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18 pages, 3920 KiB  
Article
A Multi-Parameter Optimization Method for Electromagnetic Characteristics Fitting Based on Deep Learning
by Jiaxing Hao, Sen Yang and Hongmin Gao
Appl. Sci. 2024, 14(22), 10652; https://doi.org/10.3390/app142210652 - 18 Nov 2024
Viewed by 570
Abstract
Electromagnetic technology is widely applied in numerous fields, and precise electromagnetic characteristic fitting technology has become a crucial part for enhancing system performance and optimizing design. However, it faces challenges such as high computational complexity and the difficulty in balancing the accuracy and [...] Read more.
Electromagnetic technology is widely applied in numerous fields, and precise electromagnetic characteristic fitting technology has become a crucial part for enhancing system performance and optimizing design. However, it faces challenges such as high computational complexity and the difficulty in balancing the accuracy and generalization ability of the model. For example, the Radar Cross Section (RCS) distribution characteristics of a single corner reflector model or Luneberg lens provide a relatively stable RCS value within a certain airspace range, which to some extent reduces the difficulty of radar target detection and fails to truly evaluate the radar performance. This paper aims to propose an innovative multi-parameter optimization method for electromagnetic characteristic fitting based on deep learning. By selecting common targets such as reflectors and Luneberg lens reflectors as optimization variables, a deep neural network model is constructed and trained with a large amount of electromagnetic data to achieve high-precision fitting of the target electromagnetic characteristics. Meanwhile, an advanced genetic optimization algorithm is introduced to optimize the multiple parameters of the model to meet the error index requirements of radar target detection. In this paper, by combining specific optimization variables such as corner reflectors and Luneberg lenses with the deep learning model and genetic algorithm, the deficiencies of traditional methods in handling electromagnetic characteristic fitting are effectively addressed. The experimental results show that the 60° corner reflector successfully realizes the simulation of multiple peak characteristics of the target, and the Luneberg lens reflector achieves the simulation of a relatively small RCS average value with certain fluctuations in a large space range, which strongly proves that this method has significant advantages in improving the fitting accuracy and optimization efficiency, opening up new avenues for research and application in the electromagnetic field. Full article
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<p>Structure diagram of electromagnetic characteristic parameter optimization method.</p>
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<p>Genetic algorithm basic flow diagram.</p>
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<p>Capsule neuron model.</p>
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<p>Schematic diagram of the CapsNet structure.</p>
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<p>The RCS distribution characteristic.</p>
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<p>Schematic diagram of electromagnetic characteristic parameter optimization scheme.</p>
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<p>Comparison of RCS calculation results of different algorithms.</p>
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<p>Objective function optimization results.</p>
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<p>The RCS distribution characteristics obtained by the algorithm in this paper are compared with the typical aircraft data.</p>
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<p>Compared results of the fitting results obtained using the proposed algorithm and the aircraft typical data.</p>
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<p>The fitting results of RCS distribution characteristics of some typical targets. (<b>a</b>) Ship. (<b>b</b>) Armored vehicle.</p>
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19 pages, 4889 KiB  
Article
Corner Reflector Plasmonic Nanoantennas for Enhanced Single-Photon Emission
by Pedro Chamorro-Posada
Appl. Sci. 2024, 14(22), 10300; https://doi.org/10.3390/app142210300 - 9 Nov 2024
Viewed by 561
Abstract
The emission rate of atom-like photon sources can be significantly improved by coupling them to plasmonic resonant nanostructures. These arrangements function as nanoantennas, serving the dual purpose of enhancing light–matter interactions and decoupling the emitted photons. However, there is a contradiction between the [...] Read more.
The emission rate of atom-like photon sources can be significantly improved by coupling them to plasmonic resonant nanostructures. These arrangements function as nanoantennas, serving the dual purpose of enhancing light–matter interactions and decoupling the emitted photons. However, there is a contradiction between the requirements for these two tasks. A small resonator volume is necessary for maximizing interaction efficiency, while a large antenna mode volume is essential to achieve high emission directivity. In this work, we analyze a hybrid structure composed of a noble metal plasmonic resonant nanoparticle coupled to the atom-like emitter, which is designed to enhance the emission rate, alongside a corner reflector aimed at optimizing the angular distribution of the emitted photons. A comprehensive numerical study of silver and gold corner reflector nanoantennas, employing the finite difference time domain method, is presented. The results demonstrate that a well-designed corner reflector can significantly enhance photon emission directivity while also substantially boosting the emission rate. Full article
(This article belongs to the Special Issue Quantum Optics: Theory, Methods and Applications)
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Figure 1
<p>Geometry employed in the analyses. The feeder is composed by a dipole emitter <math display="inline"><semantics> <mi mathvariant="bold">p</mi> </semantics></math> coupled to a nanosphere of diameter <span class="html-italic">d</span>. The corner, of angle <math display="inline"><semantics> <mi>ψ</mi> </semantics></math>, is assumed to be built from to sheets of the same metal as the NP with dimensions <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>×</mo> <mi>H</mi> </mrow> </semantics></math>.</p>
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<p>Calculated resonance wavelengths of silver (<b>a</b>) and gold (<b>b</b>) NPs as a function of their diameters.</p>
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<p>Purcell, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>R</mi> </msub> </semantics></math>, and loss, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>L</mi> </msub> </semantics></math>, factors of silver NPs calculated for different spherical particle diameter values <span class="html-italic">d</span> and separation values <span class="html-italic">s</span> from the the dipole emitter. (<b>a</b>,<b>c</b>) plots are the values at resonance and, (<b>b</b>,<b>d</b>) are at the target wavelength of <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>A</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>450</mn> </mrow> </semantics></math> nm.</p>
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<p>Purcell, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>R</mi> </msub> </semantics></math>, and loss, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>L</mi> </msub> </semantics></math>, factors of gold NPs calculated for different spherical particle diameter values <span class="html-italic">d</span> and separation values <span class="html-italic">s</span> from the the dipole emitter. (<b>a</b>,<b>c</b>) plots are the values at resonance, and (<b>b</b>,<b>d</b>) are at the target wavelength of <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>A</mi> <mi>u</mi> </mrow> </msub> <mo>=</mo> <mn>600</mn> </mrow> </semantics></math> nm.</p>
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<p>Values of the directivity as a function of the feeder position <span class="html-italic">S</span>, normalized to the respective target wavelength, for four different reflector film thicknesses. (<b>a</b>) Results for the silver CR, with a target wavelength of <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>A</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>450</mn> </mrow> </semantics></math> nm. (<b>b</b>) Results for the gold CR, with a target wavelength of <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>A</mi> <mi>u</mi> </mrow> </msub> <mo>=</mo> <mn>600</mn> </mrow> </semantics></math> nm.</p>
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<p>Radiation patterns of silver CR with <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> nm for values of <span class="html-italic">S</span> between <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.75</mn> </mrow> </semantics></math>.</p>
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<p>Radiation patterns of silver CR with <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> nm for values of <span class="html-italic">S</span> between <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.75</mn> </mrow> </semantics></math>.</p>
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<p>Radiation patterns of silver CR with <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>80</mn> </mrow> </semantics></math> nm for values of <span class="html-italic">S</span> between <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.75</mn> </mrow> </semantics></math>.</p>
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<p>Purcell, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>R</mi> </msub> </semantics></math>, and normalized loss, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>L</mi> </msub> </semantics></math>, factors of silver CR as a function of the normalized feeder position <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>/</mo> <msub> <mi>λ</mi> <mi>M</mi> </msub> </mrow> </semantics></math> for four different reflector film thicknesses: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> nm, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> nm, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> nm, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>80</mn> </mrow> </semantics></math> nm. The horizontal lines describe the corresponding reference levels without the CR.</p>
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<p>Radiative transition rate enhancement, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>R</mi> </msub> </semantics></math>, and normalized loss, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>L</mi> </msub> </semantics></math>, factors of gold CR as a function of the normalized feeder position <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>/</mo> <msub> <mi>λ</mi> <mi>M</mi> </msub> </mrow> </semantics></math> for four different reflector film thicknesses: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> nm, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> nm, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> nm, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>80</mn> </mrow> </semantics></math> nm.</p>
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<p>Radiation efficiency of silver (<b>a</b>) and gold (<b>b</b>) CR NA as a function of the normalized feeder position <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>/</mo> <msub> <mi>λ</mi> <mi>M</mi> </msub> </mrow> </semantics></math> for four different reflector film thicknesses <span class="html-italic">W</span>.</p>
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<p>Directivity of silver (<b>a</b>) and gold (<b>b</b>) CR antennas with and without NP coupled to the dipole emitter. Purcell (<math display="inline"><semantics> <msub> <mi>f</mi> <mi>R</mi> </msub> </semantics></math>) and loss (<math display="inline"><semantics> <msub> <mi>f</mi> <mi>L</mi> </msub> </semantics></math>) factors for silver (<b>c</b>) and gold (<b>d</b>) CRs with a single dipole emitter feeder.</p>
