esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Integrity Risk Estimation for RAIM
 \tag{4}\]  
where \(Q(z)\) is the tail cumulative distribution function (CDF) at \(z\) of a standard Gaussian distribution; \(P(T,n-m,\lambda_{i})\) is the non-central chi-square CDF at \(T\), with \(n\)-\(m\) degree of freedom and non-central parameter \(\lambda_{i}\); \(P(T,n-m)\) is the chi-square CDF at \(T\) with an \(n\)-\(m\) degree of freedom; and \(z_{i}^{+}\), \(z_{i}^{-}\) and \(z_{0}\) are defined as  
\[z_{i}^{+}=\frac{l+b_{i}\Big{|}\mathbf{A}_{q,i}\Big{|}}{\sigma_{q}^{2}},z_{i}^{-}= \frac{l-b_{i}\Big{|}\mathbf{A}_{q,i}\Big{|}}{\sigma_{q}^{2}},z_{0}=\frac{l}{\sigma _{q}^{2}} \tag{5}\]  
From (4), the RAIM integrity risk is jointly determined by the probability of the position error exceeding the alert limit in the position domain and detection fails in the detection domain, while the baseline ARAIM computes integrity risk through the bounding and manipulating of inequalities in the position domain. The effect of the integrity parameters on RAIM is therefore different from those for ARAIM. The integrity-related parameters involved in (4) can be divided into four groups as follows:  
* The first group of parameters is the fault-induced bias \(b_{i}\), which is impractical to obtain accurately. However, based on the worst-case protection concept, the effect of the bias on the integrity risk can be strictly determined. * The second group includes the parameters benefiting from the improvement in the aspects of SIS performance and probability of satellite fault, i.e., _URA_ and \(P_{\text{sat}}\). This second group will improve with the constellation modernization. The integrity loss introduced by the improved second group of parameters needs to be strictly characterized, which is the focus of this contribution. * The third group is determined by the positioning, integrity and continuity requirement, including the alert limit and the probabilities of false alarm (\(P_{\text{fa}}\)) and missed detection (\(P_{\text{md}}\)). The third group of parameters is generally constant for the specific required navigation performance (RNP): e.g., the different flight phases in civil aviation defined by the international civil aviation organization (ICAO). * The fourth group of parameters is the satellite geometry, which has a great impact on integrity performance. The influence of satellite geometry on the integrity performance cannot be neglected. To investigate the integrity loss resulting from improved parameters in the second group, we needed to consider the impact of the first, third, and fourth group of parameters on the integrity risk. In the following section, we introduce the concept of worst-case integrity risk by varying the magnitude of the first group of parameters to acquire the maximum risk. Based on it, the integrity risk error with respect to \(P_{\text{sat}}\) and _URA_ was deduced. The integrity loss introduced by the improved second group of integrity parameters can be therefore strictly characterized. The effect of the third and fourth group of parameters on integrity performance will be analyzed through a global simulation experiment.
## 3 System Models
### Control Objective  
For formation generation, the USV team starts from the respective current locations and generates a predefined formation shape in the target location. Therefore, the goal is to minimize the sum of the length of the movement path of the team of USVs,  
\[\text{min}\Big{(}\sum_{i=1}^{N}(\text{len}(s(u_{i}),e(u_{i})))\Big{)} \tag{3}\]  
where \(s(u_{i})\) is the initial position of USV \(u_{i}\), and \(e(u_{i})\) is the final position of USV \(u_{i}\) in the formation. \(\text{len}(s(u_{i}),e(u_{i}))\) is the length of the moving path for USV \(u_{i}\) from position \(s(u_{i})\) to position \(e(u_{i})\) during formation generation.  
