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Keywords = direction of arrival (DOA)

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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 96
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
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<p>Process flow diagram of DoA Estimation.</p>
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<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>
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<p>The reference system was positioned at the analyzed BS.</p>
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<p>(<b>a</b>) Coverage Area 1 and antenna orientation. (<b>b</b>) Coverage Area 2 and antenna orientation.</p>
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<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>
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<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>
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<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>
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<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>
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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 374
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
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<p>Passive radar system model.</p>
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<p>Uniform array antenna model.</p>
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<p>Hyperbolic tangent functions with different parameters.</p>
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<p>Digital TV signal simulation.</p>
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<p>Single array antenna pattern.</p>
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<p>Single target effect experiment.</p>
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<p>Three-objective effect experiment.</p>
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<p>Eight matrix DOA estimation results.</p>
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<p>DOA estimation results of four array elements.</p>
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<p>Results of 60 iterations.</p>
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<p>Simulation analysis similar to the real environment.</p>
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<p>Relationship between direction finding error and SNR.</p>
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<p>Relationship between direction finding error and angular interval.</p>
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<p>Algorithm performance versus number of snapshots.</p>
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<p>Algorithm performance versus number of array elements.</p>
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<p>Antennas and map used in the experiment.</p>
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<p>Experimental results of the measured data.</p>
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22 pages, 6513 KiB  
Article
A Novel Beam-Domain Direction-of-Arrival Tracking Algorithm for an Underwater Target
by Xianghao Hou, Weisi Hua, Yuxuan Chen and Yixin Yang
Remote Sens. 2024, 16(21), 4074; https://doi.org/10.3390/rs16214074 - 31 Oct 2024
Viewed by 348
Abstract
Underwater direction-of-arrival (DOA) tracking using a hydrophone array is an important research subject in passive sonar signal processing. In this study, a DOA tracking algorithm based on a novel beam-domain signal processing technique is proposed to ensure robust DOA tracking of an interested [...] Read more.
Underwater direction-of-arrival (DOA) tracking using a hydrophone array is an important research subject in passive sonar signal processing. In this study, a DOA tracking algorithm based on a novel beam-domain signal processing technique is proposed to ensure robust DOA tracking of an interested underwater target under a low signal-to-noise ratio (SNR) environment. Firstly, the beam-based observation is designed and proposed, which innovatively applies beamforming after array-based observation to achieve specific spatial directivity. Next, the proportional–integral–differential (PID)-optimized Olen–Campton beamforming method (PIDBF) is designed and proposed in the beamforming process to achieve faster and more stable sidelobe control performance to enhance the SNR of the target. The adaptive dynamic beam window is designed and proposed to focusing the observation on more likely observation area. Then, by utilizing the extended Kalman filter (EKF) tracking framework, a novel PIDBF-optimized beam-domain DOA tracking algorithm (PIDBF-EKF) is proposed. Finally, simulations with different SNR scenarios and comprehensive analyses are made to verify the superior performance of the proposed DOA tracking approach. Full article
(This article belongs to the Section Ocean Remote Sensing)
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<p>Configuration of the ULA-based measurement system.</p>
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<p>Comparison of beam patterns for Olen series optimization methods at different iteration counts. (<b>a</b>) 1 iteration. (<b>b</b>) 5 iterations. (<b>c</b>) 10 iterations. (<b>d</b>) 20 iterations. (<b>e</b>) 50 iterations. (<b>f</b>) 100 iterations.</p>
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<p>MSE and RMSE plots for the Olen series optimization methods. (<b>a</b>) MSE plot for the Olen series optimization methods. (<b>b</b>) RMSE plot for the Olen series optimization methods.</p>
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<p>The time required for the Olen series optimization method to achieve an RMSE of 2.</p>
