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25 pages, 9994 KiB  
Article
A Triple-Channel Network for Maritime Radar Targets Detection Based on Multi-Modal Features
by Kaiqi Wang and Zeyu Wang
Remote Sens. 2024, 16(24), 4662; https://doi.org/10.3390/rs16244662 - 13 Dec 2024
Viewed by 244
Abstract
Sea surface target detectors are often interfered by various complex sea surface factors such as sea clutter. Especially when the signal-to-clutter ratio (SCR) is low, it is difficult to achieve high-performance detection. This paper proposes a triple-channel network model for maritime target detection [...] Read more.
Sea surface target detectors are often interfered by various complex sea surface factors such as sea clutter. Especially when the signal-to-clutter ratio (SCR) is low, it is difficult to achieve high-performance detection. This paper proposes a triple-channel network model for maritime target detection based on the method of multi-modal data fusion. This method comprehensively improves the traditional multi-channel inputs by extracting highly complementary multi-modal features from radar echoes, namely, time-frequency image, phase sequence and correlation coefficient sequence. Appropriate networks are selected to construct a triple-channel network according to the internal data structure of each feature. The three features are utilized as the input of each network channel. To reduce the coupling between multi-channel data, the SE block is introduced to optimize the feature vectors of the channel dimension and improve the data fusion strategy. The detection results are output by the false alarm control unit according to the given probability of false alarm (PFA). The experiments on the IPIX datasets verify that the performance of the proposed detector is better than the existing detectors in dealing with complex ocean scenes. Full article
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Figure 1
<p>Average SCRs of primary cells in ten datasets at the four polarization modes.</p>
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<p>Typical TF spectrum of target and clutter samples from IPIX dataset in observation time of 1 s: (<b>a</b>) clutter; (<b>b</b>) target.</p>
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<p>Typical phase sequence of target and clutter samples from IPIX dataset in observation time of 1 s: (<b>a</b>) clutter; (<b>b</b>) target.</p>
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<p>Typical correlation coefficient sequence of target and clutter samples from the IPIX dataset in observation time of 1 s: (<b>a</b>) clutter; (<b>b</b>) target.</p>
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<p>Structure of the proposed detector.</p>
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<p>Structure of proposed triple-channel model.</p>
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<p>The network structures used in the Triple-channel model: (<b>a</b>) Layer1 to Layer5 in the TF processing unit; (<b>b</b>) LeNet network model in the correlation processing unit.</p>
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<p>The LSTM structure used in triple-channel model.</p>
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<p>The SE attention structure used in triple-channel model.</p>
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<p>ROC curves of different network models for each of the three input features, respectively, using #IPIX_03 with SCR of 0 dB: (<b>a</b>) ResNet18 and VGG16 performance for TF feature; (<b>b</b>) LeNet and LSTM performance for phase feature; (<b>c</b>) LeNet and LSTM performance for correlation feature.</p>
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<p>ROC curves of different network models for each of the three input features, respectively, using #IPIX_02 with SCR of 5 dB: (<b>a</b>) ResNet18 and VGG16 performance for TF feature; (<b>b</b>) LeNet and LSTM performance for phase feature; (<b>c</b>) LeNet and LSTM performance for correlation feature.</p>
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<p>ROC curves of different network models for each of the three input features, respectively, using #IPIX_10 with SCR of 12 dB: (<b>a</b>) ResNet18 and VGG16 performance for TF feature; (<b>b</b>) LeNet and LSTM performance for phase feature; (<b>c</b>) LeNet and LSTM performance for correlation feature.</p>
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<p>ROC curves of datasets in different sea states: (<b>a</b>) #IPIX_01 (HH, the fourth level sea state); (<b>b</b>) #IPIX_07 (HH, the third level sea state); (<b>c</b>) #IPIX_03 (HH, the second level sea state).</p>
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<p>False alarm loss curves of datasets in different sea states: (<b>a</b>) #IPIX_01 (HH, the fourth level sea state); (<b>b</b>) #IPIX_07 (HH, the third level sea state); (<b>c</b>) #IPIX_03 (HH, the second level sea state).</p>
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<p>Doppler shift of sea clutter of the ten IPIX datasets.</p>
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<p>Images of the #IPIX_01 dataset at the HH polarization: (<b>a</b>) the range-time intensity image; (<b>b</b>) the TF spectrum of the primary cell; (<b>c</b>) the TF spectrum of the clutter-only cell.</p>
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<p>Images of the #IPIX_03 dataset at the HH polarization: (<b>a</b>) the range-time intensity image; (<b>b</b>) the TF spectrum of the primary cell; (<b>c</b>) the TF spectrum of the clutter-only cell.</p>
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<p>Images of the #IPIX_10 dataset at the HH polarization: (<b>a</b>) the range-time intensity image; (<b>b</b>) the TF spectrum of the primary cell; (<b>c</b>) the TF spectrum of the clutter-only cell.</p>
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<p>Detection performance of different detectors in IPIX database in 1.024 s observation time: (<b>a</b>) HH; (<b>b</b>) HV; (<b>c</b>) VH; (<b>d</b>) VV.</p>
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<p>ROC curves of the proposed detector, the tri-feature detector [<a href="#B11-remotesensing-16-04662" class="html-bibr">11</a>], the TF-tri-feature detector [<a href="#B12-remotesensing-16-04662" class="html-bibr">12</a>], and the phase-feature detector [<a href="#B19-remotesensing-16-04662" class="html-bibr">19</a>] in 1.024 s observation time and different polarization modes: (<b>a</b>) HH; (<b>b</b>) HV; (<b>c</b>) VH; (<b>d</b>) VV.</p>
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22 pages, 1347 KiB  
Article
Semi-Empirical Approach to Evaluating Model Fit for Sea Clutter Returns: Focusing on Future Measurements in the Adriatic Sea
by Bojan Vondra
Entropy 2024, 26(12), 1069; https://doi.org/10.3390/e26121069 - 9 Dec 2024
Viewed by 286
Abstract
A method for evaluating Kullback–Leibler (KL) divergence and Squared Hellinger (SH) distance between empirical data and a model distribution is proposed. This method exclusively utilises the empirical Cumulative Distribution Function (CDF) of the data and the CDF of the model, avoiding data processing [...] Read more.
A method for evaluating Kullback–Leibler (KL) divergence and Squared Hellinger (SH) distance between empirical data and a model distribution is proposed. This method exclusively utilises the empirical Cumulative Distribution Function (CDF) of the data and the CDF of the model, avoiding data processing such as histogram binning. The proposed method converges almost surely, with the proof based on the use of exponentially distributed waiting times. An example demonstrates convergence of the KL divergence and SH distance to their true values when utilising the Generalised Pareto (GP) distribution as empirical data and the K distribution as the model. Another example illustrates the goodness of fit of these (GP and K-distribution) models to real sea clutter data from the widely used Intelligent PIxel processing X-band (IPIX) measurements. The proposed method can be applied to assess the goodness of fit of various models (not limited to GP or K distribution) to clutter measurement data such as those from the Adriatic Sea. Distinctive features of this small and immature sea, like the presence of over 1300 islands that affect local wind and wave patterns, are likely to result in an amplitude distribution of sea clutter returns that differs from predictions of models designed for oceans or open seas. However, to the author’s knowledge, no data on this specific topic are currently available in the open literature, and such measurements have yet to be conducted. Full article
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<p>Comparison of empirical and semi-empirical estimates of KL divergence. (<b>a</b>) Forward. (<b>b</b>) Reverse.</p>
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<p>Comparison of MSE of empirical and semi-empirical estimates of KL divergence. (<b>a</b>) Forward. (<b>b</b>) Reverse.</p>
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<p>Comparison of empirical and semi-empirical estimates. (<b>a</b>) SH distance estimation. (<b>b</b>) MSE of SH distance estimation.</p>
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<p>Comparison of empirical and semi-empirical estimates of KL divergence using GP distribution as model and real sea clutter data. (<b>a</b>) Forward. (<b>b</b>) Reverse.</p>
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<p>Comparison of empirical and semi-empirical estimates of KL divergence using K distribution as model and real sea clutter data. (<b>a</b>) Forward. (<b>b</b>) Reverse.</p>
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<p>Comparison of variances of empirical and semi-empirical estimates of KL divergence using GP and K distribution as models and real sea clutter data. (<b>a</b>) Forward. (<b>b</b>) Reverse.</p>
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<p>Comparison of empirical and semi-empirical estimates of SH distance using GP and K distribution as models and real sea clutter data. (<b>a</b>) K distribution. (<b>b</b>) GP distribution.</p>
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<p>Comparison of variances of empirical and semi-empirical estimates of SH distance using GP and K distributions as models and real sea clutter data.</p>
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<p>Semi-empirical estimation of KL divergence between an empirical dataset following a unit-mean exponential distribution, <math display="inline"><semantics> <mrow> <mi>Exp</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>, and a model distribution following a normal distribution, <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) Forward estimation. (<b>b</b>) Reverse estimation.</p>
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<p>MSE of the KL divergence estimation between an empirical dataset following a unit-mean exponential distribution, <math display="inline"><semantics> <mrow> <mi>Exp</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>, and a model distribution following a normal distribution, <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) Forward. (<b>b</b>) Reverse.</p>
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<p>Semi-empirical estimation of SH distance between empirical dataset of samples from normal distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math> and exponential model distribution <math display="inline"><semantics> <mrow> <mi>Exp</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) SH distance estimation. (<b>b</b>) MSE of SH distance estimation.</p>
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<p>Semi-empirical estimation of the KL divergence between two normal distributions, with the empirical dataset following <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and the model distribution following <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) Forward estimation. (<b>b</b>) Reverse estimation.</p>
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<p>MSE of KL divergence estimation between two normal distributions, empirical dataset following <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and model distribution following <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) Forward. (<b>b</b>) Reverse.</p>
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<p>Semi-empirical estimation of SH distance between empirical dataset of samples from normal distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and normal model distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) SH distance estimation. (<b>b</b>) MSE of SH distance estimation.</p>
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<p>Semi-empirical estimation of SH distance between empirical dataset of samples from normal distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and normal model distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) SH distance estimation. (<b>b</b>) MSE of SH distance estimation.</p>
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<p>Semi-empirical estimation of SH distance between empirical dataset of samples from normal distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and normal model distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) SH distance estimation. (<b>b</b>) MSE of SH distance estimation.</p>
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<p>Semi-empirical estimation of SH distance between empirical dataset of samples from normal distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math> and normal model distribution <math display="inline"><semantics> <mrow> <mi mathvariant="script">N</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) SH distance estimation. (<b>b</b>) MSE of SH distance estimation.</p>
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21 pages, 16950 KiB  
Article
Retrieval of Three-Dimensional Wave Surfaces from X-Band Marine Radar Images Utilizing Enhanced Pix2Pix Model
by Lingyi Hou, Xiao Wang, Bo Yang, Zhiyuan Wei, Yuwen Sun and Yuxiang Ma
J. Mar. Sci. Eng. 2024, 12(12), 2229; https://doi.org/10.3390/jmse12122229 - 5 Dec 2024
Viewed by 331
Abstract
In this study, we propose a novel method for retrieving the three-dimensional (3D) wave surface from sea clutter using both simulated and measured data. First, the linear wave superposition model and modulation principle are employed to generate simulated datasets comprising 3D wave surfaces [...] Read more.