For formation maintenance, in this paper, we aim at training USVs to learn policies to move in a predetermined formation and maintain the shape of the formation. All the followers keep a certain distance with their respective leaders, which reduces the stability error (i.e., distance difference between the current relative distance and the predefined distance). Thus, another control goal is defined as follows:  
\[\text{L}_{pg}=\underset{i}{\text{min}}\big{|}H^{\prime}{}_{i}-H_{i}\big{|}, \forall u_{i}\in\text{U}_{follower} \tag{4}\]  
\[H^{\prime}{}_{i}=p^{\prime}{}_{u_{i}}-p^{\prime}{}_{ll(u_{i})} \tag{5}\]  
where \(ll(u_{i})\) denotes the immediate leader of USV \(u_{i}\). \(U_{follower}\) is the set of all the followers except the only leader USV, and \(p^{\prime}{}_{ll(u_{i})}\) is the position of the immediate leader \(ll(u_{i})\) of USV \(u_{i}\). \(H_{i}\) is the required distance offset between USV \(u_{i}\) and its immediate leader, and \(H^{\prime}{}_{i}\) is the current relative distance between USV \(u_{i}\) and its immediate leader.
## 2 Mathematical Model
### Model Solution  
Based on the assumptions described in Section 2.2, the dimensionless governing equations can be established and the detailed derivation is presented in Appendix A. As shown in Appendix B, by the Laplace transforms with respect to \(t_{\text{D}}\) and the finite Fourier cosine transforms with respect to \(z_{\text{D}}\), the line source solution for dimensionless bottom-hole pressure is obtained as following:  
\[\widetilde{p}_{uD}=\frac{1}{q_{0}}\Big{[}\frac{E_{0}l_{0}(r_{0}q_{0})+F_{0}K_{ 0}(r_{0}q_{0})}{F_{0}K_{1}(q_{0})-E_{0}l_{1}(q_{0})}\Big{]}+2\sum_{n=1}^{\infty }\frac{\sin^{2}\left(\frac{1}{2}u_{n}u_{nD}\right)}{\left(\frac{1}{2}u_{n}u_{ nD}\right)^{2}}\frac{1}{q_{n}}\Big{[}\frac{E_{n}l_{0}(r_{0}q_{n})+F_{n}K_{0}(r_{0}q_{ n})}{F_{n}K_{1}(q_{n})-E_{n}I_{1}(q_{n})}\Big{]}\cos^{2}(u_{n}z_{uD}) \tag{5}\]  
where, \(s\) is the time variable in Laplace domain, and the expressions of \(E_{n}\), \(F_{n}\), \(G_{n}\), \(H_{n}\), \(q_{n}\), \(T_{n}\),\(f\)(s) are as following:  
\[E_{n}=q_{n}G_{n}K_{1}(R_{1D}q_{n})+M\text{{}}T_{n}H_{n}K_{0}(R_{1D}q_{n}) \tag{6}\]  
\[F_{n}=q_{n}G_{n}I_{1}(R_{1D}q_{n})-M\text{{}}T_{n}H_{n}I_{0}(R_{1D}q_{n}) \tag{7}\]  
\[G_{n}=\frac{K_{1}(R_{eD}T_{n})}{I_{1}(R_{eD}T_{n})}I_{0}(R_{1D}T_{n})+K_{0}(R_ {1D}T_{n}) \tag{8}\]  
\[H_{n}=\frac{K_{1}(R_{eD}T_{n})}{I_{1}(R_{eD}T_{n})}I_{1}(R_{1D}T_{n})-K_{1}(R_ {1D}T_{n}) \tag{9}\]  
\[q_{n}=\sqrt{s}f(s)+\frac{u_{n}^{2}}{h_{1D}^{2}} \tag{10}\]  
\[T_{n}=\sqrt{\frac{s}{\sigma}+\frac{u_{n}^{2}}{h_{2D}^{2}}} \tag{11}\]  
\[f(s)=\frac{\lambda+\sqrt{\kappa_{1}}\omega(1-\omega)s}{\lambda+\sqrt{\kappa_{ 1}}(1-\omega)s} \tag{12}\]  
As shown above, \(f\)(s) for the pseudosteady-state matrix-fracture mass exchange is slightly different from the expression of [PERSON]'s model [44] due to the consideration of anisotropy. It is noticed that if \(\kappa_{1}\) equals to 1, the expression of \(f\)(s) simplifies to the same form as isotropic dual-porosity mediums:  
\[f(s)=\frac{\lambda+\omega(1-\omega)s}{\lambda+(1-\omega)s} \tag{13}\]  