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<p>The time required for the Olen series optimization method to achieve an RMSE of 1.</p>
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<p>The time required for the Olen series optimization method to achieve an RMSE of 0.5.</p>
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<p>Comparison of various methods with an SNR of 0 dB. (<b>a</b>) Comparison of bearing angle tracking result with an SNR of 0 dB. (<b>b</b>) BEEs obtained with an SNR of 0 dB.</p>
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<p>Comparison of various methods with an SNR of −10 dB. (<b>a</b>) Comparison of bearing angle tracking result with an SNR of −10 dB. (<b>b</b>) BEEs obtained with an SNR of −10 dB.</p>
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<p>Comparison of various methods with an SNR of −20 dB. (<b>a</b>) Comparison of bearing angle tracking result with an SNR of −20 dB. (<b>b</b>) BEEs obtained with an SNR of −20 dB.</p>
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<p>Comparison of various methods with an SNR of −30 dB. (<b>a</b>) Comparison of bearing angle tracking result with an SNR of −30 dB. (<b>b</b>) BEEs obtained with an SNR of −30 dB.</p>
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<p>Comparison of various methods with the number of beams set to 3. (<b>a</b>) Comparison of bearing angle tracking result with the number of beams set to 3. (<b>b</b>) BEEs obtained with the number of beams set to 3.</p>
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<p>Comparison of various methods with the number of beams set to 5. (<b>a</b>) Comparison of bearing angle tracking result with the number of beams set to 5. (<b>b</b>) BEEs obtained with the number of beams set to 5.</p>
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<p>Comparison of various methods with the number of beams set to 9. (<b>a</b>) Comparison of bearing angle tracking result with the number of beams set to 9. (<b>b</b>) BEEs obtained with the number of beams set to 9.</p>
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<p>Comparison of various methods with the number of beams set to 15. (<b>a</b>) Comparison of bearing angle tracking result with the number of beams set to 15. (<b>b</b>) BEEs obtained with the number of beams set to 15.</p>
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<p>Comparison of various methods with the number of beams set to 18. (<b>a</b>) Comparison of bearing angle tracking result with the number of beams set to 18. (<b>b</b>) BEEs obtained with the number of beams set to 18.</p>
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<p>Comparison of various methods with the number of beams set to 25. (<b>a</b>) Comparison of bearing angle tracking result with the number of beams set to 25. (<b>b</b>) BEEs obtained with the number of beams set to 25.</p>
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22 pages, 3751 KiB  
Article
Two-Dimensional Coherent Polarization–Direction-of-Arrival Estimation Based on Sequence-Embedding Fusion Transformer
by Zihan Wu, Jun Wang and Zhiquan Zhou
Remote Sens. 2024, 16(21), 3977; https://doi.org/10.3390/rs16213977 - 25 Oct 2024
Viewed by 701
Abstract
Addressing the issue of inadequate convergence and suboptimal accuracy in classical data-driven algorithms for coherent polarization–direction-of-arrival (DOA) estimation, a novel high-precision two-dimensional coherent polarization–DOA estimation method utilizing a sequence-embedding fusion (SEF) transformer is proposed for the first time. Drawing inspiration from natural language [...] Read more.
Addressing the issue of inadequate convergence and suboptimal accuracy in classical data-driven algorithms for coherent polarization–direction-of-arrival (DOA) estimation, a novel high-precision two-dimensional coherent polarization–DOA estimation method utilizing a sequence-embedding fusion (SEF) transformer is proposed for the first time. Drawing inspiration from natural language processing (NLP), this approach employs transformer-based multitasking text inference to facilitate joint estimation of polarization and DOA. This method leverages the multi-head self-attention mechanism of the transformer to effectively capture the multi-dimensional features within the spatial-polarization domain of the covariance matrix data. Additionally, an SEF module was proposed to fuse the spatial-polarization domain features from different dimensions. The module is a combination of a convolutional neural network (CNN) with local information extraction capabilities and a feature dimension transformation function, serving to improve the model’s ability to fuse information about features in the spatial-polarization domain. Moreover, to enhance the model’s expressive capacity, we designed a multi-task parallel output mode and a multi-task weighted loss function. Simulation results demonstrate that our method outperforms classical data-driven approaches in both accuracy and generalization, and the estimation accuracy of our method is improved relative to the traditional model-driven algorithm. Full article
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<p>Array- model structure.</p>
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<p>Proposed network model.</p>
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<p>Structure of self attention mechanism fusion CNN.</p>
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<p>Structure of SEF self attention mechanism.</p>
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<p>Structure of overall SEF multi−head self attention mechanism.</p>