In this study, we propose a novel method for retrieving the three-dimensional (3D) wave surface from sea clutter using both simulated and measured data. First, the linear wave superposition model and modulation principle are employed to generate simulated datasets comprising 3D wave surfaces and corresponding sea clutter. Subsequently, we develop a Pix2Pix model enhanced with a self-attention mechanism and a multiscale discriminator to effectively capture the nonlinear relationship between the simulated 3D wave surfaces and sea clutter. The model’s performance is evaluated through error analysis, comparisons of wave number spectra, and differences in wave surface reconstructions using a dedicated test set. Finally, the trained model is applied to reconstruct wave surfaces from sea clutter data collected aboard a ship, with results benchmarked against those derived from the Schrödinger equation. The findings demonstrate that the proposed model excels in preserving high-frequency image details while ensuring precise alignment between reconstructed images. Furthermore, it achieves superior retrieval accuracy compared to traditional approaches, highlighting its potential for advancing wave surface retrieval techniques. Full article
(This article belongs to the Section Physical Oceanography)
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<p>Linear superposition model of sea waves.</p>
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<p>Example of simulated wave surface.</p>
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<p>Schematic diagram of shadow modulation.</p>
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<p>Schematic diagram of tilt modulation.</p>
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<p>Example of sea clutter.</p>
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<p>Results of sensitivity analysis. (<b>a</b>) Sensitivity analysis of spatial resolution; (<b>b</b>) sensitivity analysis of time step.</p>
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<p>3D wave surface and sea clutter data pair. (<b>a</b>) 3D wave surface; (<b>b</b>) sea clutter.</p>
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<p>Overall model structure.</p>
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<p>Structure of generator.</p>
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<p>Structure of multiscale discriminator.</p>
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<p>Comparison of wave number spectrum. Original wave surface (<b>left</b>); retrieved wave surface (<b>right</b>). (<b>a</b>) Sea state level 3, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>0.73</mn> <mo> </mo> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>9.24</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>b</b>) Sea state level 4, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>1.26</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>,</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>9.45</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>c</b>) Sea state level 5, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>2.66</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>,</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>17.59</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>d</b>) Sea state level 6, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>4.14</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>,</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>12.4</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>Comparison of wave surface difference. Original wave surface (<b>left</b>); retrieved wave surface (<b>right</b>); wave surface difference (down). (<b>a</b>) Sea state level 3, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>0.73</mn> <mo> </mo> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>9.24</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>b</b>) Sea state level 4, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>1.26</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>,</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>9.45</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>c</b>) Sea state level 5, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>2.66</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>,</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>17.59</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>d</b>) Sea state level 6, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>4.14</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>,</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>12.4</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>Software interface (<b>left</b>), example of measured radar image (<b>right</b>).</p>
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<p>Image displayed by WinWaMoS (<b>left</b>) and reproduced by MATLAB (<b>right</b>).</p>
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<p>A sequence of measured radar images.</p>
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<p>Comparison of wave height and envelopes derived from the NLS equation. (<b>a</b>) Atten-Pix2pix; (<b>b</b>) Pix2pix; (<b>c</b>) CNNSA.</p>
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23 pages, 4780 KiB  
Article
Characteristic Description and Statistical Model-Based Method for Sea Clutter Modeling
by Huafeng He, Zhen Li, Xi Zhang, Jianguang Jia, Yaomin He and Yongquan You
Remote Sens. 2024, 16(23), 4429; https://doi.org/10.3390/rs16234429 - 26 Nov 2024
Viewed by 496
Abstract
The modeling and analysis of sea clutter are of great significance in radar target detection studies in marine environments. Sea clutter typically exhibits non-Gaussian characteristics and spatiotemporal correlations, posing challenges for modeling, especially when generating simulation data of continuous correlated non-Gaussian random processes. [...] Read more.
The modeling and analysis of sea clutter are of great significance in radar target detection studies in marine environments. Sea clutter typically exhibits non-Gaussian characteristics and spatiotemporal correlations, posing challenges for modeling, especially when generating simulation data of continuous correlated non-Gaussian random processes. This paper proposes a novel method for sea clutter modeling. First, feature description functions are constructed to individually characterize the amplitude, temporal, and spatial correlations of sea clutter, allowing for an accurate depiction of its characteristics with fewer parameters. Subsequently, simulation data are generated based on these feature description functions, satisfying the amplitude distribution, temporal correlation, and spatial correlation characteristics of sea clutter. Additionally, complex signal forms are introduced in the underlying signal processing to generate texture and speckle components of sea clutter, enhancing the alignment of simulation data with actual data. Through comparison with measured sea clutter data, the proposed method has been shown to accurately simulate complex sea clutter with real-world characteristics. Full article
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<p>Flowchart of the proposed method in this paper.</p>
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<p>Amplitude feature extraction.</p>
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<p>Temporal correlation feature extraction.</p>
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<p>Spatial correlation feature extraction.</p>
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<p>Characteristic functions of the generated speckle component.</p>
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<p>Amplitude distribution function of the generated texture component.</p>
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<p>The feature functions of the mid–short–range sea clutter data from the file “20210106155330_01_staring” generated by the proposed method.</p>
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<p>The feature functions of the long-range sea clutter data from the file “20210106155330_01_staring “ generated by the proposed method.</p>
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<p>Characteristic functions of the sea clutter data from the file “19980204_221104_ANTSTEP” generated by the proposed method.</p>
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<p>Characteristic functions of the sea clutter data from the file “19980204_220325_ANTSTEP” generated by the proposed method.</p>
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18 pages, 7440 KiB  
Article
A Novel Method for the Estimation of Sea Surface Wind Speed from SAR Imagery
by Zahra Jafari, Pradeep Bobby, Ebrahim Karami and Rocky Taylor
J. Mar. Sci. Eng. 2024, 12(10), 1881; https://doi.org/10.3390/jmse12101881 - 20 Oct 2024
Viewed by 849
Abstract
Wind is one of the important environmental factors influencing marine target detection as it is the source of sea clutter and also affects target motion and drift. The accurate estimation of wind speed is crucial for developing an efficient machine learning (ML) model [...] Read more.