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<p>Calculated resonance wavelengths of silver (<b>a</b>) and gold (<b>b</b>) NPs as a function of the absolute feeder position <span class="html-italic">S</span> for four different reflector film thicknesses: <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> nm, <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> nm, <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> nm, and <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>80</mn> </mrow> </semantics></math> nm.</p>
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<p>Field strength <math display="inline"><semantics> <mrow> <mo>|</mo> <mi mathvariant="bold">E</mi> <mo>|</mo> </mrow> </semantics></math> across the <math display="inline"><semantics> <mrow> <mi>X</mi> <mi>Z</mi> </mrow> </semantics></math> plane in the environment of a <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>70</mn> </mrow> </semantics></math> nm gold NP at the origin illuminated by an unit magnitude <span class="html-italic">Z</span>-polarized E-field plane wave. The plot (<b>a</b>) displays the results for the isolated NP and (<b>b</b>) when the NP was within the CR at <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m.</p>
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<p>(<b>a</b>) Purcell, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>R</mi> </msub> </semantics></math>, and loss, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>L</mi> </msub> </semantics></math>, factors; (<b>b</b>) directivity of a <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>80</mn> </mrow> </semantics></math> nm, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m CR silver NA with the feeder at <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>0.55</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m in the presence of an interfering <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>70</mn> </mrow> </semantics></math> nm silver NP at position <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ρ</mi> <mo form="prefix">sin</mo> <mo>(</mo> <mi>α</mi> <mo>)</mo> <mo>,</mo> <mi>ρ</mi> <mo form="prefix">cos</mo> <mo>(</mo> <mi>α</mi> <mo>)</mo> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> for different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Values obtained of the directivity as a function of the feeder position <span class="html-italic">S</span> normalized to the corresponding target wavelength for three different reflector film thicknesses when the length of the CR planes was increased to <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m. (<b>a</b>) Results for silver CR. (<b>b</b>) Results for gold CR.</p>
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<p>Radiative transition rate enhancement <math display="inline"><semantics> <msub> <mi>f</mi> <mi>R</mi> </msub> </semantics></math> and normalized loss <math display="inline"><semantics> <msub> <mi>f</mi> <mi>L</mi> </msub> </semantics></math> factors of a gold CR with <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m as a function of the feeder position <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>/</mo> <msub> <mi>λ</mi> <mi>M</mi> </msub> </mrow> </semantics></math> for three different reflector film thicknesses: (<b>a</b>) silver CR <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> nm, (<b>b</b>) gold CR <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> nm, (<b>c</b>) silver CR <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> nm, (<b>d</b>) gold CR <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> nm, (<b>e</b>) silver CR <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>80</mn> </mrow> </semantics></math> nm, (<b>f</b>) gold CR <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>80</mn> </mrow> </semantics></math> nm.</p>
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<p>Nanoantenna gain as a function of the feeder position <span class="html-italic">S</span> normalized to the corresponding target wavelength for three different reflector film thicknesses when the length of the CR planes was increased to <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m. (<b>a</b>) Results for silver CR. (<b>b</b>) Results for gold CR.</p>
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25 pages, 13404 KiB  
Article
Drone SAR Imaging for Monitoring an Active Landslide Adjacent to the M25 at Flint Hall Farm
by Anthony Carpenter, James A. Lawrence, Philippa J. Mason, Richard Ghail and Stewart Agar
Remote Sens. 2024, 16(20), 3874; https://doi.org/10.3390/rs16203874 - 18 Oct 2024
Viewed by 1293
Abstract
Flint Hall Farm in Godstone, Surrey, UK, is situated adjacent to the London Orbital Motorway, or M25, and contains several landslide systems which pose a significant geohazard risk to this critical infrastructure. The site has been routinely monitored by geotechnical engineers following a [...] Read more.
Flint Hall Farm in Godstone, Surrey, UK, is situated adjacent to the London Orbital Motorway, or M25, and contains several landslide systems which pose a significant geohazard risk to this critical infrastructure. The site has been routinely monitored by geotechnical engineers following a landslide that encroached onto the hard shoulder in December 2000; current in situ instrumentation includes inclinometers and piezoelectric sensors. Interferometric Synthetic Aperture Radar (InSAR) is an active remote sensing technique that can quantify millimetric rates of Earth surface and structural deformation, typically utilising satellite data, and is ideal for monitoring landslide movements. We have developed the hardware and software for an Unmanned Aerial Vehicle (UAV), or drone radar system, for improved operational flexibility and spatial–temporal resolutions in the InSAR data. The hardware payload includes an industrial-grade DJI drone, a high-performance Ettus Software Defined Radar (SDR), and custom Copper Clad Laminate (CCL) radar horn antennas. The software utilises Frequency Modulated Continuous Wave (FMCW) radar at 5.4 GHz for raw data collection and a Range Migration Algorithm (RMA) for focusing the data into a Single Look Complex (SLC) Synthetic Aperture Radar (SAR) image. We present the first SAR image acquired using the drone radar system at Flint Hall Farm, which provides an improved spatial resolution compared to satellite SAR. Discrete targets on the landslide slope, such as corner reflectors and the in situ instrumentation, are visible as bright pixels, with their size and positioning as expected; the surrounding grass and vegetation appear as natural speckles. Drone SAR imaging is an emerging field of research, given the necessary and recent technological advancements in drones and SDR processing power; as such, this is a novel achievement, with few authors demonstrating similar systems. Ongoing and future work includes repeat-pass SAR data collection and developing the InSAR processing chain for drone SAR data to provide meaningful deformation outputs for the landslides and other geotechnical hazards and infrastructure. Full article
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Figure 1
<p>Flint Hall Farm study area (hatched red pattern), with annotated M25, Godstone, and regional UK overview map.</p>
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<p>Flint Hall Farm study area (hatched red pattern), with 1 m LiDAR Composite DTM for elevation and labelled contour lines.</p>
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<p>Zones and sub-zones at the Flint Hall Farm site, including the Flint Hall Farm Zone, Zones 1–3 (red); the Midslope Zone, Zones 1–2 (blue); and, the Rooks Nest Farm Zone, Zones 1–4 (yellow) [<a href="#B25-remotesensing-16-03874" class="html-bibr">25</a>]. The zone colour shading is more transparent than the legend colours for surface feature visibility.</p>
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<p>Landslide extents at the Flint Hall Farm site, including the Flint Hall Farm, Flint Hall Farm South, and Rooks Nest Farm Landslides [<a href="#B25-remotesensing-16-03874" class="html-bibr">25</a>].</p>
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<p>Simplified geological map of the study area, with Flint Hall Farm (red circle), and a geological cross-section for line A–A′ (green circle). Adapted from [<a href="#B26-remotesensing-16-03874" class="html-bibr">26</a>].</p>
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<p>Schematic of the Flint Hall Farm landslide, which occurred on 19 December 2000 [<a href="#B1-remotesensing-16-03874" class="html-bibr">1</a>].</p>
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<p>Geological cross-section schematic of the Flint Hall Farm landslide, which occurred on 19 December 2000 [<a href="#B1-remotesensing-16-03874" class="html-bibr">1</a>].</p>
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<p>Corner reflectors at Flint Hall Farm, with annotated M25.</p>
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<p>Photographs of the CCL horn antennas: (<b>a</b>) external view; (<b>b</b>) internal view.</p>
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<p>Drone radar payload, with the CCL horn antennas, E312 SDR and 3D-printed connection stabiliser for the SMB-SMA connectors, and Raspberry Pi (on the back).</p>
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<p>Drone radar payload attached to the drone at Flint Hall Farm.</p>
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<p>FMCW modulation: (<b>a</b>) amplitude domain; (<b>b</b>) frequency domain, where transmission (Tx) is red, and reception (Rx) is green.</p>
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<p>FMCW radar block diagram.</p>
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<p>RMA block diagram.</p>
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<p>Schematic of drone flight geometry with corner reflector target.</p>
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<p>Photograph of the drone radar system in-flight at Flint Hall Farm.</p>
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<p>(<b>a</b>) SLC SAR image from Flint Hall Farm, with annotated flight path and circled targets; the latter includes the corner reflectors (red), and other fenced areas for in situ instrumentation (yellow, blue and pink); (<b>b</b>) Google Street View imagery of Flint Hall Farm, with annotated flight path, and corresponding circled targets, as indicated by the arrows connecting (<b>a</b>,<b>b</b>).</p>
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<p>Average SAR amplitude for Flint Hall Farm (white boundary) from September 2021 to September 2023, with annotated M25 and Godstone. The zoomed image boundary is denoted by the red box. The corner reflector and in situ instrumental pixels are circled in blue.</p>
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<p>Side-by-side comparison of (<b>a</b>) average SAR amplitude for Flint Hall Farm (white boundary) from September 2021 to September 2023; the corner reflector and in situ instrumental pixels are circled in blue, and (<b>b</b>) drone SAR image from Flint Hall Farm, with circled targets, including the corner reflectors (red), and other fenced areas for in situ instrumentation (yellow, blue, and pink).</p>
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13 pages, 5330 KiB  
Article
ISAR Imaging Analysis of Complex Aerial Targets Based on Deep Learning
by Yifeng Wang, Jiaxing Hao, Sen Yang and Hongmin Gao
Appl. Sci. 2024, 14(17), 7708; https://doi.org/10.3390/app14177708 - 31 Aug 2024
Viewed by 1129
Abstract
Traditional range–instantaneous Doppler (RID) methods for maneuvering target imaging are hindered by issues related to low resolution and inadequate noise suppression. To address this, we propose a novel ISAR imaging method enhanced by deep learning, which incorporates the fundamental architecture of CapsNet along [...] Read more.