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<p>Relationship curve between epoch and loss (SEF Trans method).</p>
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<p>Relationship curve between epoch and loss (Trans method).</p>
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<p>Relationship curve between epoch and loss (MLP method).</p>
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<p>Relationship curve between epoch and test accuracy (SEF Trans method).</p>
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<p>Relationship curve between epoch and test accuracy (Trans method).</p>
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<p>Relationship curve between epoch and test accuracy (MLP method).</p>
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<p>Testing accuracy comparison of SEF Trans method for position encoding.</p>
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<p>Relationship curve between RMSE and SNR (situation with matched SNR). (<b>a</b>) Azimuth angle. (<b>b</b>) Elevation angle. (<b>c</b>) Auxiliary polarization angle. (<b>d</b>) Polarization phase difference.</p>
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<p>Relationship curve between RMSE and snapshots (situation with matched snapshots). (<b>a</b>) Azimuth angle. (<b>b</b>) Elevation angle. (<b>c</b>) Auxiliary polarization angle. (<b>d</b>) Polarization phase difference.</p>
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<p>Relationship curve between RMSE and SNR (situation with mismatched SNR). (<b>a</b>) Azimuth angle. (<b>b</b>) Elevation angle. (<b>c</b>) Auxiliary polarization angle. (<b>d</b>) Polarization phase difference.</p>
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<p>Relationship curve between RMSE and snapshots (situation with mismatched snapshots). (<b>a</b>) Azimuth angle. (<b>b</b>) Elevation angle. (<b>c</b>) Auxiliary polarization angle. (<b>d</b>) Polarization phase difference.</p>
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20 pages, 3003 KiB  
Article
Equipment Sounds’ Event Localization and Detection Using Synthetic Multi-Channel Audio Signal to Support Collision Hazard Prevention
by Kehinde Elelu, Tuyen Le and Chau Le
Buildings 2024, 14(11), 3347; https://doi.org/10.3390/buildings14113347 - 23 Oct 2024
Viewed by 426
Abstract
Construction workplaces often face unforeseen collision hazards due to a decline in auditory situational awareness among on-foot workers, leading to severe injuries and fatalities. Previous studies that used auditory signals to prevent collision hazards focused on employing a classical beamforming approach to determine [...] Read more.
Construction workplaces often face unforeseen collision hazards due to a decline in auditory situational awareness among on-foot workers, leading to severe injuries and fatalities. Previous studies that used auditory signals to prevent collision hazards focused on employing a classical beamforming approach to determine equipment sounds’ Direction of Arrival (DOA). No existing frameworks implement a neural network-based approach for both equipment sound classification and localization. This paper presents an innovative framework for sound classification and localization using multichannel sound datasets artificially synthesized in a virtual three-dimensional space. The simulation synthesized 10,000 multi-channel datasets using just fourteen single sound source audiotapes. This training includes a two-staged convolutional recurrent neural network (CRNN), where the first stage learns multi-label sound event classes followed by the second stage to estimate their DOA. The proposed framework achieves a low average DOA error of 30 degrees and a high F-score of 0.98, demonstrating accurate localization and classification of equipment near workers’ positions on the site. Full article
(This article belongs to the Special Issue Big Data Technologies in Construction Management)
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<p>Multichannel Audio-based Collision Hazard Detection Pipeline.</p>
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<p>Spectrogram for (<b>Left</b>) Crane—Mobile Equipment, (<b>Right</b>) Saw—Stationary Equipment.</p>
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<p>Sample simulation setup.</p>
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<p>Sample scenario of equipment moving toward workers on construction site. One piece of equipment is mobile, moving towards the right (left ball), and another is stationary (right ball). (<b>A</b>) initial position of both pieces of equipment sound, (<b>B</b>) the mobile equipment (left ball) approaches the workers, while the stationary equipment (right ball) remains in place, (<b>C</b>) the mobile equipment is halfway toward the workers, with a potential collision hazard emerging, (<b>D</b>) the mobile equipment reaches its closest point to the workers.</p>
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<p>Two-Stage Sound Event Detection and Localization Network.</p>
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<p>SELD Score for Scenarios with both Stationary and Mobile Equipment.</p>
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<p>SELD Score for Scenarios with Two Concurrent Mobile Equipment.</p>
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<p>DOA Error Distribution across Different Equipment Types.</p>
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26 pages, 11892 KiB  
Article
An RD-Domain Virtual Aperture Extension Method for Shipborne HFSWR
by Youmin Qu, Xingpeng Mao, Yuguan Hou and Xue Li
Remote Sens. 2024, 16(21), 3929; https://doi.org/10.3390/rs16213929 - 22 Oct 2024
Viewed by 418
Abstract
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 [...] Read more.