Wind is one of the important environmental factors influencing marine target detection as it is the source of sea clutter and also affects target motion and drift. The accurate estimation of wind speed is crucial for developing an efficient machine learning (ML) model for target detection. For example, high wind speeds make it more likely to mistakenly detect clutter as a marine target. This paper presents a novel approach for the estimation of sea surface wind speed (SSWS) and direction utilizing satellite imagery through innovative ML algorithms. Unlike existing methods, our proposed technique does not require wind direction information and normalized radar cross-section (NRCS) values and therefore can be used for a wide range of satellite images when the initial calibrated data are not available. In the proposed method, we extract features from co-polarized (HH) and cross-polarized (HV) satellite images and then fuse advanced regression techniques with SSWS estimation. The comparison between the proposed model and three well-known C-band models (CMODs)—CMOD-IFR2, CMOD5N, and CMOD7—further indicates the superior performance of the proposed model. The proposed model achieved the lowest Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), with values of 0.97 m/s and 0.62 m/s for calibrated images, and 1.37 and 0.97 for uncalibrated images, respectively, on the RCM dataset. Full article
(This article belongs to the Special Issue Remote Sensing Applications in Marine Environmental Monitoring)
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<p>Distribution of wind direction and wind speed.</p>
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<p>NRCS vs. incidence angle for different wind speeds and directions using CMOD5N and CMOD7 functions.</p>
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<p>Scatter plots of real versus calculated wind speed using (<b>a</b>) CMOD5, (<b>b</b>) CMOD-IFR, and (<b>c</b>) CMOD7 models with HH polarization.</p>
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<p>Scatter plots of real versus calculated wind speed using (<b>a</b>) CMOD5, (<b>b</b>) CMOD-IFR, and (<b>c</b>) CMOD7 models after compensation for polarization.</p>
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<p>Distribution of intensities for HH and HV polarizations at high and low wind speeds.</p>
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<p>Block diagram of proposed system.</p>
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<p>Effect of despeckling filter on RCM image.</p>
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<p>Histogram of the introduced feature extracted from calibrated data, with orange representing low wind, green representing mid wind, and purple representing high wind.</p>
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<p>Histogram of the introduced feature extracted from uncalibrated data, with orange representing low wind, green representing mid wind, and purple representing high wind.</p>
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<p>Comparisons of retrieved SSWS using concatenated models with different features from the calibrated RCM dataset.</p>
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<p>Comparisons of retrieved SSWS using concatenated models with different features from the uncalibrated RCM dataset.</p>
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<p>The closest region, where both RCM data and buoy station data are available.</p>
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<p>ERA5 vs. buoy wind speeds for the south of Greenland across all seasons in 2023.</p>
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<p>Testing the proposed model in the south of Greenland using buoy wind speed data.</p>
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22 pages, 11121 KiB  
Article
Joint Prediction of Sea Clutter Amplitude Distribution Based on a One-Dimensional Convolutional Neural Network with Multi-Task Learning
by Longshuai Wang, Liwen Ma, Tao Wu, Jiaji Wu and Xiang Luo
Remote Sens. 2024, 16(20), 3891; https://doi.org/10.3390/rs16203891 - 19 Oct 2024
Viewed by 1000
Abstract
Accurate modeling of sea clutter amplitude distribution plays a crucial role in enhancing the performance of marine radar. Due to variations in radar system parameters and oceanic environmental factors, sea clutter amplitude distribution exhibits multiple distribution types. Focusing solely on a single type [...] Read more.
Accurate modeling of sea clutter amplitude distribution plays a crucial role in enhancing the performance of marine radar. Due to variations in radar system parameters and oceanic environmental factors, sea clutter amplitude distribution exhibits multiple distribution types. Focusing solely on a single type of amplitude prediction lacks the necessary flexibility in practical applications. Therefore, based on the measured X-band radar sea clutter data from Yantai, China in 2022, this paper proposes a multi-task one-dimensional convolutional neural network (MT1DCNN) and designs a dedicated input feature set for the joint prediction of the type and parameters of sea clutter amplitude distribution. The results indicate that the MT1DCNN model achieves an F1 score of 97.4% for classifying sea clutter amplitude distribution types under HH polarization and a root-mean-square error (RMSE) of 0.746 for amplitude distribution parameter prediction. Under VV polarization, the F1 score is 96.74% and the RMSE is 1.071. By learning the associations between sea clutter amplitude distribution types and parameters, the model’s predictions become more accurate and reliable, providing significant technical support for maritime target detection. Full article
(This article belongs to the Topic Radar Signal and Data Processing with Applications)
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<p>The architecture of MT1DCNN.</p>
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<p>The overall temporal characteristics of T1 and T2 pulses: (<b>a</b>) T1 pulse echo (dB). (<b>b</b>) T2 plus Echo (dB).</p>
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<p>The data distribution of shape parameters for K and Pareto distributions: (<b>a</b>) K distribution of sea clutter in HH polarimetric radar. (<b>b</b>) Pareto distribution of sea clutter in HH polarimetric radar. (<b>c</b>) K distribution of sea clutter in VV polarimetric radar. (<b>d</b>) Pareto distribution of sea clutter in VV polarimetric radar.</p>
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<p>The data distribution of shape parameters for K and Pareto distributions: (<b>a</b>) K distribution of sea clutter in HH polarimetric radar. (<b>b</b>) Pareto distribution of sea clutter in HH polarimetric radar. (<b>c</b>) K distribution of sea clutter in VV polarimetric radar. (<b>d</b>) Pareto distribution of sea clutter in VV polarimetric radar.</p>
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<p>Sea clutter amplitude distribution joint prediction results of the MT1DCNN model are presented as follows: for the classification task, outcomes are depicted via a confusion matrix heatmap, whereas the regression task results are illustrated using scatter density plots. (<b>a</b>) Amplitude distribution types of HH polarization. (<b>b</b>) Amplitude distribution types of VV polarization. (<b>c</b>) Shape parameter of HH polarization. (<b>d</b>) Shape parameter of VV polarization. (<b>e</b>) Scale parameter of HH polarization. (<b>f</b>) Scale parameter of VV polarization.</p>
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<p>Sea clutter amplitude distribution joint prediction results of the MT1DCNN model are presented as follows: for the classification task, outcomes are depicted via a confusion matrix heatmap, whereas the regression task results are illustrated using scatter density plots. (<b>a</b>) Amplitude distribution types of HH polarization. (<b>b</b>) Amplitude distribution types of VV polarization. (<b>c</b>) Shape parameter of HH polarization. (<b>d</b>) Shape parameter of VV polarization. (<b>e</b>) Scale parameter of HH polarization. (<b>f</b>) Scale parameter of VV polarization.</p>
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<p>TEIC comparison of two methods: MLE, and MT1DCNN based on MLE. (<b>a</b>) TEIC value comparison under HH polarization. (<b>b</b>) Boxplot of TEIC values under HH polarization. (<b>c</b>) TEIC value comparison under VV polarization. (<b>d</b>) Boxplot of TEIC values under VV polarization.</p>
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<p>TEIC comparison of two methods: MLE, and MT1DCNN based on MLE. (<b>a</b>) TEIC value comparison under HH polarization. (<b>b</b>) Boxplot of TEIC values under HH polarization. (<b>c</b>) TEIC value comparison under VV polarization. (<b>d</b>) Boxplot of TEIC values under VV polarization.</p>
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<p>Comparison of results for predicting the real sea clutter amplitude distribution using different parameter estimation methods: (<b>a</b>) Prediction results under HH polarization. (<b>b</b>) Prediction results under VV polarization.</p>
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<p>Comparison of training results of different models and epochs on the HH polarization sea clutter validation set: (<b>a</b>) F1 score. (<b>b</b>) Validation loss.</p>
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<p>Comparison of training results of different models and epochs on the VV polarization sea clutter validation set: (<b>a</b>) F1 score. (<b>b</b>) Validation loss.</p>
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25 pages, 10372 KiB  
Article
A Dynamic False Alarm Rate Control Method for Small Target Detection in Non-Stationary Sea Clutter
by Yunlong Dong, Jifeng Wei, Hao Ding, Ningbo Liu, Zheng Cao and Hengli Yu
J. Mar. Sci. Eng. 2024, 12(10), 1770; https://doi.org/10.3390/jmse12101770 - 5 Oct 2024
Viewed by 729
Abstract
Sea surface non-stationarity poses significant challenges to sea-surface small target detection, particularly in maintaining a stable false alarm rate (FAR). In dynamic maritime scenarios with non-stationary characteristics, the non-stationarity of sea clutter can easily cause significant changes in the clutter feature space, leading [...] Read more.
