esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Artificial Intelligence Methods for GWL Modelling
### Support Vector Machines
The results indicate that the Gradient Tree Boosting (GTB) outperformed the ANFIS and Group Method of Data Handling (GMDH). For example, the GTB could predict GWL variations more accurately during rainy seasons with heavy rainfall. Ref. [44] investigated the performance of the Multi-Objective Genetic Algorithm and Support Vector Machine (MOGA-SVM) algorithm in predicting GWL fluctuations with different lead times in Taiwan. The results showed that this model outperformed the Self-Organisation Maps (SOM)-SVM algorithm. For instance, with seasonal and yearly variations in precipitation and evaporation, the MOGA-SVM can predict GWL changes with greater accuracy. Ref. [50] examined the performance of the Radial Basis Function-Support Vector Regression (RBF-SVR) in predicting GWL in various regions of the United States. The results indicate that this method performed better, especially in different seasons. For example, the RBF-SVR could predict GWL more accurately in areas with variable precipitation. In a study conducted by [56], the performance of two methods, SVR (Polynomial) and M5 Model Tree (M5 Tree), in predicting monthly GWL changes in Ardabil Plain, Iran, was examined. The results showed that both models accurately predicted monthly changes. For example, the M5 Tree could predict GWL more accurately during cold seasons with low-temperature fluctuations. Ref. [54] investigated the impact of variations in Total Water Storage (TWS) on GWL in India. The results indicate that TWS was identified as an  
Figure 8: Graphical representation of the trend in the number of scientific articles published between 2011 and 2023 on using SVM in groundwater studies. The size of the dots indicates the number of articles related to each country. The larger the number of articles, the bigger the dot. essential variable, and the SVR method better predicted GWL than others. The research conducted by [46] examined the performance of RBF-SVR in predicting GWL in the Indo-Gangetic Basin, India. The results show that this method performed better for improved prediction and utilised satellite data as inputs. Ref. [48] investigated the performance of a Least-Squares Support Vector Machine (LS-SVM) in predicting hourly fluctuations in GWL in England. The results indicated that this method provided superior performance in predicting these fluctuations. Ref. [49] examined the performance of RBF-SVM in predicting monthly fluctuations in GWL in China. The results showed that this method is more accurate and less uncertain, using precipitation, evaporation, and temperature as input variables. For example, in regions with hot and dry climates, RBF-SVM can predict changes in GWL more accurately. Ref. [53] compared the performance of ANNs, SVMs, and ANFIS in predicting monthly fluctuations in GWL in Florida, United States. Table S3 (Supplementary Materials) summarises the evaluated articles that used SVM methods and draws a general conclusion.
## 2 Efficient Estimation of Residual OFDM BER for Small Cells
### Computationally Efficient BER Floor for Small Cells  
Furthermore, for the power delay profile rms delay spread up to 50 ns, data transmission speed in the order of, say, 100 Mbit/s, and \(M\) equal to 2048, 4096,..., we can justifiably consider that:  
\[E\left[\frac{\Delta\tau^{-}}{\sqrt{M}_{\rm{s}}}\right],\quad E\left[\frac{ \Delta\tau^{+}}{\sqrt{M}_{\rm{s}}}\right]<<1 \tag{7}\]  
Whereas from Equation (4) it is obvious that: \(W^{-},W^{+}<1\).  
This implies that the distinct \"\(-\)\" and \"\(+\)\" rms delay spreads \(\sqrt{W^{+}E\left[\left(\frac{\Delta\tau^{+}}{\sqrt{M}_{\rm{s}}}\right)^{2} \right]}\) and \(\sqrt{W^{+}E\left[\left(\frac{\Delta\tau^{+}}{\sqrt{M}_{\rm{s}}}\right)^{2} \right]}\), respectively, are both much smaller than unity. Consequently, their product in the numerator of the subtrahend in Equation (6) is negligible with respect to their sum in the denominator, implying that the whole subtrahend can be neglected, so Equation (6) can be justifiably approximated as it follows (in simpler notation where: \(E[x]=\overline{x}\)):  
\[BER=\frac{k_{m}}{2\sqrt{\pi M}_{\rm{s}}}\cdot\left(\sqrt{W^{-}}\cdot\sqrt{ \left(\tau-\tau^{-}\right)^{2}}+\sqrt{W^{+}}\cdot\sqrt{\left(\tau-\tau^{+} \right)^{2}}\right) \tag{8}\]  
where Equation (2) is taken into account to emphasize the arbitrary sample delay \(\tau\) as the variable now.
