esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
### Datasets
#### 2.2.3. Climate Data  
The SPEI characterizes drought conditions by calculating the deviation of the difference between precipitation and potential evapotranspiration from the average state. In this study, we used data from SPEIbase v.2.10 of the Global SPEI database ([[https://spei.csic.es/database.html](https://spei.csic.es/database.html)]([https://spei.csic.es/database.html](https://spei.csic.es/database.html)), accessed on 20 October 2024), which is based on calculations from the climatic research unit (CRU) dataset at the University of East Anglia. Monthly SPEI values for four timescales (SPEI-03, SPEI-06, SPEI-12, and SPEI-24) were extracted for 2000-2020. SPEI-n represents the cumulative water surplus or deficit over the preceding n months, with different timescales capturing varying wet and dry conditions: SPEI-03 reflects short-term changes, SPEI-06 represents mid-term changes, and SPEI-12 and SPEI-24 indicate long-term changes. Thus, the SPEI at different timescales represents drought accumulation of varying durations. While SPEIbase provides robust and standardized drought indicators, uncertainties may arise from its reliance on precipitation and potential evapotranspiration (PET) data. The CRU dataset, which aggregates global climate data from meteorological stations, may exhibit variability in data quality and resolution, particularly in sparsely monitored regions like Xinjiang. Additionally, PET in SPEI is often calculated using temperature-based methods (e.g., Thornthwaite), which may not fully account for other key factors such as wind speed, solar radiation, and humidity.
## 3 Results and Discussion
### Additional Dataset  
Additional KOMPSAT-3 and KOMPSAT-3A data with different phenological properties are added in order to verify the robustness of the proposed method. The experimental area is Seoul, which mainly contains built-up areas and forests. KOMPSAT-3 and KOMPSAT-3A have the same spectral response functions and practical spectral ranges as the bands that are affected by atmospheric constituents and the surface, where the main difference between them is only the spatial resolution [53]. Therefore, the experiment is performed by resampling KOMPSAT-3 at 2.2 m, which is the same resolution as KOMPSAT-3A, and the size of the images is set to \(2000\times 1500\) pixels. Figure 12 provides the bitemporal images and normalization results. From a visual inspection, it can be seen that the normalization of the radiometric and phenological properties are properly performed. In particular, the spectral characteristics of the forest area are normalized to be the same as those of the reference image. Furthermore, as shown in Table 5, the performance for the additional area is similar to that in the previous results. In other words, it can be confirmed that the proposed method can also achieve satisfactory results with the additional dataset.
## 2 Materials and Methods
### Development of Calibration Models and Validation  
The dataset obtained with the calibration samples was employed to develop PLS (partial least squares) models for moisture and oil content in pomace. These models were obtained by considering the overall spectral interval (850-1049 nm). The 87 spectra of pomace in the dataset were randomly split into a training set (80% of the dataset) and a test set (20% of the dataset).  
The capability of the model to predict moisture and oil content in pomace was evaluated based on root mean square error of cross-calibration (RSMECV), root mean square error of prediction (RMSEP), and coefficient of determination (R\({}^{2}\)) for calibration and prediction.  
To evaluate the performance of the models, the BIAS and SLOPE parameters were also calculated.  
Bias is the difference between the mean of one dataset and the mean of the other. Typically, bias is used to describe the difference between reference values and predicted values for a sample set. The value of bias is a measure of systematic errors occur during the calibration--when bias is 0, systematic errors are absent.  
The slope of the model shows its symmetry: when a new model is calculated, it is normally perfectly symmetrical. The slope is 1, and the bias corresponds to the intercept, which is 0.  
Considering that the outliers have a strong influence on the model's performance, these were identified and removed from the calibration set. In this study, outliers were identified and eliminated from the dataset when the difference between their actual and predicted values exceeded two times the RMSECV [39].  
After outlier elimination, PCA was applied to the spectral data on both oil and water content in the pomace to obtain an overview of variation among samples. The data matrix was mean centered before PCA, and cumulative percent explained variance was used to choose the optimal number of principal components (PCs). The explained variance in a PC is the ratio (expressed as a percentage) between the variance in that PC and the total variance.  