Sea surface non-stationarity poses significant challenges to sea-surface small target detection, particularly in maintaining a stable false alarm rate (FAR). In dynamic maritime scenarios with non-stationary characteristics, the non-stationarity of sea clutter can easily cause significant changes in the clutter feature space, leading to a notable deviation between the preset FAR and the measured FAR. By analyzing the temporal and spatial variations in sea clutter, we model the relationship between the preset FAR and the measured FAR as a two-parameter linear function. To address the impact of sea surface non-stationarity on FAR, the model parameters are estimated in real time within the environment and used to guide the dynamic adjustment of the decision region. We applied the proposed method to both convex hull and support vector machine (SVM) detectors and conducted experiments using measured X-band sea-detecting datasets. Experiments demonstrate that the proposed method effectively reduces the deviation between the measured mean FAR and the preset FAR. When the preset FAR is 10−2, the proposed method achieves an average FAR of 1.067 × 10−2 with the convex hull detector and 1.043 × 10−2 with the SVM detector. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Measured radar echoes. (<b>a</b>) Measured radar echoes in #1-HH dataset. (<b>b</b>) Measured radar echoes in #4-HH dataset.</p>
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<p>Schematic diagram of density estimation.</p>
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<p>The calculation of LFSD. (<b>a</b>) Convex hull after FAR control. (<b>b</b>) LFSD.</p>
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<p>The partitioning method for training region and testing region.</p>
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<p>The relationship between the position of false alarm points and LFSD.</p>
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<p>The relationship between the LFSD difference and FAR.</p>
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<p>Clutter feature spaces. The area circled in pink is where the density changes due to the influence of sea spikes, outside of the false alarm regions. (<b>a</b>) Clutter feature spaces with different range cells. (<b>b</b>) Clutter feature spaces with different periods.</p>
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<p>The LFSD difference of improved initial FAR control method and convex hull detector [<a href="#B13-jmse-12-01770" class="html-bibr">13</a>] on all 10 datasets.</p>
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<p>The FAR of improved initial FAR control method and convex hull detector [<a href="#B13-jmse-12-01770" class="html-bibr">13</a>] on all 10 datasets.</p>
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<p>Comparison of time consumption before and after revising the initial FAR control method, where left <span class="html-italic">Y</span>-axis represents the time cost of original method and right <span class="html-italic">Y</span>-axis represents the time cost of proposed method.</p>
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<p>The relationship between the preset FAR and the measured FAR over different time periods. The relationship between the preset FAR and the measured FAR in the green box area can be expressed using a linear function (<b>a</b>) #1-HH. (<b>b</b>) #4-HH.</p>
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<p>Fitting results of dataset #1-HH. The linear fit curve and the exponential fit curve almost overlap, so we have included the MSE of the three curves in the figure to highlight the differences.</p>
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<p>MSE of all 10 datasets.</p>
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<p>The optimal parameters for the all 10 datasets. (<b>a</b>) Quadratic function. (<b>b</b>) Linear function.</p>
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<p>Modification of the relationship between the preset FAR and the measured FAR.</p>
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<p>Feature detection procedure under dynamic FAR control.</p>
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<p>Visualization of false alarms on dataset #4-HH.</p>
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<p>Measured FAR results of proposed method based on convex hull and convex hull detector [<a href="#B13-jmse-12-01770" class="html-bibr">13</a>]. (<b>a</b>) #1-HH. (<b>b</b>) #5-HH.</p>
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<p>Original method [<a href="#B13-jmse-12-01770" class="html-bibr">13</a>] and proposed method performance based on convex hull.</p>
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<p>Original method [<a href="#B27-jmse-12-01770" class="html-bibr">27</a>] and proposed method performance based on SVM.</p>
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<p>Decision region and target feature density.</p>
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<p>The relationship between the number of decision region adjustments and the measured FAR.</p>
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<p>The relationship between the preset FAR and the measured FAR over different time periods on all 10 datasets. The relationship between the preset FAR and the measured FAR in the green box area can be expressed using a linear function (<b>a</b>) #1-HH. (<b>b</b>) #2-HH. (<b>c</b>) #3-HH. (<b>d</b>) #4-HH. (<b>e</b>) #5-HH. (<b>f</b>) #1-VV. (<b>g</b>) #2-VV. (<b>h</b>) #3-VV. (<b>i</b>) #4-VV. (<b>j</b>) #5-VV.</p>
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<p>The relationship between the preset FAR and the measured FAR over different time periods on all 10 datasets. The relationship between the preset FAR and the measured FAR in the green box area can be expressed using a linear function (<b>a</b>) #1-HH. (<b>b</b>) #2-HH. (<b>c</b>) #3-HH. (<b>d</b>) #4-HH. (<b>e</b>) #5-HH. (<b>f</b>) #1-VV. (<b>g</b>) #2-VV. (<b>h</b>) #3-VV. (<b>i</b>) #4-VV. (<b>j</b>) #5-VV.</p>
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27 pages, 5540 KiB  
Article
Marine Radar Constant False Alarm Rate Detection in Generalized Extreme Value Distribution Based on Space-Time Adaptive Filtering Clutter Statistical Analysis
by Baotian Wen, Zhizhong Lu and Bowen Zhou
Remote Sens. 2024, 16(19), 3691; https://doi.org/10.3390/rs16193691 - 3 Oct 2024
Viewed by 706
Abstract
The performance of marine radar constant false alarm rate (CFAR) detection method is significantly influenced by the modeling of sea clutter distribution and detector decision rules. The false alarm rate and detection rate are therefore unstable. In order to address low CFAR detection [...] Read more.
The performance of marine radar constant false alarm rate (CFAR) detection method is significantly influenced by the modeling of sea clutter distribution and detector decision rules. The false alarm rate and detection rate are therefore unstable. In order to address low CFAR detection performance and the modeling problem of non-uniform, non-Gaussian, and non-stationary sea clutter distribution in marine radar images, in this paper, a CFAR detection method in generalized extreme value distribution modeling based on marine radar space-time filtering background clutter is proposed. Initially, three-dimensional (3D) frequency wave-number (space-time) domain adaptive filter is employed to filter the original radar image, so as to obtain uniform and stable background clutter. Subsequently, generalized extreme value (GEV) distribution is introduced to integrally model the filtered background clutter. Finally, Inclusion/Exclusion (IE) with the best performance under the GEV distribution is selected as the clutter range profile CFAR (CRP-CFAR) detector decision rule in the final detection. The proposed method is verified by utilizing real marine radar image data. The results indicate that when the Pfa is set at 0.0001, the proposed method exhibits an average improvement in PD of 2.3% compared to STAF-RCBD-CFAR, and a 6.2% improvement compared to STCS-WL-CFAR. When the Pfa is set at 0.001, the proposed method exhibits an average improvement in PD of 6.9% compared to STAF-RCBD-CFAR, and a 9.6% improvement compared to STCS-WL-CFAR. Full article
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Graphical abstract

Graphical abstract
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<p>Interpolated original radar range-azimuth map: (<b>a</b>) The first set data (wave height 2.65 m). (<b>b</b>) The second set data (wave height 2.83 m). (<b>c</b>) The third set data (wave height 3.18 m).</p>
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<p>The background clutter statistical distribution in the original radar range-azimuth map: (<b>a</b>) PDF distribution for the whole area, near area, and far area under the three datasets. (<b>b</b>) CDF distribution for the whole area, near area, and far area under the three datasets.</p>
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<p>The processed radar range-azimuth map. (<b>a</b>) The first set data (wave height 2.65 m). (<b>b</b>) The second set data (wave height 2.83 m). (<b>c</b>) The third set data (wave height 3.18 m).</p>
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<p>The statistical background clutter distribution in the processed range-azimuth map: (<b>a</b>) PDF distribution for the whole area, near area, and far area under the three datasets. (<b>b</b>) CDF distribution for the whole area, near area, and far area under the three datasets.</p>
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<p>PDF and CDF plots: the processed data, estimated Weibull, K, Log-normal, KK, WW, Generalized Pareto, and Generalized Extreme Value distribution. (<b>a</b>,<b>b</b>) The first set data (wave height 2.65 m). (<b>c</b>,<b>d</b>) The second set data (wave height 2.83 m). (<b>e</b>,<b>f</b>) The third set data (wave height 3.18 m).</p>
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<p>The errors of PDF and CDF: estimated Weibull, K, Log-normal, KK, WW, Generalized Pareto, and Generalized Extreme Value. (<b>a</b>,<b>b</b>) The first set data (wave height 2.65 m). (<b>c</b>,<b>d</b>) The second set data (wave height 2.83 m). (<b>e</b>,<b>f</b>) The third set data (wave height 3.18 m).</p>
