esa-sceva/satcom-chunk-collection huggingface dataset:
# Active Data Selection and Information Seeking
## 4 Function Approximation  
We next turn to a generic supervised learning problem--that of trying to approximate some function based upon known inputs and the observable outcomes they (stochastically) cause. Our generative model for this is straightforward:  
\[ \begin{array}{cc}P(y,\theta|\pi)=P(y|\theta,\pi)P(\theta)\\ P(\theta)=\mathcal{N}(\eta_{\theta},\Sigma_{\theta})\\ P(y|\theta,\pi)=\mathcal{N}\big{(}\phi_{\pi}\theta,\Sigma_{y}\big{)}\end{array}  \quad\Phi= \begin{bmatrix}\phi_{1}\\ \phi_{2}\\ \phi_{3}\\ \vdots\end{bmatrix}  \tag{7}\]  
The matrix (\(\Phi\)) comprises a set of concatenated row vectors (\(\phi_{i}\)). The columns of \(\Phi\) are elements of some basis set. For the simulations that follow, these are Gaussian radial basis functions. In the MATLAB demo routines that accompany this paper, alternative basis sets (including cosine and polynomial) can be chosen. We can see this model as an approximation of an unknown function whose (discretised) input is the row index of \(\Phi\) and whose output is the expected value of \(y\) corresponding to that row:  
\[\mathbb{E}[y|\theta,\pi]=\sum\
olimits_{i}\theta_{i}\Phi_{\pi,i}\triangleq \sum\
olimits_{i}\theta_{i}\Phi_{i}(x=\pi)=f_{\theta}(x=\pi) \tag{8}\]  
Our choice of \(\pi\) is used to test alternative values of the input (\(x\)) to see the output (\(y\)) that the unknown function (\(f\)) generates. Here, \(\pi\) indexes the discrete intervals of \(x\) implicit in the columns of \(\Phi\). Figure 3 illustrates a depiction of this model as a Bayesian network and a visual representation of the data-generating process. In this simulation, we move beyond our worked example in Figure 2 and consider multiple samples. In this setting, we replace our prior beliefs after each observation with our posterior beliefs, allowing a gradual refinement of our approximated function and the future choices on which this depends. The posterior probability of the parameters following an input and the marginal probability of the data are:  
\[ \begin{array}{cc}P(\theta|\pi,y)&=\mathcal{N}\Big{(}\gamma_{\pi}(\Sigma_{ \theta}^{-1}\eta_{\theta}+\phi_{\pi}^{T}\Sigma_{y}^{-1}y),\gamma_{\pi}\Big{)} \\ P(y|\pi)&=\mathcal{N}\big{(}\phi_{\pi}\eta_{\theta},\phi_{\pi}\Sigma_{\theta} \phi_{\pi}^{T}+\Sigma_{y}\big{)}\\ \gamma_{\pi}&\triangleq(\phi_{\pi}^{T}\Sigma_{y}^{-1}\phi_{\pi}+\Sigma_{\theta }^{-1})^{-1}\end{array}  \tag{9}\]  
The middle-right panel of Figure 3 shows the predictive (marginal) probability distribution after 28 random choices for \(\pi\). The lower-left panel shows the posterior probabilities of the parameters. The specific choices are shown in the lower-right panel. Even with these random choices, the 28 samples provide a reasonably good approximation to the shape of the function, as can be seen comparing the middle-left (large number of samples drawn from the function) and right panels. However, a closer look at the choices made reveals some clear inefficiencies. For instance, choices 2 and 4 and choices 6 and 7 are very close to
## 6 Conclusions  
The MTF of images is a significant index to evaluate the performance of remote-sensing cameras. However, calculating the MTF for image motion is usually difficult when the form of the image motion is complicated. In this paper, we propose a new approach to calculate the MTF for the mixed image motion of multiple forms of motion. By replacing the integral of the trigonometric functions with the summation of infinitely many terms involving the Bessel function, dynamic MTFs for the complex motion of linear motion and sinusoidal motion is expressed as an infinite sum of the integral order Bessel functions of the first kind. In order to obtain the numerical results of the MTF, the truncation  
Figure 12: The MTFs with different frequencies, measured by the point-source method.  