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. Full article
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<p>Motion model for shipborne HFSWR and moving target.</p>
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<p>Far-field equivalent motion model for the shipborne HFSWR and moving target.</p>
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<p>Flowchart of the RD-domain virtual aperture extension method for shipborne HFSWR.</p>
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<p>The correspondence between the proposed flowchart and formula parameters.</p>
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<p>Virtual aperture processing method and aperture expansion effect of the proposed method for a single target. (<b>a</b>) Virtual aperture processing method. (<b>b</b>) Aperture expansion effect when <math display="inline"><semantics> <mrow> <mo mathvariant="sans-serif">Δ</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>c</b>) Aperture expansion effect when <math display="inline"><semantics> <mrow> <mo mathvariant="sans-serif">Δ</mo> <mi>m</mi> <mo>=</mo> <mi>M</mi> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Virtual aperture processing method and aperture expansion effect of the proposed method for multiple targets when <span class="html-italic">l</span> = 1.</p>
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<p>Analysis of the far-field assumption. (<b>a</b>) <math display="inline"><semantics> <mrow> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mi>θ</mi> </mrow> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mrow> <mi>ϕ</mi> </mrow> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Impact of azimuth variation error on the virtual aperture processing.</p>
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<p>Target range or velocity variation error within the same RD cell.</p>
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<p>Impact of target range or velocity variation error on the virtual aperture processing.</p>
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<p>Non-overlapping motion error of the array.</p>
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<p>Impact of array non-overlapping motion error on the virtual aperture processing.</p>
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<p>Single target DOA estimation results based on the CBF method with different <math display="inline"><semantics> <mrow> <mi>K</mi> </mrow> </semantics></math>.</p>
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<p>Single target RMSE results based on the CBF method with different <math display="inline"><semantics> <mrow> <mi>K</mi> </mrow> </semantics></math>.</p>
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<p>Single target DOA estimation results based on the CBF method with different <math display="inline"><semantics> <mrow> <mo mathvariant="sans-serif">Δ</mo> <mi>m</mi> </mrow> </semantics></math>.</p>
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<p>Single target RMSE results based on the CBF method with different <math display="inline"><semantics> <mrow> <mo mathvariant="sans-serif">Δ</mo> <mi>m</mi> </mrow> </semantics></math>.</p>
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<p>Single target RMSE results based on the CBF method with different <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>ship</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Two targets of DOA estimation results based on the CBF method with different <math display="inline"><semantics> <mrow> <mi>K</mi> </mrow> </semantics></math>.</p>
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<p>Two target RMSE results based on the CBF method with different <math display="inline"><semantics> <mrow> <mi>K</mi> </mrow> </semantics></math>.</p>
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<p>RD spectrum of the array element 1 for case 1.</p>
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<p>DOA estimation results based on the CBF method. (<b>a</b>) Single target in an RD cell (45, 135). (<b>b</b>) Two targets in an RD cell (851, 340).</p>
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<p>RD spectrum of the array element 1 for case 2.</p>
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<p>DOA estimation results based on CBF method. (<b>a</b>) Single target in RD cell (45, 950). (<b>b</b>) Two targets in RD cell (851, 120).</p>
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14 pages, 1309 KiB  
Article
Combined Keyword Spotting and Localization Network Based on Multi-Task Learning
by Jungbeom Ko, Hyunchul Kim and Jungsuk Kim
Mathematics 2024, 12(21), 3309; https://doi.org/10.3390/math12213309 - 22 Oct 2024
Viewed by 465
Abstract
The advent of voice assistance technology and its integration into smart devices has facilitated many useful services, such as texting and application execution. However, most assistive technologies lack the capability to enable the system to act as a human who can localize the [...] Read more.