Multivariate analyses presented in this work were performed by using FOSS Calibrator version 3.5 by FOSS\({}^{\text{tm}}\).
## 4 Micro-Vibration Suppression and Image Stabilization Principle
### The Second-Order Vibration Suppression
As shown in Figure 13, the bandwidth of the disturbance attenuation function \(S_{x}\) and \(S_{y}\) are 18.7 Hz and 22.1 Hz, respectively. To evaluate the impact of controller parameters on the disturbance rejection performance related to different operating conditions of the FSM, Bode response curves corresponding to five different gain values K are plotted, as shown in Figure 14. A comparative analysis reveals that as the gain K increases, the control bandwidth correspondingly expands. Moreover, when K = 74,750, the corresponding control bandwidth reaches its maximum while still satisfying the stability margin requirements. Furthermore, to analyze the disturbance rejection characteristics of the FSM in the time domain, a sinusoidal excitation with an amplitude of A = 0.01 and a frequency of \(f\) = 2 Hz is used to simulate the micro-vibration disturbance input. The corresponding closed-loop response curve is obtained, as shown in Figure 14b. Under the FSM closed-loop condition, the micro-vibration disturbance input is significantly attenuated, which corresponds to the Bode response curves in Figure 14a. Figure 11: The LOS jitter and image stabilization mechanism of the optical payload. (**a**) Comparison before and after LOS jitter. (**b**) Comparison between the open-loop and closed-loop systems. (**c**) Control block diagram of the LOS stabilization. Figure 12.0 Disturbance suppression curve. (**a**) Bode plots with different gains and (**b**) the time domain response while K = 74,750. Figure 12.1 Frequency response and fitting of the FSM around the (**a**) X-axis and (**b**) Y-axis. Figure 12.2 Bode response of the sensitivity function around the (**a**) X-axis and (**b**) Y-axis.
# Clustering Analysis of Wind Turbine Alarm Sequences Based on Domain Knowledge-Fused Word2 vec
## 5 Results and Discussion
### Experiment Settings
#### 5.1.2 Model Parameters  
There are three key parameters in the proposed DK-Word2 vec: the vector dimension \(d\), the semantic window length \(w\), and the weight \(\lambda\) of the category loss. Owing to the relatively small size of the alarm corpus compared to natural language corpora, a modest value of 50 is chosen for the vector dimension. The semantic window length \(w\) and the weight \(\lambda\) will be selected using the labeled alarm sequences based on the external evaluation metrics proposed later.  
After obtaining the vector representations of alarms, alarm sequences are represented by vector sequences. Subsequently, the K-means is applied to cluster these alarm sequences. The distance measures employed during K-means clustering include WMD and WRD. For comparison purposes, we also compute the clustering results using AVD.