# Detection of Decision-Making Manipulation in the Pairwise Comparison Method
## 4 Problem Statement
### Advanced Algorithm  
This section describes the _advanced algorithm_, which extends the _basic algorithm_ (Section 4.2) by adding a stopping constraint. The goal is to improve the ranking of alternative \(a_{p}\) by increasing the values of as few elements as possible in the \(p\)th row and column of matrix \(\mathbf{C}\).  
The \(\alpha\) factor in this algorithm has the same properties as in the _basic algorithm_. The \(c_{pi}\) element in the \(p\)th row and its reciprocal counterpart \(c_{ip}\) in the \(p\)th column are updated sequentially, except for the \(c_{pp}\) element, as long as the ranking value (3) of the alternative \(a_{p}\) is lower than the ranking value of the reference alternative \(a_{r}\) or all feasible elements are updated. The updated value of the \(c_{pi}\) element is equal to the corresponding \(c_{ri}\) element multiplied by the \(\alpha\) factor. Unlike the basic approach, we stop updating the elements of the matrix \(\mathbf{C}\) when \(w(a_{p}^{\prime})\) becomes more significant than \(w(a_{r}^{\prime})\).  
Without loss of generality, we may assume that \(p=2\) and \(r=n\). Thus, the initial form of \(\mathbf{C}\), the intermediate form denoted by \(\mathbf{C}^{\text{step}}\), and the final form denoted by \(\mathbf{C}^{\prime}\) are as follows:  
\[\mathbf{C}=\begin{bmatrix}1&c_{12}&\cdots&c_{1n}\\ c_{21}&1&&c_{2n}\\ \vdots&&\ddots&\vdots\\ c_{n1}&c_{n2}&\cdots&1\end{bmatrix}\xrightarrow{\text{first step}}\begin{bmatrix}1&1/c_{n1}\alpha&\cdots&c_{1n}\\ ac_{n1}&1&&c_{2n}\\ \vdots&&\ddots&\vdots\\ c_{n1}&c_{n2}&\cdots&1\end{bmatrix}^{\prime}=\mathbf{C}^{1}\]  
\(\downarrow\) next \(n-2\) consecutive steps  
Figure 2: Pairwise comparison matrices for the “basic” algorithm (\(\alpha=4.84\)) are presented as a heat map. Lighter colors indicate larger values, whereas darker colors indicate smaller ones.  
\[\mathbf{C}^{n-2}=\begin{bmatrix}1&c_{12}&\cdots&c_{1n}\\ c_{21}&1&&c_{2n}\\ \vdots&&\ddots&\vdots\\ c_{n1}&c_{n2}&\cdots&1\end{bmatrix}\xrightarrow[\text{last step}]{1}\xrightarrow[ \text{last step}]{1}\begin{matrix}1&1/c_{n1}\alpha&\cdots&c_{1n}\\ \alpha c_{n1}&1&&\alpha\\ \vdots&&\ddots&\vdots\\ c_{n1}&1/\alpha&\cdots&1\end{matrix}^{\prime}=\mathbf{C}^{\prime}\]  
It is important to note that when the stopping criteria are met, the number of algorithm steps may be lower than those (\(n-1\) steps) shown in the example above.  
Figure 3 shows the heat maps for the _advanced_ algorithm. Some values in the 8 th row have been updated with the values from the 2 nd row multiplied by the \(\alpha\) factor (and similarly all reciprocal elements), while the rest remain unchanged. The algorithm stopped after the 7 th iteration of making changes to the initial _PC_ matrix \(\mathbf{C}\), promoting alternative \(a_{8}^{\prime}\) over alternative \(a_{2}^{\prime}\).