The advent of voice assistance technology and its integration into smart devices has facilitated many useful services, such as texting and application execution. However, most assistive technologies lack the capability to enable the system to act as a human who can localize the speaker and selectively spot meaningful keywords. Because keyword spotting (KWS) and sound source localization (SSL) are essential and must operate in real time, the efficiency of a neural network model is crucial for memory and computation. In this paper, a single neural network model for KWS and SSL is proposed to overcome the limitations of sequential KWS and SSL, which require more memory and inference time. The proposed model uses multi-task learning to utilize the limited resources of the device efficiently. A shared encoder is used as the initial layer to extract common features from the multichannel audio data. Subsequently, the task-specific parallel layers utilize these features for KWS and SSL. The proposed model was evaluated on a synthetic dataset with multiple speakers, and a 7-module shared encoder structure was identified as optimal in terms of accuracy, direction of arrival (DOA) accuracy, DOA error, and latency. It achieved a KWS accuracy of 94.51%, DOA error of 12.397°, and DOA accuracy of 89.86%. Consequently, the proposed model requires significantly less memory owing to the shared network architecture, which enhances the inference time without compromising KWS accuracy, DOA error, and DOA accuracy. Full article
(This article belongs to the Special Issue Computational Intelligence and Machine Learning with Applications)
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<p>Architecture of proposed MTL based model. The k, n, and s represent kernel size, number of channels, and stride for each 1D MBConv block, respectively. This model is primarily divided into shared encoder and task-specific layers. It receives a multichannel mixture as input and outputs each estimation for KWS and SSL.</p>
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<p>Difference between single-task and multi-task network architecture. (<b>a</b>) Single-task KWS and SSL network that does not share layers; (<b>b</b>) Multi-task KWS and SSL network sharing several layers.</p>
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<p>(<b>a</b>) Block diagram of the 1D MBConv block; (<b>b</b>) SE block. The blue arrows represent 1D batch normalization [<a href="#B18-mathematics-12-03309" class="html-bibr">18</a>] and Swish activation function.</p>
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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 652
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
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<p>Systolic array structure of an 8-order covariance matrix.</p>
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<p>(<b>a</b>) First rotational partition diagram. (<b>b</b>) Second rotational partition diagram.</p>
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<p>The steps of module operation.</p>
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<p>Block diagram of the MUSIC algorithm.</p>
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<p>Simulation results of eigen-decomposition iteration for (<b>a</b>) 21 times and (<b>b</b>) 28 times.</p>
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<p>Simulation results of eigen-decomposition iteration for (<b>a</b>) 21 times and (<b>b</b>) 28 times.</p>
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<p>Illustration of the direction-finding results on the UV plane in MATLAB and FPGA.</p>
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11 pages, 3680 KiB  
Communication
DOA Estimation of GNSS Signals Based on Deconvolved Conventional Beamforming
by Jian Wu, Chenglong Li, Honglei Lin, Xiaomei Tang and Feixue Wang
Remote Sens. 2024, 16(20), 3856; https://doi.org/10.3390/rs16203856 - 17 Oct 2024
Viewed by 421
Abstract
The Direction of Arrival (DOA) parameter is a key parameter in directional channel modeling for GNSS systems and multipath suppression. However, achieving high-precision, low-complexity DOA estimation of multiple signal sources without requiring a known source number is still a challenge. This paper introduces [...] Read more.
The Direction of Arrival (DOA) parameter is a key parameter in directional channel modeling for GNSS systems and multipath suppression. However, achieving high-precision, low-complexity DOA estimation of multiple signal sources without requiring a known source number is still a challenge. This paper introduces a satellite navigation DOA parameter estimation method based on deconvolution beamforming. By exploiting the translational invariance property of the uniform linear array pattern, the deconvolution process is applied to the de-spread array pattern of satellite navigation signals, achieving high-precision estimation of DOA parameters. This method can achieve high-precision blind DOA estimation of multiple signal sources while significantly reducing the estimation complexity. Compared with traditional methods, precise DOA estimation can be achieved even in low-signal-to-noise-ratio conditions and with a small number of elements in the array. The theoretical analysis and simulation results verify the effectiveness of the proposed algorithm. Full article
(This article belongs to the Special Issue Satellite Navigation and Signal Processing (Second Edition))
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<p>Multipath reflection model with one antenna.</p>
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<p>The peak of direct signal and multipath signal correlation.</p>
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<p>Array configuration of uniform linear array.</p>
