibr">33</a>] and (<b>b</b>) comparison of the proposed method to the method in [<a href="#B34-sensors-24-06205" class="html-bibr">34</a>].</p>
Full article ">Figure 12
<p>The RMSE versus the SNR of the proposed method.</p>
Full article ">Figure 13
<p>The RMSE versus the snapshot of the proposed method.</p>
Full article ">Figure 14
<p>The RMSE versus the SNR based on different arrays.</p>
Full article ">Figure 15
<p>The RMSE versus the snapshot based on different arrays.</p>
Full article ">
19 pages, 5345 KiB  
Article
Accurate Low Complexity Quadrature Angular Diversity Aperture Receiver for Visible Light Positioning
by Stefanie Cincotta, Adrian Neild, Kristian Helmerson, Michael Zenere and Jean Armstrong
Sensors 2024, 24(18), 6006; https://doi.org/10.3390/s24186006 - 17 Sep 2024
Viewed by 861
Abstract
Despite the many potential applications of an accurate indoor positioning system (IPS), no universal, readily available system exists. Much of the IPS research to date has been based on the use of radio transmitters as positioning beacons. Visible light positioning (VLP) instead uses [...] Read more.
Despite the many potential applications of an accurate indoor positioning system (IPS), no universal, readily available system exists. Much of the IPS research to date has been based on the use of radio transmitters as positioning beacons. Visible light positioning (VLP) instead uses LED lights as beacons. Either cameras or photodiodes (PDs) can be used as VLP receivers, and position estimates are usually based on either the angle of arrival (AOA) or the strength of the received signal. Research on the use of AOA with photodiode receivers has so far been limited by the lack of a suitable compact receiver. The quadrature angular diversity aperture receiver (QADA) can fill this gap. In this paper, we describe a new QADA design that uses only three readily available parts: a quadrant photodiode, a 3D-printed aperture, and a programmable system on a chip (PSoC). Extensive experimental results demonstrate that this design provides accurate AOA estimates within a room-sized test chamber. The flexibility and programmability of the PSoC mean that other sensors can be supported by the same PSoC. This has the potential to allow the AOA estimates from the QADA to be combined with information from other sensors to form future powerful sensor-fusion systems requiring only one beacon. Full article
(This article belongs to the Special Issue Sensors and Techniques for Indoor Positioning and Localization)
Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) QADA built on a prototyping board; (<b>b</b>) close-up of aperture removed from QPD.</p>
Full article ">Figure 2
<p>Circuit programmed in PSoC and external QPD.</p>
Full article ">Figure 3
<p>Histograms showing the distribution of samples for each quadrant for a QPD with no aperture and with no transmitting light.</p>
Full article ">Figure 4
<p>Histograms showing the distribution of samples for each quadrant for the case of no aperture and square-wave modulated light source.</p>
Full article ">Figure 5
<p>QADA prototype mounted on test platform in test chamber.</p>
Full article ">Figure 6
<p>QADA receiver design.</p>
Full article ">Figure 7
<p>Detail of the light spot on the quadrant photodiode.</p>
Full article ">Figure 8
<p>(<b>a</b>) Estimated angle <math display="inline"><semantics> <mover accent="true"> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> versus calculated angle <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> (black crosses) and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="false">^</mo> </mover> <mo>=</mo> <msub> <mi>α</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> (red line); (<b>b</b>) error in estimated angle <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="false">^</mo> </mover> <mo>−</mo> <msub> <mi>α</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> versus calculated angle <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> excluding outliers.</p>
Full article ">Figure 9
<p>(<b>a</b>) Estimated angle <math display="inline"><semantics> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> versus calculated angle <math display="inline"><semantics> <mrow> <msub> <mi>ψ</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> (black crosses) and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">^</mo> </mover> <mo>=</mo> <msub> <mi>ψ</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> (red line); (<b>b</b>) error in estimated angle <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">^</mo> </mover> <mo>−</mo> <msub> <mi>ψ</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> versus calculated angle.</p>
Full article ">Figure 10
<p>(<b>a</b>) Predicted positions within the room of the luminaire centroid (red dots), luminaire outline (blue lines); (<b>b</b>) predicted positions of luminaire centroid (red dots), luminaire outline (blue lines) and luminaire centroid (black asterisk) on an expanded scale. The inner blue line marks the area of the luminaire which transmits light. The outer blue lines include its metal frame.</p>
Full article ">Figure 11
<p>Predicted positions (black dots) and actual positions of QADA (red crosses). Predicted positions calculated using (9) and (10). The luminaire outline is shown in blue.</p>
Full article ">Figure 12
<p>(<b>a</b>) Position of luminaire centroid predicted using <math display="inline"><semantics> <mrow> <msub> <mi>ψ</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>; (<b>b</b>) position of luminaire centroid predicted <math display="inline"><semantics> <mover accent="true"> <mi>ψ</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi mathvariant="normal">C</mi> </msub> </mrow> </semantics></math>.</p>
Full article ">
19 pages, 10323 KiB  
Article
Numerical Modeling of Scholte Wave in Acoustic-Elastic Coupled TTI Anisotropic Media
by Yifei Chen and Deli Wang
Appl. Sci. 2024, 14(18), 8302; https://doi.org/10.3390/app14188302 - 14 Sep 2024
Viewed by 719
Abstract
Numerical modeling of acoustic-elastic media is helpful for seismic exploration in the deepwater environment. We propose an algorithm based on the staggered grid finite difference to simulate wave propagation in the interface between fluid and transversely isotropic media, where the interface does not [...] Read more.