## 2 Mid-Infrared Optical Parametric Oscillation Laser (OPO)
### AgGaSe\({}_{2}\) and AgGaS\({}_{2}\) Optical Parametric Oscillator
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Crystal**} & \multirow{2}{*}{**Year**} & **Research** & **Crystal** & \multirow{2}{*}{**Pump Source**} & **Mid-Infrared Output** & \multirow{2}{*}{**References**} \\  & & **Establishment** & & & & **Parameter** \\ \hline \multirow{9}{*}{AgGaSe\({}_{2}\)} & \multirow{3}{*}{2000} & The University of & \multirow{3}{*}{9 mm thickness} & \multirow{3}{*}{2 μm} & Output wavelength 3.5 μm \\  & & & & CO\({}^{2}\) laser & & \\  & & & & & Optical efficiency 2.4\% \\ \cline{1-1} \cline{3-5}  & \multirow{3}{*}{2013} & Changchun & \multirow{3}{*}{18 \(\times\) 18 \(\times\)} & Output wavelength 4.65 μm \\  & & Institute of & \multirow{3}{*}{52 mm\({}^{3}\)} & \multirow{3}{*}{TEACO\({}^{2}\) laser} & Average power 3.9 μm \\  & & Optics, Fine & & & & \\  & Mechanics and & & & TEACO\({}^{2}\) laser & & \\  & & Physics & & & & Optical efficiency 56\% \\  & & Huazhong & & & & \\  & & University of & \multirow{3}{*}{5 \(\times\) 5 \(\times\) 13 mm\({}^{3}\)} & \multirow{3}{*}{9.6 μm} & Output wavelength 3.2 μm \\  & & Science and & & CO\({}^{2}\) laser & & \\  & Technology & & & & Optical efficiency 0.14\% \\ \hline \multirow{9}{*}{AgGaS\({}_{2}\)} & \multirow{3}{*}{1984} & Stanford & \multirow{3}{*}{2 \(\times\) 1 \(\times\)} & \multirow{3}{*}{1.064 μm} & Output wavelength 4 μm \\  & & University & \multirow{3}{*}{0.5 mm\({}^{3}\)} & \multirow{3}{*}{Nd: yttrium} & \multirow{3}{*}{Repetition rate 10 Hz} \\  & & & & Optical efficiency 16\% \\ \cline{1-1} \cline{3-5}  & & & & Output wavelength 4.2 μm \\ \cline{1-1} \cline{3-5}  & \multirow{3}{*}{1997} & DSO National & \multirow{3}{*}{2 \(\times\) 0.7 μm} & \multirow{3}{*}{1.064 μm} & \multirow{3}{*}{Repetition rate 10 Hz} \\  & & Laboratories & \multirow{3}{*}{0.7 mm\({}^{3}\)} & Nd: YAG & Optical efficiency 10\% \\ \cline{1-1} \cline{3-5}  & & & & Output wavelength 3.9 μm \\ \cline{1-1} \cline{3-5}  & \multirow{3}{*}{1999} & American & \multirow{3}{*}{20 \(\times\) 7 \(\times\)} & \multirow{3}{*}{1.06 μm} & Average power 4 mW \\  & & Institute of & \multirow{3}{*}{10 mm\({}^{3}\)} & \multirow{3}{*}{Nd: YAG} & \multirow{3}{*}{Repetition rate 10 Hz} \\  & & Physics & & Optical efficiency 22\% \\ \cline{1-1} \cline{3-5}  & & & & Output wavelength 4 μm \\ \cline{1-1} \cline{3-5}  & \multirow{3}{*}{2006} & \multirow{3}{*}{Jilin University} & \multirow{3}{*}{10 \(\times\) 7 \(\times\)} & \multirow{3}{*}{1.06 μm} & Average power 12 mW \\  & & & 20 mm\({}^{3}\) & Nd: YAG & Repetition rate 20 Hz \\ \cline{1-1} \cline{3-5}  & & & & Optical efficiency 3.5\% \\ \hline \end{tabular}
\end{table} 
Table 4: Research and development status. Figure 4: Crystal description diagram. is also relatively small. This may be the reason why there are almost no literature reports about realizing mid-infrared laser output based on these two nonlinear crystals in the pas decade.