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<p>Normalized beam patterns using conventional beamforming method with different numbers of array elements.</p>
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<p>Super-directional beam pattern: (<b>a</b>) the comparison of CB and DCB; (<b>b</b>) the comparison of DCB under different numbers of array elements.</p>
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<p>Spatial spectrum estimation results with different DOA estimation methods (the circles represent the true DOA parameters): (<b>a</b>) estimation results under the condition of only a single direct signal; (<b>b</b>) estimation results under the condition of one direct signal and one multipath signal.</p>
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<p>Block diagram of the proposed method.</p>
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<p>Statistical results of DOA estimation under different <math display="inline"> <semantics> <mrow> <mrow> <mi>C</mi> <mo>/</mo> <mrow> <msub> <mi>N</mi> <mn>0</mn> </msub> </mrow> </mrow> </mrow> </semantics> </math> ratios: (<b>a</b>) <span class="html-italic">N</span> = 4; (<b>b</b>) <span class="html-italic">N</span> = 8; (<b>c</b>) <span class="html-italic">N</span> = 12; (<b>d</b>) <span class="html-italic">N</span> = 16.</p>
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<p>Statistical results of performance estimation for different incident angles: (<b>a</b>) <span class="html-italic">N</span> = 8; (<b>b</b>) <span class="html-italic">N</span> = 12.</p>
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<p>Estimation statistic results under different <math display="inline"> <semantics> <mrow> <mrow> <mi>C</mi> <mo>/</mo> <mrow> <msub> <mi>N</mi> <mn>0</mn> </msub> </mrow> </mrow> </mrow> </semantics> </math> ratios: (<b>a</b>) <span class="html-italic">N</span> = 8; (<b>b</b>) <span class="html-italic">N</span> = 12.</p>
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16 pages, 668 KiB  
Article
Noncircular Distributed Source DOA Estimation with Nested Arrays via Reduced-Dimension MUSIC
by Kaiyuan Chen, Weiyang Chen and Jiaqi Li
Sensors 2024, 24(20), 6653; https://doi.org/10.3390/s24206653 - 15 Oct 2024
Viewed by 623
Abstract
This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to [...] Read more.
This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to be reconsidered for CD sources with sparse arrays and many problems arise. One thorny problem is the disappearance of displacement invariance of the virtual array manifold constructed by the virtualization technique. To deal with this issue, a nested array processing method for CD sources transmitting noncircular signals is proposed in this paper. Firstly, we construct the virtual sum-and-difference co-array by leveraging the noncircular quality of signals with a nested array. Then, an approximation is made to degrade CD sources into point sources. In this way, spatial smoothing techniques can be applied to restore the rank. Finally, in order to reduce the complexity, we modify the reduced-dimension MUSIC to estimate DOAs through a one-dimensional peak-searching procedure. The simulation results prove the superiority of our algorithm against other competitors. Full article
(This article belongs to the Section Sensor Networks)
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<p>Two-level nested array.</p>
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<p>(<b>a</b>) Continuous part of the difference co-array. (<b>b</b>) Continuous part of the sum co-arrays.</p>
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<p>Comparison of complexity versus number of sensors.</p>
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<p>Comparison of complexity versus number of snapshots.</p>
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<p>Comparison of spectrums.</p>
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<p>Comparison of RMSE versus SNR.</p>
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<p>Comparison of RMSE versus number of snapshots.</p>
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<p>Comparison of success rate versus SNR.</p>
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<p>Comparison of success rate versus number of snapshots.</p>
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21 pages, 2399 KiB  
Article
Gridless DOA Estimation Method for Arbitrary Array Geometries Based on Complex-Valued Deep Neural Networks
by Yuan Cao, Tianjun Zhou and Qunfei Zhang
Remote Sens. 2024, 16(19), 3752; https://doi.org/10.3390/rs16193752 - 9 Oct 2024
Viewed by 929
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Ocean Remote Sensing Based on Radar, Sonar and Optical Techniques)
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<p>(<b>a</b>) Magnitude of Fourier coefficients at various orders. (<b>b</b>) Relationship between array steering vector error and <span class="html-italic">N</span>.</p>
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<p>Angular-domain covariance matrix reconstruction network architecture.</p>
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<p>Training loss, validation loss, and learning rate variation with epochs for the following: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>7</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