Traditional range–instantaneous Doppler (RID) methods for maneuvering target imaging are hindered by issues related to low resolution and inadequate noise suppression. To address this, we propose a novel ISAR imaging method enhanced by deep learning, which incorporates the fundamental architecture of CapsNet along with two additional convolutional layers. Pre-training is conducted through the deep learning network to establish the mapping function for reference. Subsequently, the trained network is integrated into the electromagnetic simulation software, Feko 2019, utilizing a combination of geometric forms such as corner reflectors and Luneberg spheres for analysis. The results indicate that the derived ISAR imaging effectively identifies the ISAR program associated with complex aerial targets. A thorough analysis of the imaging results further corroborates the effectiveness and superiority of this approach. Both simulation and empirical data demonstrate that this method significantly enhances imaging resolution and noise suppression. Full article
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Figure 1
<p>The spatial relationship between radar and target imaging.</p>
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<p>Capsule neuron model.</p>
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<p>Schematic diagram of the CapsNetv2 structure.</p>
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<p>The loss of CapsNet.</p>
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<p>ISAR imaging of an aircraft.</p>
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<p>The structure diagram of the simulation assembly of each part of the aircraft. (<b>a</b>) Typical head orientation. (<b>b</b>) Typical wing simulation. (<b>c</b>) Typical tail orientation. (<b>d</b>) Aircraft omnidirectional simulation.</p>
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<p>Set up the ISAR imaging script in FEKO.</p>
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<p>Recognition results of the aircraft simulation ISAR imaging.</p>
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<p>Physical model of aircraft simulation assembly.</p>
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<p>Test system.</p>
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<p>Recognition results of the aircraft ISAR imaging.</p>
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14 pages, 9865 KiB  
Article
The CornerGuard: Seeing around Corners to Prevent Broadside Collisions
by Victor Xu and Sheng Xu
Vehicles 2024, 6(3), 1468-1481; https://doi.org/10.3390/vehicles6030069 - 27 Aug 2024
Viewed by 1121
Abstract
Nearly 3700 people are killed in broadside collisions in the U.S. every year. To reduce broadside collisions, we created and tested the CornerGuard, a prototype system that senses around a corner to alert a car driver of an impending collision with a pedestrian [...] Read more.
Nearly 3700 people are killed in broadside collisions in the U.S. every year. To reduce broadside collisions, we created and tested the CornerGuard, a prototype system that senses around a corner to alert a car driver of an impending collision with a pedestrian or automobile that is not in the line of sight (LOS). The CornerGuard leverages a microwave-transceiving radar sensor mounted on the car and a curved radio wave reflector installed at the corner to sense around the corner and detect a broadside collision threat. The car’s speed is constantly read by an onboard diagnostics (OBD) system to allow the sensor to differentiate between static objects and objects approaching around the corner. Field testing demonstrated that the CornerGuard can effectively and consistently detect threats at a consistent range without blind spots under broad weather conditions. Our proof of concept study shows that the CornerGuard can be enhanced to be readily integrated into automobile construction and street infrastructure. Full article
(This article belongs to the Special Issue Emerging Transportation Safety and Operations: Practical Perspectives)
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<p>An overview of the CornerGuard’s radar subsystem, which includes (<b>a</b>) an onboard diagnostics (OBD) device and a computer that collects and analyzes data and (<b>b</b>) a radar sensor.</p>
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<p>The setup of the reflector in (<b>a</b>) blind spot tests and (<b>b</b>) field simulation tests.</p>
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<p>The relative speed at which the radar sensor and an object approach each other. (<b>a</b>) A surrounding stationary object; (<b>b</b>) an object that approaches the sensor in the reflector.</p>
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<p>(<b>a</b>) The geometric design of the reflector to avoid blind spots. (<b>b</b>) The geometric analysis of radar detection range reduction due to reflector curvature.</p>
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<p>A spectrum obtained by the FFT (fast Fourier transform), plotted as signal magnitude vs. object speed, including a red 20 dB noise threshold line.</p>
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<p>Range assessment through a straightaway test: (<b>a</b>) speed vs. time; (<b>b</b>) range vs. time.</p>
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<p>Blind spot assessment through a reflector test: (<b>a</b>) speed vs. time; (<b>b</b>) range vs. time.</p>
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<p>Error assessment of the radar sensor and OBD mounted on a car driving in stationary surroundings: (<b>a</b>) velocity vs. time; (<b>b</b>) velocity difference vs. time, where the velocity difference is the car’s velocity minus the velocity of a detected object.</p>
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<p>Detection of all objects: (<b>a</b>) velocity vs. time; (<b>b</b>) range vs. time.</p>
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<p>Detection of an approaching object: (<b>a</b>) velocity vs. time; (<b>b</b>) range vs. time.</p>
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21 pages, 9414 KiB  
Article
Analysis of the Effect of Tilted Corner Cube Reflector Arrays on Lunar Laser Ranging
by Jin Cao, Rufeng Tang, Kai Huang, Zhulian Li, Yongzhang Yang, Kai Huang, Jintao Li and Yuqiang Li
Remote Sens. 2024, 16(16), 3030; https://doi.org/10.3390/rs16163030 - 18 Aug 2024
Viewed by 976
Abstract
This paper primarily investigates the effect of the tilt of corner cube reflector (CCR) arrays on lunar laser ranging (LLR). A mathematical model was established to study the random errors caused by the tilt of the CCR arrays. The study found that, ideally, [...] Read more.