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<p>The errors of PDF and CDF: estimated Weibull, K, Log-normal, KK, WW, Generalized Pareto, and Generalized Extreme Value. (<b>a</b>,<b>b</b>) The first set data (wave height 2.65 m). (<b>c</b>,<b>d</b>) The second set data (wave height 2.83 m). (<b>e</b>,<b>f</b>) The third set data (wave height 3.18 m).</p>
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<p>Schematic diagram of CRP-CFAR detection principle.</p>
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<p>The extracted real moving target data: (<b>a</b>) The target in the 1st image of the sequence. (<b>b</b>) The target in the 15th image of the sequence. (<b>c</b>) The target in the 32nd image of the sequence.</p>
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<p>The detection results of seven detectors in first datasets: (<b>a</b>) Truth image. (<b>b</b>) OS-CFAR. (<b>c</b>) TMOS-CFAR. (<b>d</b>) GMOS-CFAR. (<b>e</b>) WH-CFAR. (<b>f</b>) WHOS-CFAR. (<b>g</b>) IE-CFAR. (<b>h</b>) LOGT-CFAR.</p>
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<p>The detection results of seven detectors in the second datasets: (<b>a</b>) Truth image. (<b>b</b>) OS-CFAR. (<b>c</b>) TMOS-CFAR. (<b>d</b>) GMOS-CFAR. (<b>e</b>) WH-CFAR. (<b>f</b>) WHOS-CFAR. (<b>g</b>) IE-CFAR. (<b>h</b>) LOGT-CFAR.</p>
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<p>The detection results of seven detectors in the third datasets: (<b>a</b>) Truth image. (<b>b</b>) OS-CFAR. (<b>c</b>) TMOS-CFAR. (<b>d</b>) GMOS-CFAR. (<b>e</b>) WH-CFAR. (<b>f</b>) WHOS-CFAR. (<b>g</b>) IE-CFAR. (<b>h</b>) LOGT-CFAR.</p>
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<p>The relation curve between PD and SCR of the seven detectors under the generalized extreme value distribution, <math display="inline"><semantics> <mrow> <mo form="prefix">Pfa</mo> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>. (<b>a</b>) The first set data. (<b>b</b>) The second set data. (<b>c</b>) The third set data. (<b>d</b>) 100 datasets average.</p>
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<p>Structure flow diagram of STAF-GEV-IE-CFAR.</p>
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<p>The detection results of five methods at <math display="inline"><semantics> <mrow> <mi>SCR</mi> <mo>=</mo> <mn>4</mn> <mspace width="3.33333pt"/> <mi>dB</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo form="prefix">Pfa</mo> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>: (<b>a</b>) STAF-GEV-IE-CFAR. (<b>b</b>) STCS-WL-CFAR. (<b>c</b>) EMD-CFAR. (<b>d</b>) STAF-RCBD-CFAR. (<b>e</b>) IE-CFAR. (<b>f</b>) KGLRTD.</p>
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<p>The detection results of five methods at <math display="inline"><semantics> <mrow> <mi>SCR</mi> <mo>=</mo> <mn>0</mn> <mspace width="3.33333pt"/> <mi>dB</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo form="prefix">Pfa</mo> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>: (<b>a</b>) STAF-GEV-IE-CFAR. (<b>b</b>) STCS-WL-CFAR. (<b>c</b>) EMD-CFAR. (<b>d</b>) STAF-RCBD-CFAR. (<b>e</b>) IE-CFAR. (<b>f</b>) KGLRTD.</p>
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<p>The detection results of five methods at <math display="inline"><semantics> <mrow> <mi>SCR</mi> <mo>=</mo> <mn>2</mn> <mspace width="3.33333pt"/> <mi>dB</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo form="prefix">Pfa</mo> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>: (<b>a</b>) STAF-GEV-IE-CFAR. (<b>b</b>) STCS-WL-CFAR. (<b>c</b>) EMD-CFAR. (<b>d</b>) STAF-RCBD-CFAR. (<b>e</b>) IE-CFAR. (<b>f</b>) KGLRTD.</p>
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<p>The detection results of five methods at <math display="inline"><semantics> <mrow> <mi>SCR</mi> <mo>=</mo> <mn>6</mn> <mspace width="3.33333pt"/> <mi>dB</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo form="prefix">Pfa</mo> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>: (<b>a</b>) STAF-GEV-IE-CFAR. (<b>b</b>) STCS-WL-CFAR. (<b>c</b>) EMD-CFAR. (<b>d</b>) STAF-RCBD-CFAR. (<b>e</b>) IE-CFAR. (<b>f</b>) KGLRTD.</p>
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<p>Comparison of ROC curves of different methods: (<b>a</b>) SCR = 2 dB. (<b>b</b>) SCR = 4 dB. (<b>c</b>) SCR = 6 dB.</p>
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<p>Comparison of detection performances of different methods: (<b>a</b>) Pfa = 0.0001. (<b>b</b>) Pfa = 0.001.</p>
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24 pages, 6042 KiB  
Article
A Methodology Based on Deep Learning for Contact Detection in Radar Images
by Rosa Gonzales Martínez, Valentín Moreno, Pedro Rotta Saavedra, César Chinguel Arrese and Anabel Fraga
Appl. Sci. 2024, 14(19), 8644; https://doi.org/10.3390/app14198644 - 25 Sep 2024
Viewed by 1326
Abstract
Ship detection, a crucial task, relies on the traditional CFAR (Constant False Alarm Rate) algorithm. However, this algorithm is not without its limitations. Noise and clutter in radar images introduce significant variability, hampering the detection of objects on the sea surface. The algorithm’s [...] Read more.
Ship detection, a crucial task, relies on the traditional CFAR (Constant False Alarm Rate) algorithm. However, this algorithm is not without its limitations. Noise and clutter in radar images introduce significant variability, hampering the detection of objects on the sea surface. The algorithm’s theoretically Constant False Alarm Rates are not upheld in practice, particularly when conditions change abruptly, such as with Beaufort wind strength. Moreover, the high computational cost of signal processing adversely affects the detection process’s efficiency. In previous work, a four-stage methodology was designed: The first preprocessing stage consisted of image enhancement by applying convolutions. Labeling and training were performed in the second stage using the Faster R-CNN architecture. In the third stage, model tuning was accomplished by adjusting the weight initialization and optimizer hyperparameters. Finally, object filtering was performed to retrieve only persistent objects. This work focuses on designing a specific methodology for ship detection in the Peruvian coast using commercial radar images. We introduce two key improvements: automatic cropping and a labeling interface. Using artificial intelligence techniques in automatic cropping leads to more precise edge extraction, improving the accuracy of object cropping. On the other hand, the developed labeling interface facilitates a comparative analysis of persistence in three consecutive rounds, significantly reducing the labeling times. These enhancements increase the labeling efficiency and enhance the learning of the detection model. A dataset consisting of 60 radar images is used for the experiments. Two classes of objects are considered, and cross-validation is applied in the training and validation models. The results yield a value of 0.0372 for the cost function, a recovery rate of 94.5%, and an accuracy rate of 95.1%, respectively. This work demonstrates that the proposed methodology can generate a high-performance model for contact detection in commercial radar images. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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<p>Detection system processes flow chart.</p>
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<p>Processes of plot extractor phase flow chart.</p>
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<p>Radar system architecture.</p>
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<p>Methodology flow chart.</p>
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<p>Preprocessing and enhancement phase flow chart.</p>
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<p>Radar image structure as matrix. Each column is an azimuth, and each row is the distance value given to all azimuths. Each index row starts with 0.</p>
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<p>Representation of a convolution in 1 dimension. * has been placed to represent the output value of the corresponding vector at that index, after convolution. Example: x1* is equal to the resulting convolution at the index where x1 was without *.</p>
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<p>Gaussian distribution with different standard deviations.</p>
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<p>(<b>Left</b>) Sperry Marine radar raw image. (<b>Right</b>) Resultant normalized image after the preprocessing and enhancement phase.</p>
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<p>Automatic cropping flow chart.</p>
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<p>Images of cutouts of objects.</p>
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<p>Object labeling interface. The red box above corresponds to a zoom section in the radar image, this zoom section is displayed at the bottom of the figure. The blue boxes at the bottom of the figure represent regions of the radar image where it is possible to find a plot. The red box at the bottom is used to frame a current plot. On the right hand side we visualise this plot framed with red and check with the previous and next lap whether at the same location, at these coordinates, the same plot exists as a persistence criterion.</p>
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<p>Training process flow chart.</p>
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<p>Criteria filtering phase flow chart.</p>
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<p>Predictions of marine vessels in the port of Callao, Perú using the Faster R-CNN model (100,000 epochs).</p>
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<p>Predictions in bounding boxes with the label and the confidence score.</p>
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<p>Confidencescores for both object classes “plot” and “no”.</p>
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18 pages, 21702 KiB  
Technical Note
Ship Wake Detection in a Single SAR Image via a Modified Low-Rank Constraint
by Yanan Guan, Huaping Xu, Wei Li and Chunsheng Li
Remote Sens. 2024, 16(18), 3487; https://doi.org/10.3390/rs16183487 - 20 Sep 2024
Viewed by 554
Abstract
Ship wake detection stands as a pivotal task in marine environment monitoring. The main challenge in ship wake detection is to improve detection accuracy and mitigate false alarms. To address this challenge, a novel procedure for ship wake detection in a single SAR [...] Read more.