## 4 Simulation Results
### Open Sky with Seven SVs
It is important to mention that with this analysis we are not trying to find an optimal solution for the receiver to re-track a satellite after losing it. Instead we are showing the advantages in terms of re-acquisition and re-tracking that can be obtained when integrating a low quality MEMS-based INS with a very simple GPS receiver having a 2 nd order PLL, and provide an assessment of the time during which we can still use the aiding component of the INS for re-tracking, under different GPS conditions as it will be shown later. Figure 10: PLL filter output before and after enabling the feed-forward component. Figure 9: Feed-forward frequency uncertainty in open-sky conditions. As explained before, the feed-forward component allows the PLL to better tolerate the dynamics, and consequently gives the possibility of decreasing its bandwidth. Figure 12 shows the PLI of SV 19 at the first turn during the trajectory with a loop bandwidth of 4 Hz and a high _C/N\({}_{o}\)_. In the case of the stand-alone GPS, the PLL loses lock as soon as there is acceleration and re -tracks again after 5 s. However for the TCAPLL it stays locked all the time. The PLI output is shown in Figure 13 for the same scenario but with a lower _C/N\({}_{0}\)_ and higher integration time. The PLL loses lock permanently for the stand-alone GPS, whereas the dynamics are compensated with the feed-forward component for the TCAPLL. This shows the importance of the feed-forward component especially in high-dynamic situations where, for the same loop parameters, the sensitivity of the receiver is improved with the TCAPLL in comparison to the GPS. Figure 14 shows the integration filter estimated turn-on to turn-on constant bias and the bias drift on each axis of the accelerometer and gyroscope, respectively. It can be seen that the TCAPLL EKF estimates correctly the inertial sensor errors. From the left graph, it can be noted that the integration filter needs roughly 100 s to converge. During this time, it is important to have good GPS conditions, otherwise there is a high probability that the integration filter converges to the wrong values. Therefore, when using low-quality MEMS inertial sensors, it is very important to start in good GPS conditions for a certain period of time allowing the integration filter to esti  
Figure 11: Carrier and code NCOs’ behavior during GPS outage. Figure 12: PLI output when _C/N\({}_{0}\)_ = 45 dB-Hz, _T\({}_{int}\)_ = 1 ms, and _B\({}_{n}\)_ = 4 Hz. states of the sensors. This duration depends on the quality of the MEMS inertial sensors and the uncertainty on their errors. In summary, during open-sky conditions the TCAPLL with MEMS inertial sensors provides a better navigation solution than a GPS alone. No re-acquisition is needed once a satellite is lost, as the receiver can continue tracking the satellite based on the aiding information from the INS. In addition, the PLL noise bandwidth can be decreased even in strong dynamic conditions, which provides better sensitivity compared to a GPS receiver with the same loop parameters.
## 2 Related Work
[44] proposed a fault-tolerant method that adaptively replicates data according to the application's requirements for data loss and latency to meet the required level of data loss tolerance and timeliness. [PERSON] et al. [45] proposed to ensure the QoS of the system through a fault-tolerant strategy provided by a third party. However, it is difficult and impractical for ordinary users to choose a suitable third-party service. Different from the above research that adopted a single fault tolerance strategy, [PERSON] et al. [46] proposed a replication and resubmitted each service in edge computing simultaneously and adjusted the size of the copy by using the impact of service resubmission to make a trade-off between the two fault tolerance strategies. Similarly, [PERSON] et al. [47] proposed a fault-tolerant scheduling algorithm for the workflow based on unbalanced resources by combining two fault-tolerant strategies of replication and resubmission, assuming that the failure rate of ESs is fixed. It can be observed that, although the current research on service migration has made some important progress, existing studies are still limited in several ways:  
* The performance fluctuations of ES are not taken into account. In the VEC environment, the processing capability and operational stability of ES are always affected by natural or human factors, but the existing research has not fully considered this issue. * The fault tolerance mechanism is single. Each fault tolerance mechanism has its applicable scenarios and shortcomings. Most of the existing researches are based on one fault tolerance mechanism for service migration, which is difficult to apply to other scenarios. The above limitations could be well avoided by using the DRPS approach proposed in this paper.