This paper primarily investigates the effect of the tilt of corner cube reflector (CCR) arrays on lunar laser ranging (LLR). A mathematical model was established to study the random errors caused by the tilt of the CCR arrays. The study found that, ideally, when the laser ranging pulse width is 10 picoseconds or less, it is possible to distinguish from which specific corner cubes within the CCR array each peak in the echo signal originates. Consequently, partial data from the echo can be extracted for signal processing, significantly reducing random errors and improving the single-shot precision of LLR. The distance obtained by extracting part of the echo can be reduced to the center position of the array, thereby providing multiple higher-precision ranging results from each measurement. This not only improves the precision of LLR but also increases the data volume. A simulation experiment based on the 1.2 m laser ranging system at Yunnan Observatories was conducted. By extracting one peak for signal processing, the single-shot precision improved from 32.24 mm to 2.52 mm, validating the theoretical analysis results. Finally, an experimental laser ranging system based on a 53 cm binocular telescope system was established for ground experiments. The experimental results indicated that the echo signal could identify the tilt state of the CCR array. By extracting the peak returned by the central CCR for signal processing, the ranging precision was greatly improved. Through theoretical analyses, simulation experiments, and ground experiments, a solution to reduce the random errors caused by the tilt of the CCR array was provided. This offers an approach to enhance the single-shot precision of future LLR and provides a reference for upgrading ground-based equipment at future laser ranging stations. Full article
(This article belongs to the Special Issue Future of Lunar Exploration)
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<p>CCR arrays. The figure displays all the CCR arrays on the lunar surface, along with some additional details. (Source: adapted from an image search result for “lunar corner cube reflector” on Bing, <a href="https://bing.com/" target="_blank">https://bing.com/</a>, accessed on 5 May 2024).</p>
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<p>The CCR array sites on the Moon. (Source: adapted from an image search result for “lunar corner cube reflector” on Bing, <a href="https://bing.com/" target="_blank">https://bing.com/</a>, accessed on 5 May 2024).</p>
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<p>Lunar libration amplitude (1 January 2000–31 December 2009. 10 years).</p>
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<p>Lunar libration amplitude (1 January 2000–31 December 2000. 1 year).</p>
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<p>Schematic diagram of a tilted CCR array with laser incidence.</p>
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<p>Schematic diagram of the Apollo 11 and 14 LLR reflector arrays (d = 46 mm, <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> = 38 mm).</p>
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<p>Envelope of different laser pulses due to the tilt of the CCR array (Apollo 11 and 14).</p>
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<p>Range echo envelopes of the CCR arrays (Apollo 11 and 14) at different tilt angles.</p>
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<p>Echo plot for the laser ranging simulation of the Apollo 11 CCR array.</p>
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<p>A schematic diagram of the local experiment.</p>
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<p>The experimental CCR array (the left image shows the 6 × 6 array of CCRs used in the experiments, the middle image depicts a single CCR, and the right image displays the manually adjustable tilt table that is capable of adjusting angles in two directions).</p>
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<p>The experimental CCR array fixed on the exterior facade of the iron tower.</p>
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<p>The optical system of the Yunnan Observatories’ 53 cm binocular telescope.</p>
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<p>Experimental procedure (<b>left</b>: photo of adjusting the telescope direction and the size of the incident spot; <b>middle</b>: plane mirror attached to the array surface for adjusting the array tilt angle; <b>right</b>: photo of the incident laser.)</p>
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<p>Laser vertically incident echos for different numbers of reflectors.</p>
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<p>Echoes of the experimental CCR array at different tilt angles.</p>
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<p>The peak value of the echo histogram changes with the tilt angle of the CCR array.</p>
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<p>The residual echoes and their histograms at different tilt angles for the experimental CCR array using two columns.</p>
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<p>The experimental results for the CCR array with three columns.</p>
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<p>The experimental results for the CCR array with three columns.</p>
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26 pages, 6691 KiB  
Article
Calibration of SAR Polarimetric Images by Covariance Matching Estimation Technique with Initial Search
by Jingke Liu, Lin Liu and Xiaojie Zhou
Remote Sens. 2024, 16(13), 2400; https://doi.org/10.3390/rs16132400 - 29 Jun 2024
Viewed by 1121
Abstract
To date, various methods have been proposed for calibrating polarimetric synthetic aperture radar (SAR) using distributed targets. Some studies have utilized the covariance matching estimation technique (Comet) for SAR data calibration. However, practical applications have revealed issues stemming from ill-conditioned problems due to [...] Read more.
To date, various methods have been proposed for calibrating polarimetric synthetic aperture radar (SAR) using distributed targets. Some studies have utilized the covariance matching estimation technique (Comet) for SAR data calibration. However, practical applications have revealed issues stemming from ill-conditioned problems due to the analytical solution in the iterative process. To tackle this challenge, an improved method called Comet IS is introduced. Firstly, we introduce an outlier detection mechanism which is based on the Quegan algorithm’s results. Next, we incorporate an initial search approach which is based on the interior point method for recalibration. With the outlier detection mechanism in place, the algorithm can recalibrate iteratively until the results are correct. Simulation experiments reveal that the improved algorithm outperforms the original one. Furthermore, we compare the improved method with Quegan and Ainsworth algorithms, demonstrating its superior performance in calibration. Furthermore, we validate our method’s advancement using real data and corner reflectors. Compared with the other two algorithms, the improved performance in crosstalk isolation and channel imbalance is significant. This research provides a more reliable and effective approach for polarimetric SAR calibration, which is significant for enhancing SAR imaging quality. Full article
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<p>Parameter iterative estimation procedure. (<b>a</b>) The ideal calibration processes; (<b>b</b>) the actual calibration process, where <math display="inline"><semantics> <mrow> <mi>θ</mi> </mrow> </semantics></math> represents the rotation angle induced by the introduction of the imaginary part.</p>
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<p>Parameter estimation error and loss function values. (<b>a</b>) R by Ainsworth algorithm in dB; (<b>b</b>) R by Quegan algorithm in dB; (<b>c</b>) R by Comet algorithm in dB; (<b>d</b>) the value of loss function in dB.</p>
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<p>Minimum target values. The blue line represents the observed minimum target values. The green line represents the estimated minimum target values.</p>
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<p>Classification results. (<b>a</b>) Real classification; (<b>b</b>) predicted classification. The figure solely illustrates the relationship between the classification results and the chosen two-dimensional features. The abscissa and ordinate respectively represent the first and third dimensions of the feature vectors to characterize the distribution of five-dimensional features.</p>
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<p>R with Comet IS in dB.</p>
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<p>Measured information graph. (<b>a</b>) Optical images of the test area; (<b>b</b>) polarimetric SAR image of the corner reflector calibration site.</p>
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<p>Crosstalk amplitude. (<b>a</b>) Ainsworth; (<b>b</b>) Quegan; (<b>c</b>) Comet IS.</p>
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<p>Crosstalk amplitude. (<b>a</b>) Ainsworth; (<b>b</b>) Quegan; (<b>c</b>) Comet IS.</p>
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<p>SAR image (Pauli). (<b>a</b>) Raw SAR image; (<b>b</b>) image processed by Ainsworth algorithm; (<b>c</b>) image processed by Quegan algorithm; (<b>d</b>) image processed by Comet IS.</p>
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<p>Magnified section of SAR image. (<b>a</b>) Raw image; (<b>b</b>) image calibrated by Ainsworth algorithm; (<b>c</b>) image calibrated by Quegan algorithm; (<b>d</b>) image calibrated by Comet IS algorithm.</p>
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<p>Signatures of corner reflector RH9. (<b>a</b>−<b>d</b>) The x-pol signatures. (<b>e</b>−<b>f</b>) The co-pol signatures. (<b>a</b>,<b>e</b>) Rraw data; (<b>b</b>,<b>f</b>) data calibrated by Ainsworth algorithm; (<b>c</b>,<b>g</b>) data calibrated by Quegan algorithm; (<b>d</b>,<b>h</b>) data calibrated by Comet IS algorithm.</p>
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20 pages, 38601 KiB  
Article
Interferometric Calibration Model for the LuTan-1 Mission: Enhancing Digital Elevation Model Accuracy
by Jingwen Mou, Yu Wang, Jun Hong, Yachao Wang, Aichun Wang, Shiyu Sun and Guikun Liu
Remote Sens. 2024, 16(13), 2306; https://doi.org/10.3390/rs16132306 - 24 Jun 2024
Viewed by 1006
Abstract
The LuTan-1 (LT-1) mission, China’s first civilian bistatic spaceborne Synthetic Aperture Radar (SAR) mission, comprises two L-band SAR satellites. These satellites operate in bistatic InSAR strip map mode, maintaining a formation flight with an adjustable baseline to generate global digital elevation models (DEMs) [...] Read more.