Ship wake detection stands as a pivotal task in marine environment monitoring. The main challenge in ship wake detection is to improve detection accuracy and mitigate false alarms. To address this challenge, a novel procedure for ship wake detection in a single SAR image is proposed in this study. Initially, an entropy distance similarity criterion is designed to measure nonlocal image patch similarity. Based on the proposed criterion, a low-rank and sparse decomposition method is modified using nonlocal similar patch matrix construction to separate the sparse wake. Subsequently, a field-of-experts (FOE) model is introduced to generate a series of multi-view wake feature maps, which are fused to construct an enhanced feature map. The sparse wake is further enhanced in the Radon domain with the enhanced feature map. The experimental results demonstrate the effectiveness of the proposed method on real SAR ship wake images. Full article
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<p>The outline of the proposed wake detection framework.</p>
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<p>A schematic diagram of the construction of an NPM. The purple boxes in the grayscale SAR image on the left are similar image patches. The <span class="html-italic">n</span> most similar patches are shown in the middle; the little square on the right represents the visual pixel intensity.</p>
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<p>An illustration of generated feature maps and an SAR image.</p>
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<p>Comparison of the low-rank properties between an enhanced feature map and an SAR image.</p>
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<p>Experimental SAR image samples from different SAR satellites. (<b>a</b>–<b>c</b>) the GF-3 SAR images; (<b>d</b>) the SAR image sample from Iceye satellite; (<b>e</b>) SAR image sample from HRSID dataset.</p>
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<p>The decomposition and enhanced feature map results for <a href="#remotesensing-16-03487-f005" class="html-fig">Figure 5</a>a. From left to right: (<b>a</b>) the low-rank component; (<b>b</b>) the sparse wake; and (<b>c</b>) the enhanced feature map, respectively.</p>
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<p>The Radon output and its clustering center point distribution. (<b>a</b>) The Radon outcome for the sparse wake; (<b>b</b>) center point distribution of (<b>a</b>); (<b>c</b>) Radon outcome for the enhanced feature map; (<b>d</b>) center point distribution of (<b>c</b>); (<b>e</b>) the extracted potential wake peak point.</p>
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<p>Comparison of the results of ship wake detection in sample images in <a href="#remotesensing-16-03487-f005" class="html-fig">Figure 5</a>a with different methods. (<b>a</b>) Proposed method; (<b>b</b>) LRSD; (<b>c</b>) GMC; (<b>d</b>) wavelet-based method; (<b>e</b>) fast Radon method.</p>
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<p>Comparison of the results of ship wake detection in sample images in <a href="#remotesensing-16-03487-f005" class="html-fig">Figure 5</a>b with different methods. (<b>a</b>) Proposed method; (<b>b</b>) LRSD; (<b>c</b>) GMC; (<b>d</b>) wavelet-based method; (<b>e</b>) fast Radon method.</p>
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<p>Comparison of the results of ship wake detection in sample images in <a href="#remotesensing-16-03487-f005" class="html-fig">Figure 5</a>c with different methods. (<b>a</b>) Proposed method; (<b>b</b>) LRSD; (<b>c</b>) GMC; (<b>d</b>) wavelet-based method; (<b>e</b>) fast Radon method.</p>
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<p>Comparison of the results of ship wake detection in sample images in <a href="#remotesensing-16-03487-f005" class="html-fig">Figure 5</a>d with different methods. (<b>a</b>) Proposed method; (<b>b</b>) LRSD; (<b>c</b>) GMC; (<b>d</b>) wavelet-based method; (<b>e</b>) fast Radon method.</p>
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<p>Comparison of the results of ship wake detection in sample images in <a href="#remotesensing-16-03487-f005" class="html-fig">Figure 5</a>e by using different methods. (<b>a</b>) Proposed method; (<b>b</b>) LRSD; (<b>c</b>) GMC; (<b>d</b>) wavelet-based method; (<b>e</b>) fast Radon method.</p>
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35 pages, 5645 KiB  
Article
High-Resolution Sea Surface Target Detection Using Bi-Frequency High-Frequency Surface Wave Radar
by Dragan Golubović, Miljko Erić, Nenad Vukmirović and Vladimir Orlić
Remote Sens. 2024, 16(18), 3476; https://doi.org/10.3390/rs16183476 - 19 Sep 2024
Viewed by 1158
Abstract
The monitoring of the sea surface, whether it is the state of the sea or the position of targets (ships), is an up-to-date research topic. In order to determine localization parameters of ships, we propose a high-resolution algorithm for primary signal processing in [...] Read more.
The monitoring of the sea surface, whether it is the state of the sea or the position of targets (ships), is an up-to-date research topic. In order to determine localization parameters of ships, we propose a high-resolution algorithm for primary signal processing in high-frequency surface wave radar (HFSWR) which operates at two frequencies. The proposed algorithm is based on a high-resolution estimate of the range–Doppler (RD-HR) map formed at every antenna in the receive antenna array, which is an essential task, because the performance of the entire radar system depends on its estimation. We also propose a new focusing method allowing us to have only one RD-HR map in the detection process, which collects the information from both these carrier frequencies. The goal of the bi-frequency mode of operation is to improve the detectability of targets, because their signals are affected by different Bragg-line interference patterns at different frequencies, as seen on the RD-HR maps during the primary signal processing. Also, the effect of the sea (sea clutter) manifests itself in different ways at different frequencies. Some targets are masked (undetectable) at one frequency, but they become visible at another frequency. By exploiting this, we increase the probability of detection. The bi-frequency architecture (system model) for the localization of sea targets and the novel signal model are presented in this paper. The advantage of bi-frequency mode served as a motivation for testing the detectability of small boats, which is otherwise a very challenging task, primarily because such targets have a small radar reflective surface, they move quickly, and often change their direction. Based on experimentally obtained results, it can be observed that the probability of detection of small boats can also be significantly improved by using a bi-frequency architecture. Full article
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<p>A monostatic system model of the HFSWR which operates at two frequencies.</p>
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<p>Practical implementation of used antenna arrays: (<b>a</b>) The layout of the linear Rx antenna subarray in the planar array (<b>b</b>) and the appearance of the Tx antenna array.</p>
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<p>The planar Rx antenna array geometry in the xy plane consisting of two linear subarrays.</p>
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<p>Chirp signals (solid blue line) at the Tx side and chirp signal at the Rx side (dashed red line).</p>
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<p>The concept of chirp signal generation at the Tx side for a bi-frequency system.</p>
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<p>The model of Rx antenna array used in the bi-frequency system.</p>
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<p>The appearance of the real and imaginary components of the received signal on all antennas for a successfully synchronized bi-frequency system.</p>
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<p>Block diagram of high-resolution primary signal processing in bi-frequency HFSWR.</p>
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<p>An example of the appearance of a high-resolution RD map at 9.2 MHz.</p>
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<p>The comparison of existing signal processing methods and the proposed method for systems that operate at two frequencies.</p>
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<p>The method for the focusing of RD maps in bi-frequency HFSWRs.</p>
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<p>An example of focusing one normalized frequency on the corresponding axis.</p>
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<p>Comparative display of axes with normalized frequencies in the case when <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>The result of target detection procedure in bi-frequency HFSWR (detections are denoted by “+” markers, and blue peaks represent the criterion function of the MUSIC-based algorithm).</p>
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<p>Azimuth estimation of an arbitrarily chosen target from the RD-HR map.</p>
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<p>(<b>a</b>) The appearance of the averaged RD-HR map for frequencies 4.6 MHz (<b>b</b>) and then for 9.2 MHz adjusted to the frequency 4.6 MHz, (<b>c</b>) as well as the appearance of the focused HR-HR map.</p>
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<p>Averaged number of detections per one integration period obtained by high-resolution bi-frequency algorithm using different values of algorithm parameters.</p>
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<p>Cumulative display of detections for the frequency 4.6 MHz and selected 10 ships (green contours).</p>
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<p>Cumulative display of detections for the frequency 9.2 MHz and selected 10 ships (green contours).</p>
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<p>Cumulative display of detections for the bi-frequency mode of operation and selected 10 ships (green contours).</p>
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<p>The number of detections for each of the ships in the bi-frequency mode of operation (8 + 8 antennas).</p>
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<p>(<b>a</b>) The boat used for testing (<b>b</b>) and its trajectory.</p>
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<p>(<b>a</b>) Filtered boat detections according to the spatial criterion (<b>b</b>) and the fitted curve between the obtained detections.</p>
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<p>The number of small boat detections for different high-resolution algorithm parameters in the bi-frequency mode of operation.</p>
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<p>Small boat probability of detection for different high-resolution algorithm parameters in the bi-frequency mode of operation.</p>
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11 pages, 4274 KiB  
Brief Report
Spectral Detection of a Weak Frequency Band Signal Based on the Pre-Whitening Scale Transformation of Stochastic Resonance in a Symmetric Bistable System in a Parallel Configuration
by Zhijun Qin, Tengfei Xie, Chen Xie and Di He
Electronics 2024, 13(18), 3637; https://doi.org/10.3390/electronics13183637 - 12 Sep 2024
Viewed by 456
Abstract
The spectral detection of weak frequency band signals poses a serious problem in many applications, especially when the target is within a certain frequency band under low signal-to-noise ratio (SNR) conditions. A kind of novel technique based on the pre-whitening scale transformation of [...] Read more.