On the basis of superposition principle [45], the relationship between the dimensionless bottom-hole pseudopressure solution at a fixed constant rate inner boundary and the dimensionless flow rate solution at a fixed bottom-hole pressure can be written as:  
\[\overline{q}_{uD}=\frac{\overline{p}_{uD}}{s^{2}} \tag{14}\]  
With a numerical Laplace inversion algorithm proposed by [PERSON] [46], the solution of dimensionless production rate in real time domain can be obtained, and the dimensional production rate can be calculated based on the following equation:  
\[q_{g}=q_{wD}\frac{k_{fhi}h\Big{[}p_{p}(p_{i})-p_{p}(p_{wf})\Big{]}}{\alpha_{p }\mu_{gi}B_{gi}} \tag{15}\]  
where, \(q_{g}\) denotes production rate; \(k_{fhi}\) denotes horizontal fracture permeability at initial reservoir pressure; \(\alpha_{p}\) is the unit conversion coefficient.
# Sign Language Recognition Using Two-Stream Convolutional Neural Networks with Wi-Fi Signals
## 3 Experimental Results
### SignFi Dataset Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network Model** & **Modality** & **Preprocessing** & **Accuracy** \\ \hline SignFi [1] (9-layer CNN) & combination & no & 93.98\% \\ \hline SignFi [1] (9-layer CNN) & combination & Phase Shift & 98.91\% \\ \hline HOS-Re [3] (SVM) & combination & no & 98.26\% \\ \hline Single-stream ResNet18 & combination & no & 97.90\% \\ \hline Single-stream ResNet18 & combination & SVD\_20 & 97.83\% \\ \hline Single-stream ResNet50 & combination & no & 99.02\% \\ \hline Single-stream ResNet50 & combination & SVD\_20 & 98.87\% \\ \hline Dual-output two-stream with ResNet18 & combination + difference & no & 97.75\% \\ \hline Dual-output two-stream with ResNet18 & combination + difference & SVD\_20 & 98.55\% \\ \hline Dual-output two-stream with ResNet50 & combination + difference & no & 98.88\% \\ \hline Dual-output two-stream with ResNet50 & combination + difference & SVD\_20 & 99.13\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparisons of dual-output two-stream network with other methods on Home276 group. According to Tables 3-6, we can conclude that using SVD preprocessing can indeed improve the performance of our dual-output two-stream network. As the CNN model in our dual-output dual-stream network, ResNet50 is more suitable for CSI data in sign language recognition tasks than ResNet18. Although the accuracy of our proposed method is lower than other methods in the Lab276 group and Lab150 group, the best results can be obtained in a mixed environment. This means that our method has better generalization capability than other methods.
## 3 Case Study Analysis
### Effects of Soil Parameter Spatial Variability on Failure Probability
#### 3.2.2 Effects of Correlation Lengths on Failure Probability  
Figures 11 and 12 present the parametric analysis results for Case II, with horizontal correlation lengths (\(L_{h}\)) ranging from 10 m to 50 m and vertical correlation lengths (\(L_{v}\)) spanning 1 m to 3.5 m. Based on prior research [40], the coefficients of variation (\(Cov\)) for cohesion (\(Cov_{c}\)) and internal friction angle (\(Cov_{\varphi}\)) are set to 0.1\(\sim\)0.5 and 0.05\(\sim\)0.4, respectively. Four distinct parameter combinations are analyzed in these two figures. The parameter for the failure surface width ratio (\(B/H\)) is fixed at 5.0 for all scenarios.  