Figure 13: The calculated MTF and the measured MTF for sinusoidal motion with different frequencies, namely: (**a**) 0.5 Hz, (**b**) 1 Hz, (**c**) 2 Hz, and (**d**) 4 Hz.  
error obtained by the use of finite order sum approximations instead of infinite sums is calculated, which gives satisfactory results. The MTF calculated model indicates that, with the same blur radius, the image degradation due to high-frequency vibration is more severe than that for low-frequency vibration. To verify the validity of the MTF calculation formula, a simulation method is proposed to calculate the MTF for the image motion. The results of the simulation experiment show that the mean value of the difference between the calculation model and the simulation method is less than 5%. Furthermore, laboratory experiments were carried out, and the average relative error was less than 12%. Hence, the proposed method improves the calculation accuracy and the applicability of the MTF calculation method for complex motion. This study will be of great significance for indicator design and image restoration of remote-sensing imaging.  
For research articles with several authors, the author [PERSON] conceived and designed the study. [PERSON] and [PERSON] edited and reviewed the manuscript. [PERSON] and [PERSON] performed the experiments and rendered the figures. All authors have given approval to the final version of the manuscript.  
This research was funded by the National Key R&D Program of China [2016 YFF0103603].  
The authors declare no conflict of interest.
# An Intelligent DOA Estimation Error Calibration Method Based on Transfer Learning
## 2 Background
### The Error of Signals  
Equation (3) is the expression of the array signal received under ideal conditions. In the actual environment, the signal of the antenna array changes a lot due to various error factors. Considering various error factors, the vector form of the signal can be written as follows:  
\[X(t)=\tilde{A}S(t)+N(t) \tag{10}\]  
where \(\tilde{A}=C\Gamma\Phi A\), \(C\) is the mutual coupling error between array elements, \(\Gamma\) is amplitude, and the phase error of the array channel and \(\Phi\) is the array element position error. Due to  
Figure 3: Schematic diagram of M-element uniform circular array.  
various errors in the actual environment, there is a great difference between actual signal samples and ideal simulation signal samples. When considering a five-element uniform circular array with a radius of \(r=0.75\) m, the frequency is 163-167 MHz, the angle step is \(5^{\circ}\), and the frequency interval is 1 MHz. Figure 4a shows the phase difference between the two array elements of 300 simulation signal samples generated by a computer under ideal conditions. Figure 4b shows the phase difference between two array elements of 300 actual signal samples collected in the actual environment.  
It can be seen that the phase difference in the ideal condition is very different from the phase difference in the actual environment due to various error factors in the actual environment. Because the signal in the actual environment is affected by many complex error factors, such as mutual coupling error, amplitude and phase error of array channel, and array element position error, these errors make the DOA estimation performance of the model sharply decline in the actual environment. A deep neural network (DNN) can learn the complex mapping relationship between signals and their azimuths. However, it is difficult to collect a large number of actual signal samples for training. Therefore, we propose the error calibration method based on transfer learning to make the DNN-based DOA estimation models work well in the actual environment. The large number of ideal signal samples generated by computer simulation are used to train a DNN-based model and learn the mapping between signals and their azimuths. The small number of actual signal samples are used to fine-tune the model based on transfer learning and learn the complex error factors. As such, the model is transferred from the ideal condition to the actual environment, and hence error calibration is achieved.
Thus, the development of an optical system along with a thorough analysis of the associated theoretical fundamentals via simulations and experiments is crucially relevant for the advancement of the field of FP imaging [6,8]. Additionally, improving the working distance to 2 m and reporting the 4\(\times\) spatial resolution improvement certainly are tangible examples of the contribution made by this study. First, the far-field imaging process of the system is derived on the basis of the Fraunhofer diffraction mechanism and the transmissive imaging model. Second, a transmissive imaging experimental setup is built to verify the reconstruction effect under different overlap ratios, and a partition reconstruction algorithm is used for HR complex field recovery to overcome the influence of system aberrations more effectively [9, 10, 11]. In this study, by introducing an imaging lens before the sample, we can place the Fourier transform plane at the imaging lens (and hence at the pupil function of the system). Therefore, scanning the camera + imaging lens has a clearly defined effect of shifting the point spread function (PSF). This is in contrast to previous work, which affected the PSF less dramatically for each scan position. We first analyzed the imaging process of the optical system using Fresnel diffraction theory to help us understand the macroscopic FP imaging process more effectively. Second, we showed that our prototype setup can bypass the diffraction limit of a conventional photographic lens and achieve HR in the far field. Third, we demonstrated the resolution gains using two real captured experimental datasets with different scanning steps and further explored the potential to achieve remote sensing imaging. Finally, we summarized the results, discussed the limitations of our work, and presented future research avenues. In this study, we demonstrate a transmissive far-field FP imaging system using camera scanning, which uses a small aperture to synthesize a large aperture and an equivalent aperture expansion to improve the spatial resolution of the system. We show that for far-field applications, FP can overcome the limitation of aperture size in passive imaging systems, as well as the requirement of confocal and co-phase sparse aperture in active imaging.