Numerical modeling of acoustic-elastic media is helpful for seismic exploration in the deepwater environment. We propose an algorithm based on the staggered grid finite difference to simulate wave propagation in the interface between fluid and transversely isotropic media, where the interface does not need to consider the boundary condition. We also derive the stability conditions of the proposed method. Scholte waves, which are generated at the seafloor, exhibit distinctly different propagation behaviors than body waves in ocean-bottom seismograms. Numerical examples are used to characterize the wavefield of Scholte waves and discuss the relationship between travel time and the Thomsen parameters. Thomsen parameters are assigned clear physical meanings, and the magnitude of their values directly indicates the strength of the anisotropy in the media. Numerical results show that the velocity of the Scholte wave is positively correlated with ε and negatively correlated with δ. And the curve of the arrival time of the Scholte wave as a whole is sinusoidal and has no symmetry in inclination. The velocity of the Scholte wave in azimuth is positively related to the polar angle. The energy of the Scholte wave is negatively correlated with the distance from the source to the fluid-solid interface. The above results provide a basis for studying oceanic Scholte waves and are beneficial for utilizing the information provided by Scholte waves. Full article
Show Figures

Figure 1

Figure 1
<p>Coordinate transformation diagram of Bond matrix.</p>
Full article ">Figure 2
<p>3D staggered grid and parameter definition diagram. The stresses and the pressure field are defined at the standard grid points. The velocity components and Thomsen parameters of the acoustic-elastic coupled media are defined on the staggered grid points.</p>
Full article ">Figure 3
<p>Snapshots of particle-velocity components (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.5</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The red line denotes the fluid-solid interface.</p>
Full article ">Figure 4
<p>Snapshots of particle-velocity components (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> </mrow> </semantics></math> with spectral element method at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.5</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The red line denotes the fluid-solid interface.</p>
Full article ">Figure 5
<p>The vibration curve of the Scholte wave.</p>
Full article ">Figure 6
<p>Arrival time of the Scholte wave with a different polar angle.</p>
Full article ">Figure 7
<p>Arrival time of the Scholte wave with different Thomsen parameters (<b>a</b>) <math display="inline"><semantics> <mi>ε</mi> </semantics></math> and (<b>b</b>) δ. In plot (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mo>−</mo> <mn>0.05</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>; In plot (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>The orientation of the observation line. <math display="inline"><semantics> <mi>φ</mi> </semantics></math> denotes the orientation of the observation line. The points are used to test the arrival time of the Scholte wave.</p>
Full article ">Figure 9
<p>Snapshots of the components (<b>left</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> </mrow> </semantics></math>, (<b>centre</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>y</mi> </msub> </mrow> </semantics></math>, and (<b>right</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The red line denotes the fluid-solid interface. The plane of parameter <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math> is XOZ plane, and the plane of parameter <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>90</mn> <mo>°</mo> </mrow> </semantics></math> is YOZ plane. The Thomsen parameters are <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mo>−</mo> <mn>0.05</mn> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>γ</mo> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Snapshots of the components (<b>left</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> </mrow> </semantics></math>, (<b>centre</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>y</mi> </msub> </mrow> </semantics></math>, and (<b>right</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> </mrow> </semantics></math> on the fluid-solid interface at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The Thomsen parameters are <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mo>−</mo> <mn>0.05</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>γ</mo> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Arrival time of the Scholte wave at point A, B, C, and D with different polar angles. The blue, red, yellow, and purple lines are point A, B, C, and D, respectively. The Thomsen parameters are <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mo>−</mo> <mn>0.05</mn> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>γ</mo> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p>Acoustic-elastic coupled Marmousi-2 model. Plots (<b>a</b>–<b>d</b>) are the P- and SV-wave vertical velocities and the Thomsen parameters <math display="inline"><semantics> <mo>ε</mo> </semantics></math> and <math display="inline"><semantics> <mo>δ</mo> </semantics></math>, respectively. The red line is the fluid-solid interface. The icon S represents the point source.</p>
Full article ">Figure 13
<p>Snapshots of particle-velocity components (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1.1</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The red line denotes the fluid-solid interface.</p>
Full article ">Figure 14
<p>Seismograms from the Marmousi2 model. The water layer is <math display="inline"><semantics> <mrow> <mn>0.75</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> thick. (<b>a</b>): The source is located at <math display="inline"><semantics> <mrow> <mi mathvariant="normal">x</mi> <mo>=</mo> <mn>4.62</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">z</mi> <mo>=</mo> <mn>0.7375</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math>; (<b>b</b>): The source is located at <math display="inline"><semantics> <mrow> <mi mathvariant="normal">x</mi> <mo>=</mo> <mn>4.62</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">z</mi> <mo>=</mo> <mn>0.725</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math>; (<b>c</b>): The source is located at <math display="inline"><semantics> <mrow> <mi mathvariant="normal">x</mi> <mo>=</mo> <mn>4.62</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">z</mi> <mo>=</mo> <mn>0.7</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 14 Cont.
<p>Seismograms from the Marmousi2 model. The water layer is <math display="inline"><semantics> <mrow> <mn>0.75</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> thick. (<b>a</b>): The source is located at <math display="inline"><semantics> <mrow> <mi mathvariant="normal">x</mi> <mo>=</mo> <mn>4.62</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">z</mi> <mo>=</mo> <mn>0.7375</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math>; (<b>b</b>): The source is located at <math display="inline"><semantics> <mrow> <mi mathvariant="normal">x</mi> <mo>=</mo> <mn>4.62</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">z</mi> <mo>=</mo> <mn>0.725</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math>; (<b>c</b>): The source is located at <math display="inline"><semantics> <mrow> <mi mathvariant="normal">x</mi> <mo>=</mo> <mn>4.62</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">z</mi> <mo>=</mo> <mn>0.7</mn> <mo> </mo> <mi>km</mi> </mrow> </semantics></math>.</p>
Full article ">
Back to TopTop