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<p>DOA estimation performance of CDNNs with truncation orders <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>7</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> at different target angular separations. (<b>a</b>) RMSE and (<b>b</b>) RP for <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">θ</mi> <mo>=</mo> <mfenced separators="" open="[" close="]"> <mrow> <msup> <mrow> <mn>85</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mrow> <mn>95</mn> </mrow> <mo>∘</mo> </msup> </mrow> </mfenced> </mrow> </semantics></math>. (<b>c</b>) RMSE and (<b>d</b>) RP for <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">θ</mi> <mo>=</mo> <mfenced separators="" open="[" close="]"> <mrow> <msup> <mrow> <mn>80</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mrow> <mn>100</mn> </mrow> <mo>∘</mo> </msup> </mrow> </mfenced> </mrow> </semantics></math>. (<b>e</b>) RMSE and (<b>f</b>) RP for <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">θ</mi> <mo>=</mo> <mfenced separators="" open="[" close="]"> <mrow> <msup> <mrow> <mn>70</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mrow> <mn>110</mn> </mrow> <mo>∘</mo> </msup> </mrow> </mfenced> </mrow> </semantics></math>.</p>
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<p>DOA estimation results. The proposed method, source numbers (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>. MUSIC, source numbers (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>. SPICE, source numbers (<b>g</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>i</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>. SBL, source numbers (<b>j</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>k</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>l</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>DOA estimation results. The proposed method, source numbers (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>. MUSIC, source numbers (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>. SPICE, source numbers (<b>g</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>i</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>. SBL, source numbers (<b>j</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>k</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and (<b>l</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>Relationship between SNR and both RMSE and RP under spatio-temporal Gaussian white noise conditions.(<b>a</b>) RMSE and (<b>b</b>) RP for <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">θ</mi> <mo>=</mo> <mfenced separators="" open="[" close="]"> <mrow> <msup> <mrow> <mn>80</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mrow> <mn>100</mn> </mrow> <mo>∘</mo> </msup> </mrow> </mfenced> </mrow> </semantics></math>. (<b>c</b>) RMSE and (<b>d</b>) RP for <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">θ</mi> <mo>=</mo> <mfenced separators="" open="[" close="]"> <mrow> <msup> <mrow> <mn>70</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mrow> <mn>110</mn> </mrow> <mo>∘</mo> </msup> </mrow> </mfenced> </mrow> </semantics></math>.</p>
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<p>Relationship between RP and RMSE with respect to angle separation. (<b>a</b>) RMSE. (<b>b</b>) RP.</p>
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<p>Algorithm performance under different snapshot conditions. (<b>a</b>) RMSE. (<b>b</b>) RP.</p>
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<p>Schematic of the Swellex-96 Event S59 experiment scenario [<a href="#B38-remotesensing-16-03752" class="html-bibr">38</a>].</p>
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<p>BTR results using different methods. (<b>a</b>) GPS. (<b>b</b>) CBF. (<b>c</b>) Proposed method. (<b>d</b>) MUSIC. (<b>e</b>) SPICE. (<b>f</b>) SBL.</p>
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<p>BTR results using different methods. (<b>a</b>) GPS. (<b>b</b>) CBF. (<b>c</b>) Proposed method. (<b>d</b>) MUSIC. (<b>e</b>) SPICE. (<b>f</b>) SBL.</p>
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<p>Processing results of Swellex-96 Event S59 data using different methods. (<b>a</b>) RP. (<b>b</b>) RMSE. (<b>c</b>) CPU time.</p>
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16 pages, 2194 KiB  
Article
DOA Estimation Method for Vector Hydrophones Based on Sparse Bayesian Learning
by Hongyan Wang, Yanping Bai, Jing Ren, Peng Wang, Ting Xu, Wendong Zhang and Guojun Zhang
Sensors 2024, 24(19), 6439; https://doi.org/10.3390/s24196439 - 4 Oct 2024
Viewed by 628
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Optical Sensors)
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<p>Two-dimensional vector hydrophone array signal receiving model.</p>
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<p>RMSE variation curves with the number of snapshots under different signal source conditions. (<b>a</b>) For 1 signal source, (<b>b</b>) 3 signal sources, and (<b>c</b>) 5 signal sources.</p>
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<p>RMSE variation curves with SNR under different signal source conditions. (<b>a</b>) For 1 signal source, (<b>b</b>) 3 signal sources, and (<b>c</b>) 5 signal sources.</p>
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<p>RMSE variation curves with angular difference under different signal source conditions. (<b>a</b>) For 3 signal sources and (<b>b</b>) 5 signal sources.</p>
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<p>Comparison of the performance under coherent source conditions. (<b>a</b>) RMSE variation curves with the number of snapshots, (<b>b</b>) RMSE variation curves with SNR, and (<b>c</b>) RMSE variation curves with angular difference.</p>
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<p>Curve of success rate versus signal-to-noise ratio.</p>
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<p>Schematic diagram of an experiment conducted at a reservoir in Taiyuan, Shanxi Province.</p>
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<p>Measurement results of the Vector-SBL algorithm.</p>
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18 pages, 3827 KiB  
Article
Direction of Arrival Estimation Based on DNN and CNN
by Wu Cao, Wen Ren, Zhenyu Zhang, Weiqiang Huang, Jun Zou and Guangzu Liu
Electronics 2024, 13(19), 3866; https://doi.org/10.3390/electronics13193866 - 29 Sep 2024
Viewed by 434
Abstract
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 [...] Read more.