## 1 Introduction
The drone-captured images were subsequently aggregated to produce lower-resolution imagery with pixel sizes spanning from 3.6 m to 30 m. The results from [27] demonstrated that errors in R\({}_{\text{n}}\) and G were relatively consistent across various RS resolutions. In contrast, errors in H and LE fluxes exhibited a clear relationship with the spatial resolution of the RS data. Another study by [28] investigated the effect of pixel heterogeneity for tree-grass when predicting ET\({}_{\text{a}}\) using hyperspectral airborne imagery (1.5 m to 1000 m spatial resolution) and Sentinel imagery products at 20 m and 1000 m using a TSEB RS algorithm in central Spain. They found that large uncertainty, when estimating ET\({}_{\text{a}}\), occurred for coarse spatial resolutions. Even though these studies have contributed to science, there have not been comprehensive studies that evaluate the differences in accuracy of the TSEB RS of ET\({}_{\text{a}}\) algorithms using multispectral images from multiscale RS platforms such as those from proximal, airborne, and spaceborne sensors. The published studies focused only on a few RS sensors or platforms, often resampling (upscaling) their images to generate different pixel spatial resolutions. Therefore, in this study, it is hypothesized that, depending on the source of a given RS image (e.g., spaceborne, airborne, proximal platforms, sensor type, and imagery post-processing corrections), the accuracy of ET\({}_{\text{a}}\) mapping products will vary for a given RS of the ET\({}_{\text{a}}\) algorithm. If the stated hypothesis is valid, determining the optimal RS spectral and spatial resolution becomes necessary (critical) to better sustain irrigated agriculture by improving the estimation of ET\({}_{\text{a}}\) when sub-optimal RS platforms (data) are used with a given RS of the ET\({}_{\text{a}}\) algorithm. Therefore, the objectives of the study were to (a) assess the impact (errors) on hourly ET\({}_{\text{a}}\) estimation associated with the use of different spectral and spatial resolution RS data from multispectral spaceborne, airborne, and proximal RS sensors and when using two different TSEB algorithms, and (b) identify the RS spectral and spatial data (resolution) that provides the most accurate TSEB-based maize ET\({}_{\text{a}}\) predictions for a specific algorithm.
# Portable L-Band Radiometer (PoLRa): Design and Characterization
## 3 Radiometer Characterization
### Radiometer Stability
The theoretical NEAT is provided, along with the experimental value, in Table 2. The theoretical values are likely slightly lower (\(\sim\)20%) because the radiometer was not perfectly stable in temperature during the experiment, and the bandwidth of the ideal rectangular filter assumed in Equation (11) overestimates the bandwidth of the real filter. The experimentally-determined NEAT values do closely follow the trend of the respective theoretical values, suggesting that the radiometer is indeed measuring Gaussian thermal noise. The difference between the mean noise temperature of the external resistive sources and their mean physical temperature was 0.02 K for the H polarization port, and 0.26 K for the V polarization port. The larger difference for the vertical polarization port could have been due to non-uniform heating of the cable or non-ideal thermal contact of the temperature sensor to the resistive source. The absolute accuracy specification of the thermocouple sensors is only 1 K. Considering this, measured noise temperatures of the external resistive source (attached to the H port) agree with its physical temperatures within the uncertainty of the sensors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Integration Time \(\tau\)** & **Total (4 Port) Time** & **Experimental** & **Experimental** & **Theoretical** \\
**(ms)** & **(ms)** & **NEAT V pol. (K)** & **NEAT H pol. (K)** & **NEAT (K)** \\ \hline
16 & 69 & 1.15 & 1.17 & 0.95 \\
64 & 276 & 0.51 & 0.50 & 0.48 \\
112 & 483 & 0.40 & 0.40 & 0.36 \\
256 & 1102 & 0.28 & 0.28 & 0.24 \\
512 & 2205 & 0.20 & 0.19 & 0.17 \\
1024 & 4409 & 0.14 & 0.14 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table of experimental radiometer noise equivalent delta (\(\Delta\)) temperatures (NEATs) for the two polarizations and different integration times. Figure 7: Radiometer-measured noise temperatures during matched resistive source attached to the radiometer’s H port for quantifying PoLRA’s stability. (**a**) Noise temperature time series from different integration times \(\tau\) are plotted along with the physical temperature of the source. (**b**) Histogram of raw \(\tau\ =\ 16\) ms samples shown in (**a**) and Gaussian fit of the distribution.