## 2 Study Area and Data
### Data  
Sentinel-1 is an imaging SAR mission of the Copernicus programme that provides continuous, all-weather, day-night imagery for the C-band. It potentially images all global landmasses at regular intervals, at least every 12 days (6 days over Europe), with a typical resolution of 20 m. The mission consists of two satellites, the first of which was launched in 2014, followed by the second in 2016. Practically, this means that there is generally a good archive of data going back around 4-5 years from the present day. The free, full, and open data policy adopted for the Copernicus programme means that access to the imagery is freely available to all commercial, academic and institutional users. Accordingly, Sentinel-1 provides an excellent basis for a sustainable and cost-effective ground motion monitoring system anywhere around the world.  
Over the Lake Sarez study area, two stacks of Sentinel-1 imagery were identified for the period September 2017-September 2019. The stacks comprised 60 SAR images acquired from ascending track N\({}^{\circ}\) 100 and 58 images from descending track N\({}^{\circ}\) 5. The temporal spacing of the images from each track was 12 days. The data are provided by the European Space Agency and were obtained from the Copernicus Open Access Hub ([[https://scichub.copernicus.eu/dhus/#/home](https://scichub.copernicus.eu/dhus/#/home)]([https://scichub.copernicus.eu/dhus/#/home](https://scichub.copernicus.eu/dhus/#/home)) (accessed on 27 November 2019)). Data products in the Interferometric Wide format were selected for processing. The footprint of each track and frame is shown in Figure 1a.  
The processing of the SAR data was supported using a 90 m Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) [48]. Created in 2000, the SRTM DEM was used to remove the topographic phase from the interferograms and help identify areas affected by geometric distortions. Additionally, the SRTM DEM was used to geocode all ground motion outputs to a Universal Transverse Mercator (UTM) projection.
## 3 Effect of Wave on Load and Aerodynamic Torque of Wind Turbines
### Effect of Regular Waves on Tower  
The forced vibration of a structure will occur under the action of external forces. The forced vibration equation of the single degree of freedom system is expressed as follows:  
\[m\ddot{u}+ci\dot{u}+ku=p(t) \tag{5}\]  
where \(m\) is the mass of the system; \(k\) is the bending stiffness; \(c\) is the damping coefficient; \(u\) is the displacement; \(\dot{u}\) is the velocity; \(\ddot{u}\) is the acceleration; \(p(t)\) is the load varying with time.  
When the load \(p(t)\) is arbitrary periodic, it can be represented as a Fourier series as follows:  
\[p(t)= a_{0}+\sum_{n=1}^{\infty}a_{n}cos\widetilde{\omega}_{n}t+\sum_{n=1}^{ \infty}b_{n}sin\widetilde{\omega}_{n}t \tag{6}\]  
where \(a_{0}\), \(a_{n}\), \(b_{n}\) are the coefficients and \(\widetilde{\omega}_{n}\) is the frequency of the \(n\)-th external load.  
The steady-state response of the system can be expressed as follows [32]:  
\[u(t)= \frac{1}{k}(a_{0}+\sum_{n=1}^{\infty}\frac{1}{{(1-\gamma_{n}{}^{2})}^{2}+ (2\xi\gamma_{n})^{2}}\{[a_{n}2\xi\gamma_{n}+b_{n}(1-\gamma_{n}{}^{2})]sin \widetilde{\omega}_{n}t+[a_{n}(1-\gamma_{n}{}^{2})-b_{n}2\xi\gamma_{n}]cos \widetilde{\omega}_{n}t\}) \tag{7}\]  
where the frequency ratio is \(\gamma_{n}=\frac{\widetilde{\omega}_{n}}{\omega}\); \(\omega\) is the natural frequency of the system; \(\xi\) is the ratio of the system damping to the critical damping.  