The LuTan-1 (LT-1) mission, China’s first civilian bistatic spaceborne Synthetic Aperture Radar (SAR) mission, comprises two L-band SAR satellites. These satellites operate in bistatic InSAR strip map mode, maintaining a formation flight with an adjustable baseline to generate global digital elevation models (DEMs) with high accuracy and spatial resolution. This research introduces a dedicated interferometric calibration model for LT-1, tackling the unique challenges of the bistatic system, such as interferometric parameter coupling and the π-ambiguity problem caused by synchronization phase errors. This study validates the model using SAR images from LT-1 and Xinjiang corner reflector data, achieving interferometric phase accuracy better than 0.1 rad and baseline accuracy better than 2 mm, thereby producing high-precision DEMs with a height accuracy meeting the 5 m requirement. Full article
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<p>Interferometric calibration workflow of LT-1.</p>
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<p>The composition of the interferometric phase.</p>
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<p>The geometric diagram. (<b>a</b>) Illustration of the observation of ground point P within the bistatic system. (<b>b</b>) Baseline decomposition and projection diagram.</p>
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<p>Location of the calibration site. (<b>a</b>) Xinjiang, China. (<b>b</b>) Location of test site A. (<b>c</b>) Location of test site B. (<b>d</b>,<b>e</b>) Topographic conditions of the study area. (<b>f</b>,<b>g</b>) Deployment of corner reflectors.</p>
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<p>Initial interferometric phase result. (<b>a</b>) Master SAR image with SceneID 29607. (<b>b</b>) Unwrapped phase with SceneID 29607. (<b>c</b>) Flat-Earth phase with SceneID 29607. (<b>d</b>) Master SAR image with SceneID 30278. (<b>e</b>) Unwrapped phase with SceneID 30278. (<b>f</b>) Flat-Earth phase with SceneID 30278. (<b>g</b>) Master SAR image with SceneID 49960. (<b>h</b>) Unwrapped phase with SceneID 49960. (<b>i</b>) Flat-Earth phase with SceneID 49960. (<b>j</b>) Master SAR image with SceneID 51501. (<b>k</b>) Unwrapped phase with SceneID 51501. (<b>l</b>) Flat-Earth phase with SceneID 51501.</p>
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<p>Box chart of interferometric phase shift result. (<b>a</b>) Formation 1. (<b>b</b>) Formation 2.</p>
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<p>Initial baseline value. (<b>a</b>) <span class="html-italic">T</span>-axis baseline with SceneID 29607. (<b>b</b>) <span class="html-italic">C</span>-axis baseline with SceneID 29607. (<b>c</b>) <span class="html-italic">N</span>-axis baseline with SceneID 29607. (<b>d</b>) Total baseline length with SceneID 29607. (<b>e</b>) <span class="html-italic">T</span>-axis baseline with SceneID 30278. (<b>f</b>) <span class="html-italic">C</span>-axis baseline with SceneID 30278. (<b>g</b>) <span class="html-italic">N</span>-axis baseline with SceneID 30278. (<b>h</b>) Total baseline length with SceneID 30278. (<b>i</b>) <span class="html-italic">T</span>-axis baseline with SceneID 49960. (<b>j</b>) <span class="html-italic">C</span>-axis baseline with SceneID 49960. (<b>k</b>) <span class="html-italic">N</span>-axis baseline with SceneID 49960. (<b>l</b>) Total baseline length with SceneID 49960. (<b>m</b>) <span class="html-italic">T</span>-axis baseline with SceneID 51501. (<b>n</b>) <span class="html-italic">C</span>-axis baseline with SceneID 51501. (<b>o</b>) <span class="html-italic">N</span>-axis baseline with SceneID 51501. (<b>p</b>) Total baseline length with SceneID 51501.</p>
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<p>Baseline error result. (<b>a</b>) Formation 1. (<b>b</b>) Formation 2.</p>
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<p>DEM of four sample images generated by LT-1 interferometer. (<b>a</b>) SceneID 29607. (<b>b</b>) SceneID 30278. (<b>c</b>) SceneID 49960. (<b>d</b>) SceneID 51501.</p>
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<p>Height error histogram of four sample images. (<b>a</b>) SceneID 29607. (<b>b</b>) SceneID 30278. (<b>c</b>) SceneID 49960. (<b>d</b>) SceneID 51501.</p>
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<p>The accuracy of DEM.</p>
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<p>The sensitivity of interferometric parameters to height. (<b>a</b>) <math display="inline"><semantics> <mfrac> <mrow> <mo>∂</mo> <mi>H</mi> </mrow> <mrow> <mo>∂</mo> <mi>ϕ</mi> </mrow> </mfrac> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mfrac> <mrow> <mo>∂</mo> <mi>H</mi> </mrow> <mrow> <mo>∂</mo> <msub> <mi>B</mi> <mi>T</mi> </msub> </mrow> </mfrac> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mfrac> <mrow> <mo>∂</mo> <mi>H</mi> </mrow> <mrow> <mo>∂</mo> <msub> <mi>B</mi> <mi>C</mi> </msub> </mrow> </mfrac> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mfrac> <mrow> <mo>∂</mo> <mi>H</mi> </mrow> <mrow> <mo>∂</mo> <msub> <mi>B</mi> <mi>N</mi> </msub> </mrow> </mfrac> </semantics></math>.</p>
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22 pages, 4817 KiB  
Article
An Identification Method of Corner Reflector Array Based on Mismatched Filter through Changing the Frequency Modulation Slope
by Le Xia, Fulai Wang, Chen Pang, Nanjun Li, Runlong Peng, Zhiyong Song and Yongzhen Li
Remote Sens. 2024, 16(12), 2114; https://doi.org/10.3390/rs16122114 - 11 Jun 2024
Viewed by 896
Abstract
The corner reflector is an effective means of interference for radar seekers due to its high jamming intensity, wide frequency band, and combat effectiveness ratio. Properly arranging multiple corner reflectors in an array can form dilution jamming that resembles ships, substantially enhancing the [...] Read more.
The corner reflector is an effective means of interference for radar seekers due to its high jamming intensity, wide frequency band, and combat effectiveness ratio. Properly arranging multiple corner reflectors in an array can form dilution jamming that resembles ships, substantially enhancing the interference effect. This results in a significant decline in the precision attack efficiency of radar seekers. Hence, it is critical to accurately identify corner reflector array. The common recognition methods involve extracting features on the high-resolution range profile (HRRP) and polarization domain. However, the former is constrained by the number of corner reflectors, while the latter is affected by the accuracy of polarization measurement, both of which have limited performance on the identification of corner reflector array. In terms of the evident variations in physical structures, there must be differences in their scattering characteristics. To highlight the differences, this paper proposes a new method based on the concept of mismatched filtering, which involves changing the frequency modulation slope of the chirp signal in the filter. Then, the variance of width and intervals within a specific scope are extracted as features to characterize these differences, and an identification process is designed in combination with the support vector machine. The simulation experiments demonstrate that the proposed method exhibits stable discriminative performance and can effectively combat dilution jamming. Its accuracy rate exceeds 0.86 when the signal-to-noise ratio is greater than 0 dB. Compared to the HRRP methods, the recognition accuracy of the proposed algorithm improves 15% in relation to variations in the quantity of corner reflectors. Full article
(This article belongs to the Special Issue Remote Sensing of Target Object Detection and Identification II)
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<p>The mismatched filter by modifying frequency modulation slope. (<b>a</b>) Time−frequency scheme of LFM signal in mismatched filter. (<b>b</b>) The outputs of different modulation factor.</p>
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<p>The modulation factor−range two−dimensional images of different scenarios. (<b>a</b>) Scenario 1. (<b>b</b>) Scenario 2. (<b>c</b>) Scenario 3. (<b>d</b>) Scenario 4.</p>
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<p>Simulated range profile and reconstructed range profile. (<b>a</b>) Ship. (<b>b</b>) Corner reflector array.</p>
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<p>Modulation factor−range two−dimensional image. (<b>a</b>) Ship. (<b>b</b>) Corner reflector array.</p>
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<p>The distribution of points within the range of −5 dB. (<b>a</b>) Ship. (<b>b</b>) Corner reflector array.</p>
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<p>The intuitive illustration of the two extracted features.</p>
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<p>The identification process of corner reflector array.</p>
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<p>The models of ships and corner reflector arrays. (<b>a</b>) Ship 1. (<b>b</b>) Ship 2. (<b>c</b>) Ship 3. (<b>d</b>) Ship 4. (<b>e</b>) Corner reflector array 1. (<b>f</b>) Corner reflector array 2.</p>
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<p>The identification performance of single modulation factor. (<b>a</b>) Different modulation factor but within the same range of −5 dB. (<b>b</b>) Same modulation factor within different ranges.</p>
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<p>The distribution of characteristics. (<b>a</b>) The variance of width. (<b>b</b>) The variance of intervals.</p>
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<p>The joint distribution of the two features.</p>
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<p>The identification performance of different methods. Where the HRRP method is in Ref. [<a href="#B8-remotesensing-16-02114" class="html-bibr">8</a>], polarization modulation is in Ref. [<a href="#B7-remotesensing-16-02114" class="html-bibr">7</a>], polarization invariant is in Ref. [<a href="#B41-remotesensing-16-02114" class="html-bibr">41</a>], Cloude decomposition is in Ref. [<a href="#B39-remotesensing-16-02114" class="html-bibr">39</a>], krogager decomposition is in Ref. [<a href="#B40-remotesensing-16-02114" class="html-bibr">40</a>].</p>
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<p>The identification performance under noise of different distributions.</p>
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<p>The identification performance under different parameters. (<b>a</b>) Different range of modulation factors but within the same range of −5 dB. (<b>b</b>) Different range of point extraction but within the same range of modulation factors.</p>
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<p>The identification performance of different conditions. (<b>a</b>) Training and testing using different pitch angles. (<b>b</b>) Training and testing using different yaw angles.</p>
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<p>The two−dimensional distribution of different methods. (<b>a</b>) The HRRP method in [<a href="#B8-remotesensing-16-02114" class="html-bibr">8</a>]. (<b>b</b>) The proposed features in HRRP.</p>
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<p>The two−dimensional distribution of different methods under different quantities of corner reflectors. (<b>a</b>,<b>d</b>) Based on the proposed method. (<b>b</b>,<b>e</b>) Based on the HRRP method in [<a href="#B8-remotesensing-16-02114" class="html-bibr">8</a>]. (<b>c</b>,<b>f</b>) Based on the proposed features in HRRP.</p>
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<p>The identification accuracy rate of different methods under two sets of experiments. (<b>a</b>) A single array of corner reflectors. (<b>b</b>) Two arrays of corner reflectors.</p>
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15 pages, 14003 KiB  
Article
Analysis of the Dihedral Corner Reflector’s RCS Features in Multi-Resource SAR
by Jie Liu, Tao Li, Sijie Ma, Yangmao Wen, Yanhao Xu and Guigen Nie
Appl. Sci. 2024, 14(12), 5054; https://doi.org/10.3390/app14125054 - 10 Jun 2024
Viewed by 1061
Abstract
Artificial corner reflectors are widely used in the vegetated landslide for time series InSAR monitoring due to their permanent scattering features. This paper investigated the RCS features of a novel dihedral CR under multi-resource SAR datasets. An RCS reduction model for the novel [...] Read more.