## 5 Numerical Experiments

Table 2: Dimensions of the SP instances. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & \(\epsilon_{x}\) & **NI** & **Time** & \(f_{\star}\) \\ \hline
1 & \(10^{-2}\) & 250 & 80.86 & \(2.549490\times 10^{5}\) \\
3 & \(10^{-3}\) & 144 & 49.12 & \(2.549466\times 10^{5}\) \\
3 & \(10^{-4}\) & 165 & 57.49 & \(2.549463\times 10^{5}\) \\
4 & \(10^{-5}\) & 164 & 54.12 & \(2.549460\times 10^{5}\) \\
5 & \(10^{-6}\) & 211 & 72.42 & \(2.549461\times 10^{5}\) \\
6 & \(10^{-7}\) & 178 & 62.19 & \(2.549459\times 10^{5}\) \\
7 & \(10^{-8}\) & 132 & 44.56 & \(2.549457\times 10^{5}\) \\
8 & \(10^{-9}\) & 175 & 61.53 & \(2.549461\times 10^{5}\) \\
9 & \(10^{-10}\) & 132 & 49.53 & \(2.549457\times 10^{5}\) \\
10 & \(10^{-11}\) & 258 & 99.69 & \(2.549457\times 10^{5}\) \\
11 & \(10^{-12}\) & 175 & 67.70 & \(2.549461\times 10^{5}\) \\
12 & \(10^{-13}\) & 183 & 71.52 & \(2.549461\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Numerical results for 20-term (50) with fixed tolerances. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & \(\mu\) & **NI** & **Time** & \(f_{\star}\) \\ \hline
1 & \(10^{-3}\) & - & - & - \\
2 & \(10^{-4}\) & 201 & 50.54 & 4.838163 \\
3 & \(10^{-5}\) & 202 & 49.07 & 4.838163 \\
4 & \(10^{-6}\) & 190 & 49.21 & 4.838247 \\
5 & \(10^{-7}\) & 132 & 32.26 & 4.838156 \\
6 & \(10^{-8}\) & 105 & 27.10 & 4.838238 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Numerical results for SSN (100) with dynamic tolerances. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & \(\epsilon_{x}\) & **NI** & **Time** & \(f_{\star}\) \\ \hline
1 & \(10^{-2}\) & 227 & 141.74 & \(2.532914\times 10^{5}\) \\
2 & \(10^{-3}\) & - & - & - \\
3 & \(10^{-4}\) & 140 & 96.02 & \(2.532879\times 10^{5}\) \\
4 & \(10^{-5}\) & 179 & 117.71 & \(2.532877\times 10^{5}\) \\
5 & \(10^{-6}\) & 152 & 99.29 & \(2.532879\times 10^{5}\) \\
6 & \(10^{-7}\) & 139 & 95.07 & \(2.532876\times 10^{5}\) \\
7 & \(10^{-8}\) & 173 & 128.44 & \(2.532876\times 10^{5}\) \\
8 & \(10^{-9}\) & 143 & 103.51 & \(2.532878\times 10^{5}\) \\
9 & \(10^{-10}\) & - & - & - \\
10 & \(10^{-11}\) & 159 & 110.21 & \(2.532877\times 10^{5}\) \\
11 & \(10^{-12}\) & 150 & 112.37 & \(2.532878\times 10^{5}\) \\
12 & \(10^{-13}\) & 132 & 99.46 & \(2.532878\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Numerical results for 20-term (100) with fixed tolerances.
## 4 Conclusions  
In summary, this study proposed to use CYGNSS data to monitor the occurrence of floods in China during the typhoon and extreme precipitation events of 2017. The SR calculated from CYGNSS DDM SNR was used as the main observable to extract the flood inundation area. The CYGNSS-derived flood inundation area was qualitatively consistent with the GPM-derived precipitation and SMAP/SMOS-derived T\({}_{\text{bC}}\). Despite the lack of quantitative evaluation, the results of this study further consolidate the conclusions presented in previous studies. In addition to its primary objective, which was the measurement of ocean surface wind speeds in hurricanes and tropical cyclones, the CYGNSS constellation was demonstrated to have potential in monitoring flood dynamics triggered by typhoon and extreme precipitation events with high temporal resolution. With the further development of the payload and models, more spaceborne GNSS-R data (e.g., CYGNSS follow-on, Cookie [20; 21]) will be acquired in the near future with higher spatial/temporal resolution and higher quality, and this improvement could bring more potential applications in land surface hydrology.  