As depicted in Figure 11, \(P_{f}\) escalates with a growing horizontal correlation length \(L_{h}\), while \(F_{s}\) decreases correspondingly. Notably, under the specific combination of \(Cov_{c}=0.3\), \(Cov_{\varphi}=0.2\), and \(\rho(c,\,\varphi)=0\), the increment in \(P_{f}\) is the most pronounced, surging by 94% (from 0.0026 to 0.0407) as \(L_{h}\) grows from 10 m to 50 m. This increase is significantly  
Figure 8: Variation curves of \(P_{f}\) and \(F_{s}\) with respect to \(Cov_{\varphi}\) (different combinations of \(L_{h}\) and \(L_{v}\)).  
higher than that observed in the other three combinations. When focusing solely on the variability of the internal friction angle (i.e., with \(Cov_{c}=0\), \(Cov_{\varphi}=0.2\), and \(\rho(c,\,\varphi)=0\)), \(P_{f}\) exhibits the second most significant increase, climbing from 0.0001 to 0.0074. Conversely, when considering only the variability of cohesion (i.e., with \(Cov_{c}=0.3\), \(Cov_{\varphi}=0\), and \(\rho(c,\,\varphi)=0\)), the rise in \(P_{f}\) is nearly negligible (\(<\)0.1% variation). From the four combinations in Figure 11, \(F_{s}\) tends to slightly decrease, with the maximum reduction not surpassing 2%.  
In addition, an opposing trend to that of the horizontal correlation length is observed in Figure 12. As the vertical correlation length \(L_{v}\) increases, \(P_{f}\) rises, and interestingly \(F_{s}\) simultaneously escalates, contrasting with the pattern seen for parameter \(L_{h}\). Under the combination of \(Cov_{c}=0.3\), \(Cov_{\varphi}=0.2\), and \(\rho(c,\,\varphi)=0\), the maximum increase in \(P_{f}\) occurs when \(L_{v}\) is augmented from 1.0 m to 3.5 m, jumping from 0.0053 to 0.0425. This increase is notably greater than that of the other three combinations, with an approximate 88% rise. When accounting only for the variability of the internal friction angle (i.e., with \(Cov_{c}=0\), \(Cov_{\varphi}=0.2\), and \(\rho(c,\,\varphi)=0\)), \(P_{f}\) experiences the second highest increase. In contrast, when solely considering the variability of cohesion (i.e., with \(Cov_{c}=0.3\), \(Cov_{\varphi}=0\), and \(\rho(c,\,\varphi)=0\)), the increase in \(P_{f}\) is almost negligible. In all four combinations, \(F_{s}\) generally trends upward, with the increase never exceeding 2%, highlighting anisotropic dependence on \(L_{v}\).
# A Low Complexity Persistent Reconnaissance Algorithm for FANET
## 3 Algorithm Description  
By taking into consideration the mobility of the monitored targets and the dynamic changes at the scene, we present a description of how to build and run a continuous reconnaissance FANET under problem (5).  
In order to facilitate readers' understanding, we first introduce the principle of the basic PSO algorithm. Then, based on the PSO algorithm, we develop the TARF. Considering the MUs' movement toward the reconnaissance targets and the dynamic change of threat information in real scenarios, the TARF has difficulty meeting real-time requirements. So, inspired by graph edit distance [31], we design the TED to measure the changes in network topology and scenario's threat distribution at different times. Finally, combined with those mentioned above, we develop the TA&CRFO algorithm. This algorithm realizes the dynamic continuous reconnaissance goal of the FANET in a low-complexity way.