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. Full article
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<p>Received model.</p>
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<p>DNN structure.</p>
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<p>CNN structure.</p>
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<p>Overall framework.</p>
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<p>The comparison of validation loss for different learning rates in the DNN network.</p>
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<p>The comparison of the RMSE with different SNRs.</p>
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<p>DOA estimation results under different signals.</p>
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<p>Comparison of validation loss for different learning rates in the CNN network.</p>
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<p>CNN network output value.</p>
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<p>DOA estimation error under different quantization numbers.</p>
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<p>DOA estimation error under different SNRs.</p>
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<p>DOA estimation error under different numbers of receive antennas.</p>
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<p>DOA estimation error under different algorithms.</p>
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18 pages, 876 KiB  
Article
Robust Underwater Direction-of-Arrival Estimation Method Using Acoustic Sensor Array under Unknown Swing Deviation Elements
by Weidong Wang, Linya Ma, Wentao Shi and Wasiq Ali
Remote Sens. 2024, 16(19), 3634; https://doi.org/10.3390/rs16193634 - 29 Sep 2024
Viewed by 3166
Abstract
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 [...] Read more.
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. Full article
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<p>The AVSA models. (<b>a</b>) The ideal model of AVSA. (<b>b</b>) The model of AVSA under unknown SDEs in the <span class="html-italic">v</span>-th STS.</p>
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<p>RMSE versus SNR for two sources at (−<math display="inline"><semantics> <mrow> <msup> <mn>14</mn> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mn>31</mn> <mo>∘</mo> </msup> <mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>2000</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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<p>RMSE versus snapshot for two sources at (−<math display="inline"><semantics> <mrow> <msup> <mn>14</mn> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mn>31</mn> <mo>∘</mo> </msup> <mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> with SNR = 3 dB, <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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<p>RMSE versus V for two sources at (−<math display="inline"><semantics> <mrow> <msup> <mn>14</mn> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mn>31</mn> <mo>∘</mo> </msup> <mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> with SNR = 3 dB, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>2000</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>ρ</mi> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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<p>RMSE versus <math display="inline"><semantics> <mi>μ</mi> </semantics></math> for two sources at (−<math display="inline"><semantics> <mrow> <msup> <mn>14</mn> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mn>31</mn> <mo>∘</mo> </msup> <mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> with SNR = 3 dB, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>2000</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>ρ</mi> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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<p>The configuration of the AVSA.</p>
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<p>The experimental setup for DOA estimation of underwater sources.</p>
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<p>The processing results.</p>
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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 536
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
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Figure 1
<p>Unfolded coprime linear array (UCLA).</p>
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<p>The relationship between the phase ambiguity problem and the inter-element spacing.</p>
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<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>
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<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>
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<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>
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<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>
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<p>(<b>a</b>) The unfolded coprime linear array. (<b>b</b>) The designed and improved unfolded coprime linear array.</p>
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<p>The reconstructed array configuration can achieve the full DOFs of three source signals.</p>
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<p>The reconstructed array configuration can achieve the full DOFs of seven source signals.</p>
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<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>
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<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>
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<p>The RMSE versus the SNR of the proposed method.</p>
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<p>The RMSE versus the snapshot of the proposed method.</p>
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<p>The RMSE versus the SNR based on different arrays.</p>
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<p>The RMSE versus the snapshot based on different arrays.</p>
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