Artificial corner reflectors are widely used in the vegetated landslide for time series InSAR monitoring due to their permanent scattering features. This paper investigated the RCS features of a novel dihedral CR under multi-resource SAR datasets. An RCS reduction model for the novel dihedral corner reflector has been proposed to evaluate the energy loss caused by the deviation between the SAR incident angle and the CR’s axis. On the Huangtupo slope, Badong county, Hubei province, tens of dihedral CRs had been installed and the TSX–spotlight and Sentinel-TOPS data had been collected. Based on the observation results of CRs with more than ten deviation angles, the proposed reduction model was tested with preferable consistency under a real dataset, while 2 dBsm of systematic bias was verified in those datasets. The maximum incident angle deviation in the Sentinel data overlapping area is over 12°, which leads to a 2.4 dBsm RCS decrease for horizontally placed dihedral CRs estimated by the proposed model, which has also been testified by the observed results. The testing results from the Sentinel data show that in high, vegetation-covered mountain areas like the Huangtupo slope, the dihedral CRs with a 0.4 m slide length can be achieve 1 mm precision accuracy, while a side length of 0.2 m can achieve the same accuracy under TSX–spotlight data. Full article
(This article belongs to the Special Issue Latest Advances in Radar Remote Sensing Technologies)
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<p>(<b>a</b>) The schematic diagram of the cross-section of the effective scattering area for the dihedral reflector. (<b>b</b>) The 3D schematic diagram of the effective scattering area of the dihedral reflector.</p>
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<p>(<b>a</b>) The schematic diagram of the RCS increase caused by the CR’s side length. (<b>b</b>) The RCS reduction curve caused by the CR’s deviation angle.</p>
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<p>(<b>a</b>) The schematic diagram of the Sentinel and TSX data coverage test area; (<b>b</b>) the schematic diagram of the Huangtupo slope area and the location of the CRs; (<b>c</b>) the photos and installation time of multiple types of corner reflectors.</p>
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<p>The structure of the novel dihedral CR; (<b>a</b>,<b>c</b>) are the dihedral CR with semicircular and square panels; (<b>b</b>,<b>d</b>) are the corresponding trapezoidal structure.</p>
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<p>(<b>a</b>,<b>b</b>) Are the average intensity images of the Sentinel (Track 084) and TSX (ascending track) of the CR array on the Huangtupo slope; (<b>c</b>,<b>d</b>) are the enlarged intensity images of the CRs under the Sentinel and TSX data.</p>
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<p>(<b>a</b>,<b>c</b>) Are the RCS reduction results caused by the deviation angle β in the Sentinel and TSX data; (<b>b</b>,<b>d</b>) are the RCS discrepancy between the model and the measured results in the Sentinel and TSX data.</p>
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<p>The RCS time series of the triangular CR under Sentinel (<b>a</b>) and TSX (<b>b</b>) data.</p>
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<p>The RCS time series of the horizontally placed dihedral reflector under Sentinel (<b>a</b>) and TSX (<b>b</b>) data.</p>
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<p>The RCS time series of the dihedral reflector with a tilt angle of 10°under Sentinel (<b>a</b>) and TSX (<b>b</b>) data.</p>
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<p>The RCS time series of the dihedral reflector with a tilt angle of 15° under Sentinel (<b>a</b>) and TSX (<b>b</b>) data.</p>
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<p>The theoretical deformation monitoring accuracy of the CR array in the Sentinel (<b>a</b>) and TSX (<b>b</b>) data.</p>
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11 pages, 3065 KiB  
Communication
Implementation of MIMO Radar-Based Point Cloud Images for Environmental Recognition of Unmanned Vehicles and Its Application
by Jongseok Kim, Seungtae Khang, Sungdo Choi, Minsung Eo and Jinyong Jeon
Remote Sens. 2024, 16(10), 1733; https://doi.org/10.3390/rs16101733 - 14 May 2024
Cited by 1 | Viewed by 1238
Abstract
High-performance radar systems are becoming increasingly popular for accurately detecting obstacles in front of unmanned vehicles in fog, snow, rain, night and other scenarios. The use of these systems is gradually expanding, such as indicating empty space and environment detection rather than just [...] Read more.
High-performance radar systems are becoming increasingly popular for accurately detecting obstacles in front of unmanned vehicles in fog, snow, rain, night and other scenarios. The use of these systems is gradually expanding, such as indicating empty space and environment detection rather than just detecting and tracking the moving targets. In this paper, based on our high-resolution radar system, a three-dimensional point cloud image algorithm is developed and implemented. An axis translation and compensation algorithm is applied to minimize the point spreading caused by the different mounting positions and the alignment error of the Global Navigation Satellite System (GNSS) and radar. After applying the algorithm, a point cloud image for a corner reflector target and a parked vehicle is created to directly compare the improved results. A recently developed radar system is mounted on the vehicle and it collects data through actual road driving. Based on this, a three-dimensional point cloud image including an axis translation and compensation algorithm is created. As a results, not only the curbstones of the road but also street trees and walls are well represented. In addition, this point cloud image is made to overlap and align with an open source web browser (QtWeb)-based navigation map image to implement the imaging algorithm and thus determine the location of the vehicle. This application algorithm can be very useful for positioning unmanned vehicles in urban area where GNSS signals cannot be received due to a large number of buildings. Furthermore, sensor fusion, in which a three-dimensional point cloud radar image appears on the camera image, is also implemented. The position alignment of the sensors is realized through intrinsic and extrinsic parameter optimization. This high-performance radar application algorithm is expected to work well for unmanned ground or aerial vehicle route planning and avoidance maneuvers in emergencies regardless of weather conditions, as it can obtain detailed information on space and obstacles not only in the front but also around them. Full article
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<p>Different positions of the radar and GNSS.</p>
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<p>Comparison of images before (<b>a</b>) and after (<b>b</b>) misalignment correction for the accumulation of point target data collected in driving.</p>
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<p>The multi-frame point cloud image was realized by rotating around the parked vehicle. Before misalignment correction (<b>a</b>) the point blurred the object shape, but after calibration (<b>b</b>) the shape and boundary of the object become clear.</p>
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<p>A point cloud map image is generated in real time on an urban road using a fabricated radar system mounted on a vehicle. The figure also shows the 3D view image with elevation information added.</p>
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<p>The QtWeb-based road map API is displayed in real time and overlaps with the two-dimensional radar point cloud map image. It is easy to capture the exact location and the surrounding information of the vehicle. (<b>a</b>) The top view of the real map image, and (<b>b</b>) the overlapping image.</p>
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<p>Camera image and the radar point cloud map image are combined to implement a sensor fusion image. (<b>a</b>) The fused image and (<b>b</b>) a three-dimensional point cloud image of the radar.</p>
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35 pages, 15218 KiB  
Article
An Advanced Quality Assessment and Monitoring of ESA Sentinel-1 SAR Products via the CyCLOPS Infrastructure in the Southeastern Mediterranean Region
by Dimitris Kakoullis, Kyriaki Fotiou, Nerea Ibarrola Subiza, Ramon Brcic, Michael Eineder and Chris Danezis
Remote Sens. 2024, 16(10), 1696; https://doi.org/10.3390/rs16101696 - 10 May 2024
Cited by 2 | Viewed by 1710
Abstract
The Cyprus Continuously Operating Natural Hazards Monitoring and Prevention System, abbreviated CyCLOPS, is a national strategic research infrastructure devoted to systematically studying geohazards in Cyprus and the Eastern Mediterranean, Middle East, and North Africa (EMMENA) region. Amongst others, CyCLOPS comprises six permanent sites, [...] Read more.