# Photovoltaic Cell and Module I-V Characteristic Approximation Using Bezier Curves
## 4 Results
### Data Fitting Using the Least Squares Method  
Data fitting using the least squares method is a standard approach in data analysis [31; 32]. A good overview of curve fitting using Bezier cubic curves in image processing is given by [PERSON] et al. in [33], while [PERSON] et al. [34] extend this method using a genetic algorithm for parameter optimization for Bezier curve fitting. In Section 4.2. we have shown that for the studied PV cell, the best results arise when the \(x\) coordinates of the middle end points are set at \(0.5V_{oc}\) and \(0.75V_{oc}\) respectively. A similar conclusion arises if the least squares method is used for the same cell modeling. Running the least squares method for the MSMD290 AS-36_EU Monocrystalline PV module proved that the minimum error occurs when the control end points are set again at \(0.5V_{oc}\) and \(0.75V_{oc}\) respectively. Table 5 summarizes the data fitting results for the same PV cell used in Section 4.1. and Section 4.2., where the results from the two approaches are very close. The graphical representation of the date fitting is given in Figure 12, where only the endpoints are represented.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Least Squares Method**} & \multicolumn{2}{c}{**Proposed Method**} \\ \hline Point & \(x\) coordinate (V) & \(y\) coordinate (A) & \(x\) coordinate (V) & \(y\) coordinate (A) \\  & & First Bézier cubic curve & & \\ \(P_{00}\) & 0 & 9.207 & 0 & 9.207 \\ \(P_{01}\) & 0.1165 & 9.206 & 0.1165 & 9.206 \\ \(P_{02}\) & 0.2330 & 9.204 & 0.2330 & 9.204 \\ \(P_{03}\) & 0.3495 & 9.202 & 0.3495 & 9.202 \\  & & Second Bézier cubic curve & & \\ \(P_{10}\) & 0.3495 & 9.202 & 0.3495 & 9.202 \\ \(P_{11}\) & 0.4076 & 9.183 & 0.4078 & 9.197 \\ \(P_{12}\) & 0.4658 & 9.245 & 0.4660 & 9.210 \\ \(P_{13}\) & 0.5239 & 9.103 & 0.5243 & 9.074 \\  & & Third Bézier cubic curve & & \\ \(P_{20}\) & 0.5239 & 9.103 & 0.5243 & 9.074 \\ \(P_{21}\) & 0.5823 & 8.9646 & 0.5825 & 8.939 \\ \(P_{22}\) & 0.6406 & 8.6724 & 0.6408 & 8.616 \\ \(P_{23}\) & 0.6990 & 0.004 & 0.6990 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Control point coordinates comparison. On the left, the least squares method is used for computation, on the right the same values as in Table 4 are listed.  
Figure 11: The relative error of our model compared with the actual data. Good performance can be observed in the 0–0.5 V interval and near \(V_{mp}\). Higher errors occur near \(V_{oc}\) for low output currents.  
Figure 13 depicts the relative error of the modeled I-V characteristic compared with the actual data taken from our previous work [12]. In the 0-0.96\(V_{oc}\) range, the relative error is below 2%. Furthermore, above 0.96\(V_{oc}\), the absolute error is less than 66 mA, while the reference short circuit current is 9.207 A.
## 2 Literature Survey
### Routing Protocols
#### 2.3.1 Optimized Link State Routing (OLSR) (Table-Driven)  
OLSR is an optimization of a pure link state algorithm for mobile _Ad hoc_ networks that used the concept of Multi-point Relays (MPR) for forwarding control traffic. It is a proactive link-state routing protocol, which uses hello and topology control (TC) messages to discover and then disseminate link state information. OLSR is intended for diffusion into the entire network. The MPR set is selected such that it covers all nodes that are two hops away. The forwarding path for TC messages is not shared among all nodes, but vary depending on the source, and only a subset of nodes source link state information, and not all links of a node are advertised but only those that represent MPR selections.  
Being a proactive protocol, routes to all destinations within the network are known and maintained before use. Having the routes available within the standard routing table can be useful for some systems and network applications as there is no route discovery delay associated with finding a new route [19].