The spectral detection of weak frequency band signals poses a serious problem in many applications, especially when the target is within a certain frequency band under low signal-to-noise ratio (SNR) conditions. A kind of novel technique based on the pre-whitening scale transformation of stochastic resonance (SR) in a symmetric bistable system in a parallel configuration is proposed to solve the problem. Firstly, pre-whitening can ensure the Gaussian distribution of the receiving signal fits the requirements for SR processing. Secondly, scale transformation can help to effectively utilize the properties of a weak signal, especially under a low-frequency band. Thirdly, the SR in a symmetric bistable system in a parallel configuration can try to smoothly reduce the variances in the clutter and additive noise. Fourthly, by subtracting the steady state response of the SR in the selected symmetric bistable system from the parallel output, the spectral detection of a weak signal can be realized successfully. Experiment results based on actual sea clutter radar data guarantee the effectiveness and applicability of the proposed symmetric bistable PSR processing approach. Full article
(This article belongs to the Special Issue Nonlinear Circuits and Systems: Latest Advances and Prospects)
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<p>Block diagram of the proposed approach.</p>
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<p>SR processing structure in a symmetric bistable system in a parallel configuration.</p>
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<p>Spectra of the weak frequency band signal under SNR = −15 dB.</p>
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<p>Spectra of the weak frequency band signal under SNR = −15 dB.</p>
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<p>Spectra of the weak frequency band signal under SNR = 0 dB before and after performing the proposed processing method.</p>
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<p>Spectra of the weak frequency band signal under SNR = −5 dB before and after performing the proposed processing method.</p>
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<p>Spectra of the weak frequency band signal under SNR = −10 dB before and after performing the proposed processing method.</p>
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<p>Spectra of the weak frequency band signal under SNR = −10 dB before and after performing the proposed processing method.</p>
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<p>ROC performance comparison results under SNR = −15 dB.</p>
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<p>ROC performance comparison results under SNR = −15 dB with a low P<sub>fa</sub>.</p>
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19 pages, 5790 KiB  
Article
Self-Supervised Marine Noise Learning with Sparse Autoencoder Network for Generative Target Magnetic Anomaly Detection
by Shigang Wang, Xiangyuan Zhang, Yifan Zhao, Haozi Yu and Bin Li
Remote Sens. 2024, 16(17), 3263; https://doi.org/10.3390/rs16173263 - 3 Sep 2024
Viewed by 722
Abstract
As an effective physical field feature to perceive ferromagnetic targets, magnetic anomaly is widely used in covert marine surveillance tasks. However, its practical usability is affected by the complex marine magnetic noise interference, making robust magnetic anomaly detection (MAD) quite a challenging task. [...] Read more.
As an effective physical field feature to perceive ferromagnetic targets, magnetic anomaly is widely used in covert marine surveillance tasks. However, its practical usability is affected by the complex marine magnetic noise interference, making robust magnetic anomaly detection (MAD) quite a challenging task. Recently, learning-based detectors have been widely studied for the discrimination of magnetic anomaly signal and achieve superior performance than traditional rule-based detectors. Nevertheless, learning-based detectors require abundant data for model parameter training, which are difficult to access in practical marine applications. In practice, target magnetic anomaly data are usually expensive to acquire, while rich marine magnetic noise data are readily available. Thus, there is an urgent need to develop effective models to learn discriminative features from the abundant marine magnetic noise data for newly appearing target anomaly detection. Motivated by this, in this paper we formulate MAD as a single-edge detection problem and develop a self-supervised marine noise learning approach for target anomaly classification. Specifically, a sparse autoencoder network is designed to model the marine noise and restore basis geomagnetic field from the collected noisy magnetic data. Subsequently, reconstruction error of the network is used as a statistical decision criterion to discriminate target magnetic anomaly from cluttered noise. Finally, we verify the effectiveness of the proposed approach on real sea trial data and compare it with seven state-of-the-art MAD methods on four numerical indexes. Experimental results indicate that it achieves a detection accuracy of 93.61% and has a running time of 21.06 s on the test dataset, showing superior MAD performance over its counterparts. Full article
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<p>Overall implementation process of the proposed marine target magnetic anomaly detection scheme. The different colored boxes in the data represent sample points with different magnetic intensities.</p>
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<p>Illustration of the magnetic fields measured by an underwater stationary sensor platform in the presence of a ferromagnetic target.</p>
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<p>General network structure of the designed sparse denoising autoencoder for marine magnetic noise learning.</p>
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<p>Illustration of the output waveforms of various layers in the designed network on a typical marine magnetic noise sequence.</p>
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<p>Loss curves of the designed network model on the training and validation datasets.</p>
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<p>Illustration of the experimental scenario for real sea trials. A fluxgate sensor is carried on the underwater watertight platform for transboundary detection of surface ship magnetic anomaly.</p>
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<p>Typical target samples with different SNRs collected by the underwater platform during the voyage experiments. (<b>a</b>,<b>b</b>) are two real target samples collected under different conditions.</p>
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<p>Denoising reconstruction results of the trained SDAE network on the validation dataset. (<b>a</b>) and (<b>b</b>) are, respectively, the marine magnetic data collected by the underwater fluxgate sensor platform.</p>
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<p>Denoising reconstruction results of the trained SDAE network for target samples on the test dataset. (<b>a</b>) and (<b>b</b>) are, respectively, the target magnetic data collected by the underwater fluxgate sensor platform.</p>
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<p>Projection result of OBF for a noisy target sample in the energy domain. (<b>a</b>) is the noisy target sample data to be detected and (<b>b</b>) is its energy function result obtained by OBF.</p>
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<p>Projection result of MED for a pure noise sample in the entropy domain. (<b>a</b>,<b>b</b>) are, respectively, the pure noise sample and its projection result in the entropy domain.</p>
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<p>Output channel features of the encoder networks on a marine magnetic noise sample. (<b>a</b>) and (<b>b</b>) are, respectively, the results of DAE and SDAE networks.</p>
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<p>Spectrum diagrams of the typical target samples in <a href="#remotesensing-16-03263-f007" class="html-fig">Figure 7</a>. (<b>a</b>) and (<b>b</b>) are respectively the spectrum diagrams of the two real target samples.</p>
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<p>Low-pass filtered results of the typical target samples in <a href="#remotesensing-16-03263-f007" class="html-fig">Figure 7</a>. (<b>a</b>) and (<b>b</b>) are respectively the low-pass filtered results of the two real target samples.</p>
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<p>Composited noisy target magnetic data under 4 different SNR values. (<b>a</b>) is a typical simulated target anomaly signal, (<b>b</b>) is a real marine magnetic noise, and from (<b>c</b>–<b>f</b>) are their composited noisy target magnetic data with SNRs being, respectively, 5 dB, 0 dB, −5 dB, and −10 dB.</p>
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<p>Probability of detection indexes of the various detectors under different SNRs.</p>
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18 pages, 6860 KiB  
Article
Weak Target Detection Based on Full-Polarization Scattering Features under Sea Clutter Background
by Yifei Fan, Duo Chen, Shichao Chen, Jia Su, Mingliang Tao, Zixun Guo and Ling Wang
Remote Sens. 2024, 16(16), 2987; https://doi.org/10.3390/rs16162987 - 14 Aug 2024
Cited by 2 | Viewed by 786
Abstract
Aiming at the low observable target detection under sea clutter backgrounds, this paper emphasizes the exploration of distinguishable full-polarization features between target and sea clutter echoes. To overcome the shortcomings of the existing polarization feature-based methods, the full-polarization features of sea clutter are [...] Read more.