In Equation (7), the vibration frequency of the system is the same as that of the external load, but there is a certain phase difference [32]. Therefore, when the waves periodically act on the tower, the fluctuating component of the hydrodynamic frequency in the load on the tower at the MWL will increase.  
The part of the tower above the elevation of the wave surface is not directly affected by the wave, but it also faces the impact because the low frequency vibration caused by the wave will run through the whole tower system due to the small damping matrix term of the steel tube tower structure. The relationship between the bending moment at the bottom of the tower \(M(t)\) and the horizontal displacement at the top of the tower \(u_{top}(t)\) satisfies  
\[M(t)=Ku_{top}(t)H \tag{8}\]  
where \(K\) is the bending stiffness of the tower, the bending stiffness is the resistance of a member against bending deformation; and \(H\) is the height of the tower.  
Therefore, the top displacement and the bottom moment of the tower have the same waveform, that is, the vibration caused by wave will be transmitted from the bottom of the tower to the top of the tower. During this process, the vibration energy will be weakened because of the damping effect, but the vibration frequency will remain unchanged.
# Stable Evaluation of 3D Zernike Moments for Surface Meshes
## 2 Moments from 3D Shapes
### Basis Function: Monomials  
A very popular set of functions \(\boldsymbol{\Psi}\) are the monomials \(x^{i}y^{j}z^{k}\), where \(i,j,k\) are non negative integers. The corresponding moments are referred to as geometric moments, \(G_{ijk}\), and defined by  
\[G_{ijk}=\int_{D}f(\boldsymbol{x})x^{i}y^{j}z^{k}\mathrm{d}x, \tag{3}\]  
The geometric moments are easy to compute, both for grid-based and surface-based representations of shapes. The geometric monomials, however, are neither orthonormal, nor complete.
###### Abstract  
As an essential infrastructure that provides positioning, navigation, and timing services, China constructed the BeiDou Navigation Satellite System (BDS). The last BDS satellite was launched in June 2020, which represents the completion of BDS. BDS's constellation consists of Medium Earth Orbit (MEO), Inclined Geosynchronous Orbit (IGSO), and Geostationary Orbit satellites. The precise modeling of non-conservative forces for BDS satellites is a challenging task. As an independent observation, Satellite Laser Ranging (SLR) is an important validation method of GNSS orbit modeling. In this paper, we validated the precise orbit products of different Analysis Centers (ACs) by using SLR observations, focusing on the BDS orbit modeling. By comparing BDS precise orbit products generated by four ACs with respect to SLR observations for the period of February 2017 to March 2021, we proved that an obvious satellite signature effect exists in the SLR residuals of BDS observed by multi-photon stations. The result indicates that multi-photon stations have a root mean square (RMS) of SLR residuals about 5 mm lower than that of single-photon detectors. The slope of SLR residuals with regard to anid angle of IGSO satellites for single-photon and multi-photon stations is \(-2.0\) and \(-2.5\) mm/deg, respectively, while the slope of MEO satellites for these stations is about \(-0.6\) to \(-0.3\) and \(-1.0\) to \(-0.4\) mm/deg, respectively. To assess the effect of non-conservative force modeling, we selected seven high-performing stations, including five single-photon and two multi-photon stations. By comparing the SLR residuals of four ACs' orbits, we analyzed the effect of the solutions of orbit processing, especially solar radiation pressure (SRP) models. We found that some centers may have modeling defects, including BDS-3 orbits of the Deutsches GeoForschungsZentrum and BDS-2 orbits of the European Space Agency, inferred from the large RMS of SLR residuals. Modeling the SRP of BDS satellites is challenging, while an appropriate prior box-wing model can improve the accuracy of SRP modeling and provide a more stable performance.  
SLR; BDS; satellite signature effect; non-conservative force modeling Article