# An Intelligent Method for C++ Test Case Synthesis Based on a Q-Learning Agent
## 2 Materials and Methods
### Reinforcement Learning Components
\begin{table}
\begin{tabular}{c c} \hline \hline
**RL Component** & **Implementation** \\ \hline Value Function & The agent maintains a Q-table that estimates the expected cumulative reward for each state-action pair (Section 2.3). \\ \hline Reward & After executing a test case, the agent observes a reward computed as a combination of code coverage increase, redundancy reduction, and length penalty. Our reward function is presented in Section 2.5. \\ \hline Learning algorithm & The learning process follows the Q-learning paradigm. The agent maintains a Q-table which stores expected values of actions in given states. At the beginning of training, the Q-table is initialized as an empty map. At each step, the agent selects an action using \(\varepsilon\)-Greedy policy Equation (4), updates the TC, and applies the Bellman equation Equation (1) to update Q-values. The Q-table is updated after every step, ensuring fast feedback propagation. The learning algorithms are presented in Section 2.4. \\ \hline Learning Phases & The Terraining phase. For each TC from original TS, the agent performs imitation learning by replaying the sequence of recorded API calls using Algorithm 1. This allows the initializing of the Q-table with meaningful state-action estimates and capturing common action patterns observed during prior executions. The pretraining procedure is applied sequentially to each test case in the original suite. \\  & The Training phase. After pretraining, the agent performs reinforcement learning using Algorithm 2. For each TC from original TS, a fixed number of training episodes is performed, during which the agent interacts with the environment and updates its Q-function. The same Q-table is retained and reused between different test cases, allowing the agent to transfer learned experience across structurally similar sequences. \\ \hline Invalid Action Handling & When the agent selects an invalid action that leads to an incorrect or semantically incompatible test case, a rollback is performed, and another action is selected. This process is repeated up to a predefined rollback limit (Algorithm 2). \\ \hline Convergence Criteria & Training continues until a predefined number of episodes is reached or until the loss function, defined as the mean squared Bellman error, Equation (8) stabilizes. The total reward \(R_{total}\) is also tracked per episode as an auxiliary signal of learning progress. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 1: Q-learning-based agent reinforcement learning flowchart.
## 2 Proposed Framework
### System Model and Problem Formulation
To provide a quantitative counterpart to the qualitative t-SNE visualization results shown in Figure 1, we compute the silhouette score [22], which evaluates how well each sample is clustered with respect to its assigned label, i.e., modulation type. \[s(i)=\frac{b(i)-a(i)}{\max\{a(i),b(i)\}}, \tag{4}\]  
where \(a(i)\) denotes the average distance from sample \(i\) to all other samples in the same class and \(b(i)\) denotes the minimum average distance from \(i\) to all samples in any other class. The silhouette score \(s(i)\in[-1,1]\), and the overall score is computed as the average over all samples. Values close to 1 indicate well-separated and compact clusters, while values near or below 0 suggest overlapping or poorly separated classes. As shown in Figure 2, we evaluate the silhouette score using three types of features. In Figure 2a, we vary the number of retained singular values while keeping the Hankelized matrix structure to be nearly square, following the definition in (2). On the other hand, in Figure 2b, we fix the number of singular values to use all available values and vary the row size when forming the Hankelized matrix. In both cases, singular values of \(\mathbf{R}_{f}\) (with the FFT-processed signal) consistently yield higher silhouette scores than the other approaches. Notably, as the structure of Hankelized matrix becomes more square-like, the FFT-based features show improved class separability. Therefore, in this work, we follow the Hankelization strategy that attempts to construct a nearly square matrix. Figure 1: Data visualization based on t-SNE analysis. (**a**) Absolute values of signal. (**b**) Singular values of \(\mathbf{R}_{f}\) (with original signal). (**c**) Singular values of \(\mathbf{R}_{f}\) (with FFT-processed signal). Figure 2: Silhouette score according to (**a**) the number of singular values; (**b**) row size for the Hankelized matrix. Based on this observation, we design a NN architecture that takes the singular values of the Hankelized matrix as input and performs modulation classification. The overall architecture of the proposed model is illustrated in Figure 3.