The Cyprus Continuously Operating Natural Hazards Monitoring and Prevention System, abbreviated CyCLOPS, is a national strategic research infrastructure devoted to systematically studying geohazards in Cyprus and the Eastern Mediterranean, Middle East, and North Africa (EMMENA) region. Amongst others, CyCLOPS comprises six permanent sites, each housing a Tier-1 GNSS reference station co-located with two calibration-grade corner reflectors (CRs). The latter are strategically positioned to account for both the ascending and descending tracks of SAR satellite missions, including the ESA’s Sentinel-1. As of June 2021, CyCLOPS has reached full operational capacity and plays a crucial role in monitoring the geodynamic regime within the southeastern Mediterranean area. Additionally, it actively tracks landslides occurring in the western part of Cyprus. Although CyCLOPS primarily concentrates on geohazard monitoring, its infrastructure is also configured to facilitate the radiometric calibration and geometric validation of Synthetic Aperture Radar (SAR) imagery. Consequently, this study evaluates the performance of Sentinel-1A SAR by exploiting the CyCLOPS network to determine key parameters including spatial resolution, sidelobe levels, Radar Cross-Section (RCS), Signal-to-Clutter Ratio (SCR), phase stability, and localization accuracy, through Point Target Analysis (PTA). The findings reveal the effectiveness of the CyCLOPS infrastructure to maintain high-quality radiometric parameters in SAR imagery, with consistent spatial resolution, controlled sidelobe levels, and reliable RCS and SCR values that closely adhere to theoretical expectations. With over two years of operational data, these findings enhance the understanding of Sentinel-1 SAR product quality and affirm CyCLOPS infrastructure’s reliability. Full article
(This article belongs to the Special Issue Calibration and Validation of SAR Data and Derived Products)
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<p>The CyCLOPS permanent network. Green triangles denote the co-located GNSS CORS and CRs sites [<a href="#B6-remotesensing-16-01696" class="html-bibr">6</a>].</p>
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<p>A representative example of a CyCLOPS permanent segment: (<b>a</b>) the site’s collocation in the Alevga area; (<b>b</b>) a CR with the ID ALEV02, oriented on the descending pass of Sentinel-1; (<b>c</b>) the GNSS CORS monumented based on the UNAVCO shallow drilled braced-type (SDBM) and equipped with a solar panel, tiltmeter, and weather station; and (<b>d</b>) a CR with the ID ALEV01, oriented on the ascending pass of Sentinel-1.</p>
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<p>An example of the relative orbits 160 and 167, S-1A acquisitions over Cyprus.</p>
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<p>The normalization areas of β<sub>0</sub> and σ<sup>0</sup>. A<sub>β</sub> is the blue-coloured area, whereas the red-coloured area defines A<sub>σ</sub> which is aligned with a ground plane as modelled by a reference ellipsoid. Redrawn from [<a href="#B27-remotesensing-16-01696" class="html-bibr">27</a>].</p>
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<p>The geometry of a triangular trihedral CR [<a href="#B6-remotesensing-16-01696" class="html-bibr">6</a>]. (<b>a</b>) θ represents the azimuth angle and ψ the elevation angle; (<b>b</b>) an adjustment of a triangular trihedral CR. ψ represents the elevation angle, Φ the off-nadir angle, and α the CR baseplate elevation angle.</p>
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<p>The sinc function magnitude of a point target as a cut through the peak in the slant range.</p>
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<p>Point target response area for IRF analysis. The blue-coloured point indicates the point target peak, the blue rectangle outlines the mainlobe area encompassing 2 × 2 resolution cells, and the outer area of the ISLR is defined as the green rectangle which equals 20 × 20 resolution cells.</p>
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<p>The IRF of a TTCR depicts the spatial resolution image quality parameter in slant range.</p>
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<p>The PSLR estimation in an IRF graph. Green dots highlight the maximum intensity in the peak and maximum sidelobe.</p>
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<p>The TTCR response function of SOUN01, after interpolation, in the S-1A IW VV images of 17.10.2023, for the ascending pass. (<b>a</b>,<b>b</b>) The plots represent a cut through the peak in the slant range and azimuth direction, respectively, while (<b>c</b>) illustrates the point target relative power in a 3D plot.</p>
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<p>The TTCR response function of SOUN01, after interpolation, in the S-1A IW VV images of 17.10.2023, for the ascending pass. (<b>a</b>,<b>b</b>) The plots represent a cut through the peak in the slant range and azimuth direction, respectively, while (<b>c</b>) illustrates the point target relative power in a 3D plot.</p>
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<p>The temporal variation in spatial resolution from the TTCR in ASGA corresponding to the ascending pass, for the monitoring period. (<b>a</b>) Spatial resolution in range, and (<b>b</b>) spatial resolution in azimuth.</p>
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<p>The temporal variation in spatial resolution from the TTCR in ASGA corresponding to the ascending pass, for the monitoring period. (<b>a</b>) Spatial resolution in range, and (<b>b</b>) spatial resolution in azimuth.</p>
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<p>A representative example of the definition of the TROU02 point target response area. The yellow square target window outlines the outer area (20 × 20). Within it, the red window defines the mainlobe area. The green cross, encompassing the sidelobes of the CR’s response, separates this defined area from the clutter area, which consists of four quadrants.</p>
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<p>The soil and dust deposition at ALEV02 which led to the obstruction of the drainage hole, resulting in poor water drainage, and therefore a dramatic reduction in RCS response.</p>
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<p>The differences in the RCS for each TTCR compared to RCS<sub>T</sub> (theoretical RCS–actual RCS). The estimates are derived by averaging the values measured in GRD images using the integral method. The error bars are the standard 1-sigma errors (1σ) of these observations.</p>
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<p>The results of the analysis derived from the peak method. The RCS difference for each TTCR, from theory. RCS estimates are derived by averaging the values measured in SLC images. The error bars are the standard 1-sigma errors (1σ) of these observations.</p>
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<p>Average estimated RCS difference for all TTCRs for both methods.</p>
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<p>The average estimations of the average displacement error in LoS, for each TTCR. Error bars are the standard deviations of these observations. The CR IDs are as defined in <a href="#remotesensing-16-01696-t005" class="html-table">Table 5</a>.</p>
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<p>The positioning corrections in range and azimuth performed individually for each SAR acquisition. Blue-coloured triangles represent the initial position in a single S-1A acquisition, whereas black-coloured triangles are the final positions after the analysis. (<b>a</b>) The ALE of the AKMS01 TTCR (ascending), and (<b>b</b>) the ALE of the AKMS02 TTCR (descending).</p>
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<p>The TTCR response function of SOUN02, after interpolation, in the S-1A IW VV images of 18 October 2023, for the descending pass. (<b>a</b>,<b>b</b>) The plots represent a cut through the peak in the slant range and azimuth direction, respectively, while (<b>c</b>) illustrates the point target relative power in a 3D plot.</p>
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<p>The temporal variation in spatial resolution from the TTCR in ASGA corresponding to the descending pass, for the monitoring period.</p>
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<p>The time series of the TTCRs’ RCS and SCR responses, for the monitoring period, using the integral method.</p>
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<p>The time series of the TTCRs’ RCS and SCR responses, for the monitoring period, using the integral method.</p>
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<p>The time series of the TTCRs’ RCS and SCR responses, for the monitoring period, using the peak method. The black-coloured dashed vertical line represents the TTCR installation date. The magenta-coloured dashed vertical line, where applicable, represents the reorientation date.</p>
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<p>The time series of the TTCRs’ RCS and SCR responses, for the monitoring period, using the peak method. The black-coloured dashed vertical line represents the TTCR installation date. The magenta-coloured dashed vertical line, where applicable, represents the reorientation date.</p>
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<p>The time series of the TTCRs’ RCS and SCR responses, for the monitoring period, using the peak method. The black-coloured dashed vertical line represents the TTCR installation date. The magenta-coloured dashed vertical line, where applicable, represents the reorientation date.</p>
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<p>The time series of the TTCRs’ RCS and SCR responses, for the monitoring period, using the peak method. The black-coloured dashed vertical line represents the TTCR installation date. The magenta-coloured dashed vertical line, where applicable, represents the reorientation date.</p>
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18 pages, 5414 KiB  
Article
Dynamic Doppler Characteristics of Maritime Airborne Corner Reflector
by Lingang Wu, Shengliang Hu, Chengxu Feng, Yasong Luo, Zhong Liu and Li Lin
J. Mar. Sci. Eng. 2024, 12(5), 727; https://doi.org/10.3390/jmse12050727 - 27 Apr 2024
Viewed by 951
Abstract
The maritime airborne corner reflector (ACR) is a radar reflector that can measure wind speed in an unknown sea area in real time over a long distance. To improve our understanding of how the ACR works, we investigated the Doppler characteristics of the [...] Read more.