Aiming at the low observable target detection under sea clutter backgrounds, this paper emphasizes the exploration of distinguishable full-polarization features between target and sea clutter echoes. To overcome the shortcomings of the existing polarization feature-based methods, the full-polarization features of sea clutter are modeled and analyzed in detail by using Van Zyl polarization decomposition. Then, three polarimetric features (the relative surface scattering energy, the relative dihedral scattering energy and the relative diffuse scattering energy) are extracted from the fully polarimetric radar sea clutter echoes, which improve the feature differences between sea clutter and targets. And a tri-polarimetric feature detector with constant false alarm rate (CFAR) is constructed based on the fast convex hull learning algorithm. The experimental results on the real measured IPIX radar datasets prove that the proposed full-polarization feature detector obtains more competitive detection performance and lower computational complexity than the several existing feature-based detectors. Full article
(This article belongs to the Special Issue Technical Developments in Radar—Processing and Application)
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<p>Flowchart of the proposed feature-based detector.</p>
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<p>The range-time-intensity image of the sea clutter datasets. (<b>a</b>) #26 HH polarization. (<b>b</b>) #26 HV polarization. (<b>c</b>) #26 VH polarization. (<b>d</b>) #26 VV polarization.</p>
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<p>The average SCRs of ten sets of datasets.</p>
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<p>Polarization feature distributions of sea clutter range bins and target range bins (<math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>512</mn> </mrow> </semantics></math>). (<b>a</b>) Prs distribution of sea clutter range bins. (<b>b</b>) Prs distribution of target range bins. (<b>c</b>) Prd distribution of sea clutter range bins. (<b>d</b>) Prd distribution of target range bins. (<b>e</b>) Prf distribution of sea clutter range bins. (<b>f</b>) Prf distribution of target range bins.</p>
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<p>Polarization feature distributions of sea clutter range bins and target range bins (<math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>512</mn> </mrow> </semantics></math>). (<b>a</b>) Prs distribution of sea clutter range bins. (<b>b</b>) Prs distribution of target range bins. (<b>c</b>) Prd distribution of sea clutter range bins. (<b>d</b>) Prd distribution of target range bins. (<b>e</b>) Prf distribution of sea clutter range bins. (<b>f</b>) Prf distribution of target range bins.</p>
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<p>Polarization feature distributions of sea clutter range bins and target range bins (<math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>2048</mn> </mrow> </semantics></math>). (<b>a</b>) Prs distribution of sea clutter range bins. (<b>b</b>) Prs distribution of target range bins. (<b>c</b>) Prd distribution of sea clutter range bins. (<b>d</b>) Prd distribution of target range bins. (<b>e</b>) Prf distribution of sea clutter range bins. (<b>f</b>) Prf distribution of target range bins.</p>
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<p>Polarization feature distributions of sea clutter range bins and target range bins (<math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>2048</mn> </mrow> </semantics></math>). (<b>a</b>) Prs distribution of sea clutter range bins. (<b>b</b>) Prs distribution of target range bins. (<b>c</b>) Prd distribution of sea clutter range bins. (<b>d</b>) Prd distribution of target range bins. (<b>e</b>) Prf distribution of sea clutter range bins. (<b>f</b>) Prf distribution of target range bins.</p>
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<p>Polarization feature distributions of sea clutter range bins and target range bins (<math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>4096</mn> </mrow> </semantics></math>). (<b>a</b>) Prs distribution of sea clutter range bins. (<b>b</b>) Prs distribution of target range bins. (<b>c</b>) Prd distribution of sea clutter range bins. (<b>d</b>) Prd distribution of target range bins. (<b>e</b>) Prf distribution of sea clutter range bins. (<b>f</b>) Prf distribution of target range bins.</p>
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<p>Distributions of feature points of target bins and pure clutter in 3-D space when the length of subsequence L is set as (<b>a</b>) L = 512, (<b>b</b>) L = 1024, (<b>c</b>) L = 2048, (<b>d</b>) L = 4096.</p>
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<p>The decision convex hull with a false alarm of 1‰. (<b>a</b>) Distributions of clutter feature points in 3-D space, (<b>b</b>) decision convex hull constructed by clutter feature points.</p>
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<p>Detection probabilities of the proposed detector, tri-polarization feature detector [<a href="#B32-remotesensing-16-02987" class="html-bibr">32</a>] and DBEA detector [<a href="#B31-remotesensing-16-02987" class="html-bibr">31</a>] for ten datasets when the length of subsequence <math display="inline"><semantics> <mi>L</mi> </semantics></math> is set as (<b>a</b>) 512, (<b>b</b>) 1024, (<b>c</b>) 2048 and (<b>d</b>) 4096.</p>
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<p>Detection probabilities of the proposed detector, tri-polarization feature detector [<a href="#B32-remotesensing-16-02987" class="html-bibr">32</a>] and DBEA detector [<a href="#B31-remotesensing-16-02987" class="html-bibr">31</a>] for ten datasets when the length of subsequence <math display="inline"><semantics> <mi>L</mi> </semantics></math> is set as (<b>a</b>) 512, (<b>b</b>) 1024, (<b>c</b>) 2048 and (<b>d</b>) 4096.</p>
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<p>Comparison average ROC curves. (<b>a</b>) The proposed detector and classical polarization detector, (<b>b</b>) the proposed detector and joint-fractal detector, (<b>c</b>) the proposed detector and tri-feature detector, (<b>d</b>) the proposed detector and graph connectivity detector.</p>
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<p>Comparison average ROC curves. (<b>a</b>) The proposed detector and classical polarization detector, (<b>b</b>) the proposed detector and joint-fractal detector, (<b>c</b>) the proposed detector and tri-feature detector, (<b>d</b>) the proposed detector and graph connectivity detector.</p>
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22 pages, 4522 KiB  
Article
Compound-Gaussian Clutter Model with Weibull-Distributed Textures and Parameter Estimation
by Pengjia Zou, Siyuan Chang and Penglang Shui
Remote Sens. 2024, 16(16), 2912; https://doi.org/10.3390/rs16162912 - 9 Aug 2024
Viewed by 867
Abstract
Compound-Gaussian models (CGMs) are widely used to characterize sea clutter. Various types of texture distributions have been developed so that the CGMs can cover sea clutter in different conditions. In this paper, the Weibull distributions are used to model textures of sea clutter, [...] Read more.
Compound-Gaussian models (CGMs) are widely used to characterize sea clutter. Various types of texture distributions have been developed so that the CGMs can cover sea clutter in different conditions. In this paper, the Weibull distributions are used to model textures of sea clutter, and the CGM with Weibull-distributed textures is used to derive the CGWB distributions, a new type of biparametric distribution. Like the classic K-distributions and Compound-Gaussian with lognormal texture (CGLN) distributions, the biparametric CGWB distributions without analytical expressions can be represented by the closed-form improper integral. Further, the properties of the CGWB distributions are investigated, and four moment-based estimators using sample moments, fractional-order sample moments, and generalized sample moments are given to estimate the parameters of the CGWB distributions. Their performance is compared by simulated clutter data. Moreover, measured sea clutter data are used to examine the suitability of the CGWB distributions. The results show that the CGWB distributions can provide the best goodness-of-the-fit for low-resolution sea clutter data as alternatives to the classic K-distributions. Full article
(This article belongs to the Special Issue Technical Developments in Radar—Processing and Application)
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<p>Comparison of the CGWB distributions and Weibull distributions. (<b>a</b>) Bodies of the PDFs. (<b>b</b>) Tails of the PDFs.</p>
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<p>Numerical characteristics of the amplitude <span class="html-italic">z</span> of CGWB-distributed clutter when <span class="html-italic">η</span> alters; (<b>a</b>) mean; (<b>b</b>) variance; (<b>c</b>) CV; (<b>d</b>) Skew; and (<b>e</b>) Kurt.</p>
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<p>KSD and KLD between the CGWB distribution and the Rayleigh distribution; (<b>a</b>) KSD; and (<b>b</b>) KLD.</p>
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<p>RRMSE of the shape parameter and average KLD of four estimators of CGWB distribution with varying sample sizes when <span class="html-italic">η</span> = 0.5 (<b>a</b>,<b>b</b>), and <span class="html-italic">η</span> = 2 (<b>c</b>,<b>d</b>).</p>
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<p>RRMSEs (<b>a</b>) and average KLD (<b>b</b>) of the four estimators on the shape parameter when it varies from 0.1 to 10.</p>
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<p>(<b>a</b>) Amplitude map and CMC division of the low-resolution sea clutter data from a shore-based C-band radar; (<b>b</b>) data after abnormal spatial resolution cells are removed.</p>
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<p>Fitting results of the sixth and eighth CMCs for the six types of distributions. (<b>a</b>) Fitting comparison on the sixth CMC; (<b>b</b>) fitting comparison on the eighth CMC; (<b>c</b>) parameter estimation comparison of the CGWB distributions on the sixth CMC; and (<b>d</b>) parameter estimation comparison of the CGWB distributions on the eigth CMC.</p>
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<p>(<b>a</b>) Fitting results of the 23rd CMC for the six types of distributions; (<b>b</b>) parameter estimation comparison of the CGWB distributions on the 23rd CMC in data after removing abnormal spatial resolution cells; (<b>c</b>) parameter estimation comparison of the CGWB distributions on the 23rd CMC in data without removing outliers.</p>
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<p>(<b>a</b>) Amplitude map of the original sea clutter data of the dataset TFC15_014; (<b>b</b>) Amplitude map of the low-resolution sea clutter data after the range resolution conversion.</p>
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<p>Fitting results of the low-resolution data generated from the dataset TFC15_014. (<b>a</b>) Fitting comparison of the six types of distributions; (<b>b</b>) parameter estimation comparison of the CGWB distributions.</p>
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