Conceptualization, W.W., X.C. ([PERSON]) and Y.H.; methodology, W.W., B.L., Z.Z., X.C. ([PERSON]) and L.X.; validation, G.W. and Z.Z.; formal analysis, W.W., B.L., X.C. ([PERSON]) and L.X.; resources, Y.H.; writing--original draft preparation, W.W.; writing--review and editing, Y.H., Z.Z. and B.L.; supervision, Y.H. and X.C. ([PERSON]); funding acquisition, W.W. and Y.H.  
This study is financially supported by the Key R&D Program of the Ministry of Science and Technology, China (Grant No. 2018 YFC1506504). The work related to CYGNSS data processing is supported by the National Natural Science Foundation of China (NSFC) project (Grant No. 41501360).  
The first author is grateful to [PERSON] for her contributions to the text writing of this manuscript.  
The authors declare no conflict of interest. The funding sponsors had no role in the design of the study, in the collection, analyses, or interpretation of data, in the writing of the manuscript, and in the decision to publish the results.
# A QoS-Guaranteed and Congestion-Controlled SDN Routing Strategy for Smart Grid
## 3 Design of QCORS Algorithm
### Link Congestion Degree Judgment  
The algorithm proposed in this paper uses OpenFlow to detect the status of the network. When an application is activated suddenly in SG, it may introduce huge quantities of emergency messages in certain links [45; 46], thus resulting in transient congestion. Then, QCORS will make decisions on whether the packets need to be processed by sensing the condition of congestion from the link.  
**Definition 1**.: _Link load \(C(P_{sd}^{t})\). For a given network topology, the SDN controller is expected to regulate the entire network based on the network load dynamically. Then time slot \(t\), the packet transmission path \(P_{sd}^{t}\) consist of a series of node pairs \(\{(n_{s},n_{s1}),\cdots,(n_{j},n_{i})\,(n_{i},n_{k}),\cdots,(n_{d1},n_{d})\}\). To simplify, we denote \((n_{i},n_{j})\) as \(p_{ij}\). Then, the average transmission rate between the \(n_{j}\) and \(n_{i}\) is \(v(p_{ij})\). Thus, for the time duration \(t\), the overall link load \(C(P_{sd}^{t})\) equals the average transmission rates \(\{v(p_{ij})|p_{ij}\in P_{sd}^{t}\}\) divided by the bandwidth of the link:_  
\[C(P_{sd}^{t})=\frac{\sum_{p_{ij}\in P_{sd}^{t}}v(p_{ij})}{B_{sd}}, \tag{1}\]  
_where \(p_{ij}\) denotes the physical link between node \(n_{i}\) and \(n_{j}\). The flow rate of each data stream is \((v_{1},\cdots,v_{k},\cdots,v_{n})\) respectively, and \(B_{sd}\) indicates the bandwidth of link \(P_{sd}\)._  
The SDN controller can master the global topology of the entire network and evaluate the degree of congestion in the network by periodic monitoring of the network. In Equation (1), the sum of all the data flows in link \(P_{sd}\) occupying the bandwidth of the link can reflect the load of the different links in the network well. The more data streams, the higher the link load.  
However, in traditional methods, the route is expected to be switched once the link load is identified as large [47; 48]. This brings a negative effect on the network stability. Thus, how to reduce the frequency of route switching is also critical. In this paper, the exponentially weighted moving average (EWMA) algorithm is introduced here to calculate the rectified link load. The controller periodically monitors the status of the link every \(\Omega\) seconds and calculates the rectified link load in successive cycles as follows:  
\[\overline{C(P_{sd}^{t})}=(1-\alpha)C(P_{sd}^{t})-\alpha C(P_{sd}^{(t-1)}), \tag{2}\]  
where \(\alpha\) is transition probability of congestion which ranged between 0 and 1. Generally, \(\alpha\) is set to 0.1 or 0.01 [24], and we set \(\alpha\) to 0.1 in this paper. By introducing Equation (1), Equation (2) can be rewritten as:  
\[\overline{C(P_{sd}^{t})}=\frac{(1-\alpha)\sum\limits_{p_{ij}\in P_{sd}^{t}}v(p _{ij})+\alpha\sum\limits_{p_{ij}\in P_{sd}^{(t-1)}}v(p_{ij})}{B_{sd}}. \tag{3}\]Then, we could calculate the congestion level according to Table 2, where the \(C(P_{sd})_{law}\) and \(C(P_{sd})_{high}\) are identified through the empirical analysis.