The maritime airborne corner reflector (ACR) is a radar reflector that can measure wind speed in an unknown sea area in real time over a long distance. To improve our understanding of how the ACR works, we investigated the Doppler characteristics of the ACR for the first time from a dynamic perspective. First, we constructed a radar echo signal model of the ACR. Then, we obtained the dynamic Doppler characteristics through pulse Doppler processing and discussed the special phenomenon of Doppler broadening. Finally, we proposed a rectangular window decomposition method to analyze the inner principle of the Doppler broadening phenomenon in more detail. In conclusion, this study provides valuable insights into the Doppler characterization of an ACR from a dynamic viewpoint, which contributes to enriching the basic theory of this equipment. Full article
(This article belongs to the Special Issue Ocean Observations)
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<p>Typical modality of ACR. (<b>a</b>) Structure of Octahedral Reflector. (<b>b</b>) Parachute stagnation assist.</p>
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<p>Pulsed Doppler radar workflow diagram.</p>
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<p>Processing of pulsed Doppler data.</p>
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<p>Fast-time–slow-time data graph.</p>
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<p>RD data graph.</p>
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<p>Sequential Doppler spectrogram.</p>
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<p>Target false dismissal caused by Doppler spectrum broadening.</p>
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<p>Time-sequential kurtosis diagram.</p>
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<p>Time-sequential false dismissal judgement diagram.</p>
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<p>Doppler broadening phenomenon under different parameter schemes. (<b>a</b>) Doppler broadening severity for different parameter values. (<b>b</b>) Doppler broadening frequency for different parameter values.</p>
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<p>Broadening spectrum and its original slow-time series. (<b>a</b>) Amplitude fluctuation in the original slow-time series. (<b>b</b>) Doppler spectrum with broadening phenomena.</p>
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<p>Simplified rectangular window for slow-time series amplitude.</p>
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<p>Doppler spectrum of slow-time series with rectangular window.</p>
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<p>Omnidirectional RCS of ACR.</p>
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18 pages, 2670 KiB  
Article
Absolute Calibration of a UAV-Mounted Ultra-Wideband Software-Defined Radar Using an External Target in the Near-Field
by Asem Melebari, Piril Nergis, Sepehr Eskandari, Pedro Ramos Costa and Mahta Moghaddam
Remote Sens. 2024, 16(2), 231; https://doi.org/10.3390/rs16020231 - 6 Jan 2024
Cited by 3 | Viewed by 1299
Abstract
We describe a method to calibrate a Software-Defined Radar (SDRadar) system mounted on an uncrewed aerial vehicle (UAV) with an ultra-wideband (UWB) waveform operated in the near-field region. Radar calibration is a prerequisite for using the full capabilities of the radar system to [...] Read more.
We describe a method to calibrate a Software-Defined Radar (SDRadar) system mounted on an uncrewed aerial vehicle (UAV) with an ultra-wideband (UWB) waveform operated in the near-field region. Radar calibration is a prerequisite for using the full capabilities of the radar system to retrieve geophysical parameters accurately. We introduce a framework and process to calibrate the SDRadar with the UWB waveform in the 675 MHz–3 GHz range in the near-field region. Furthermore, we present the framework for computing the near-field radar cross section (RCS) of an external passive calibration target, a trihedral corner reflector (CR), using HFSS software and with consideration for specific antennas. The calibration performance was evaluated with various distances between the calibration target and radar antennas. The necessity for the knowledge of the near-field RCS to calibrate SDRadar was demonstrated, which sets this work apart from the standard method of using a trihedral CR for backscatter radar calibration. We were able to achieve approximately 0.5 dB accuracy when calibrating the SDRadar in the anechoic chamber using a trihedral CR. In outdoor field conditions, where the ground rough surface scattering effects are present, the calibration performance was lower, approximately 1.5 dB. A solution is proposed to overcome the ground effect by elevating the CR above the ground level, which enables applying time-gating around the CR echo, excluding the reflection from the ground. Full article
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<p>The CR in the field site with the hexacopter UAV.</p>
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<p>Near-field and far-field regions for the CR.</p>
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<p>The triangular trihedral CR.</p>
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<p>The far-field RCS of the CR with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>54</mn> <mo>.</mo> <msup> <mn>73</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>=</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>The far-field RCS of the CR with <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>=</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Geometric view for the HFSS simulation. (<b>a</b>) Geometric view for the background. (<b>b</b>) Geometric view for the total.</p>
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<p>Simulated near-field RCS of CR using HFSS.</p>
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<p>RFSPACE TSA600 antennas’ gain.</p>
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<p>The reflection coefficient of the RFSPACE TSA600 antennas.</p>
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<p>The elevation antenna pattern of the RFSPACE TSA600 antenna.</p>
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<p>The SDRadar and CR measurement set up in the anechoic chamber. (<b>a</b>) The SDRadar system at one end of the chamber. (<b>b</b>) The CR at the other end of the chamber.</p>
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<p>Measured S-parameters of CR in the anechoic chamber in time domain.</p>
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<p>Measured near-field RCS of CR in the anechoic chamber.</p>
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<p>Comparison between the near-field RCS calculated via VNA and HFSS.</p>
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<p>Estimated calibration factor for the anechoic chamber. (<b>a</b>) Estimated calibration factor. (<b>b</b>) Standard deviation.</p>
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<p>Estimated calibration factor for the field experiment. (<b>a</b>) Estimated calibration factor. (<b>b</b>) Standard deviation.</p>
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<p>Estimated calibration factor for the field experiment after applying the thresholds. (<b>a</b>) Estimated calibration factor. (<b>b</b>) Standard deviation.</p>
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18 pages, 8055 KiB  
Article
The Structural Reliability of the Usumacinta Bridge Using InSAR Time Series of Semi-Static Displacements
by German Michel Guzman-Acevedo, Juan A. Quintana-Rodriguez, Jose Ramon Gaxiola-Camacho, Guadalupe Esteban Vazquez-Becerra, Vanessa Torres-Moreno and Jesus Guadalupe Monjardin-Quevedo
Infrastructures 2023, 8(12), 173; https://doi.org/10.3390/infrastructures8120173 - 4 Dec 2023
Cited by 3 | Viewed by 2093
Abstract
In recent years, Interferometric Synthetic Aperture Radar (InSAR) technology has been able to determine the semi-static behavior of bridges. However, most of the research about the use of InSAR in the monitoring of bridges has been applied only in deterministic assessments of their [...] Read more.
In recent years, Interferometric Synthetic Aperture Radar (InSAR) technology has been able to determine the semi-static behavior of bridges. However, most of the research about the use of InSAR in the monitoring of bridges has been applied only in deterministic assessments of their performance. Therefore, in the current manuscript, the Usumacinta Bridge, located in Mexico, was evaluated based on a probabilistic methodology to define structural reliability using images from Sentinel-1. In addition, a controlled experiment was developed using a corner reflector (CR) to evaluate the capabilities of InSAR for determining vertical displacements. In the trial, the CR was designed, oriented, and implemented, finding discrepancies concerning leveling of less than 2 mm. On the other hand, the case of the alternative probabilistic approach integrates the reliability of structures theory and probability density functions (PDFs) of displacements obtained via InSAR technology. In summary, the proposed study focused on the analysis of two years of vertical displacements and monthly velocities; then, implementing the alternative probabilistic approach, the reliability index (β) and probability of risk (PR) of the bridge were extracted, respectively. Based on the results of the experimental part of the paper, the displacements indicated maximum and minimum values of reliability index of 8.1 and 3.4, respectively. Within this context, the mean and standard deviation obtained were 5.9 and 1.4, respectively. On the other hand, the monthly velocities showed a maximum probability of risk of 2.61%, minimum value of 1.5 × 10−5%, mean of 0.4%, and standard deviation of 0.8%. Hence, the above-documented results indicate that the Usumacinta Bridge did not suffer any damage during its overloading condition period. Full article
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<p>Vehicles that affected the Usumacinta Bridge: (<b>a</b>) eighteen-wheeler vehicle of total length of 30 m; (<b>b</b>) eighteen-wheeler vehicle of a total length of 68 m.</p>
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<p>Geographic location of the Usumacinta Bridge.</p>
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<p>Usumacinta Bridge: (<b>a</b>) panoramic view; (<b>b</b>) side view.</p>
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<p>PDF with threshold limits <span class="html-italic">a</span> and <span class="html-italic">b</span> for displacements.</p>
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<p>CR prior to being installed.</p>
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<p>Positioning and movement of CR.</p>
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<p>Location of the CR in the reflectivity map.</p>
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<p>Resulting points on the Usumacinta Bridge.</p>
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<p>Resulting displacements on the Usumacinta Bridge.</p>
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<p>Resulting monthly velocities on the Usumacinta Bridge.</p>
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<p>Displacements of the point number 4.</p>
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<p>Statistical distribution of the resulting displacements in point number 4.</p>
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<p>Monthly velocities in point number 3.</p>
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<p>Statistical distribution of the resulting monthly velocities in point number 3.</p>
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