## 2 Mathematical Formulation
### Set of Constraints  
The set of constraints in the problem of the optimal placement and sizing of PV sources in grid-connected distribution networks includes active and reactive power balance constraints, voltage regulation bounds, and devices capabilities, among other constraints [19]. The complete list of constraints is listed from Equations (4)-(11) [6]:  
\[p_{i,h}^{cg}+p_{i}^{pv}G_{h}^{pv}-P_{i,h}^{d}=v_{i,h}\sum_{j\in \mathcal{N}}Y_{ij}v_{j,h}\cos\left(\theta_{i,h}-\theta_{j,h}-\varphi_{ij} \right),\ \{\forall i\in\mathcal{N},\ \forall h\in\mathcal{H}\}, \tag{4}\] \[q_{i,h}^{cg}-Q_{i,h}^{d}=v_{i,h}\sum_{j\in\mathcal{N}}Y_{ij}v_{j, h}\sin\left(\theta_{i,h}-\theta_{j,h}-\varphi_{ij}\right),\ \{\forall i\in\mathcal{N},\ \forall h\in \mathcal{H}\},\] (5) \[p_{i}^{cg,\min}\leq p_{i,h}^{cg}\leq p_{i}^{cg,\max},\ \{\forall i\in \mathcal{N},\ \forall h\in\mathcal{H}\}\] (6) \[q_{i}^{cg,\min}\leq q_{i,h}^{cg}\leq q_{i}^{cg,\max},\ \{\forall i\in \mathcal{N},\ \forall h\in\mathcal{H}\}\] (7) \[x_{i}p_{i}^{pv,\min}\leq p_{i}^{pv}\leq x_{i}p_{i}^{pv,\max},\ \{ \forall i\in\mathcal{N}\},\] (8) \[v_{i}^{\min}\leq v_{i,h}\leq v_{i}^{\max},\ \{\forall i\in \mathcal{N},\ \forall h\in\mathcal{H}\}\] (9) \[\sum_{i\in\mathcal{N}}x_{i}\leq N_{pv}^{aaa},\] (10) \[x_{i}\in\{0,1\},\ \{\forall i\in\mathcal{N}\}, \tag{11}\]  
where \(p_{i,h}^{d}\) and \(Q_{i,h}^{d}\) are the active and reactive power demands at node \(i\) during the period of time \(h\); \(q_{i,h}^{cg}\) is the reactive power injection in the conventional source connected to node \(i\) during the period of time \(h\); \(v_{i,h}\) and \(v_{j,h}\) are the voltage magnitudes at nodes \(i\) and \(j\) in the period of time \(h\), respectively; \(Y_{ij}\) is the magnitude of the admittance that relates nodes \(i\) and \(j\) which has an angle \(\varphi_{ij}\); \(\theta_{i,h}\) and \(\theta_{j,h}\) are the voltage angle values in nodes\(i\) and \(j\) during each period of time; \(p_{i}^{cg,\text{min}}\) and \(p_{i}^{cg,\text{max}}\) are the active generation bounds associated with the conventional generator connected to node \(i\); and \(q_{i}^{cg,\text{min}}\) and \(q_{i}^{cg,\text{max}}\) are the corresponding reactive power generation bounds, respectively. \(x_{i}\) is the binary variable associated with the installation (\(x_{i}=1\)) or not (\(x_{i}=0\)) of a PV source at node \(i\); \(p_{i}^{pv,\text{min}}\) and \(p_{i}^{pv,\text{max}}\) are the minimum and maximum sizes allowed for the PV integration in the distribution grid. \(\overset{\text{min}}{i}\) and \(\overset{\text{max}}{i}\) represent the minimum and maximum voltage regulation bounds allowed at node \(i\); and \(N_{pv}^{avg}\) is a constant parameter associated with the maximum number of PV sources available for installation along with the distribution grid.
# A 200-MS/s 10-Bit SAR ADC Applied in WLAN Systems
## 3 Circuit Implementation
### Cdc  
In general, the CDAC occupies a significant portion of the ADC chip area. As described before, the 4-reference voltage switching strategy can significantly reduce the required number of unit capacitors in the CDAC, thereby greatly reducing the area of the CDAC. In addition, combining this approach with a binary-scaled recombination redundancy design can greatly relax the design requirements for the input buffer and RVB.  
Based on the CDAC scheme shown in Figure 3, Table 1 lists the weight scheme and corresponding redundancy arrangement in this design.  
The equivalent weight is calculated based on the charge conservation principle, where the equivalent weight is equal to the product of bit weight and 8\(\times\)Reference. The range of redundancy indicates the maximum tolerable error in the current bit.  
Due to the fact that the MSB capacitor switching induces a large disturbance on the VREF, which is the main error source of incomplete settling in CDAC, most of the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bit-Cycling** & **Bit Weight** & \begin{tabular}{c} **Reference** \\ **(VREF)** \\ \end{tabular} & \
\begin{tabular}{c} **Equivalent** \\ **Weight** \\ \end{tabular} &
\begin{tabular}{c} **Redundancy** \\ **(LSBs)** \\ \end{tabular} \\ \hline
1 & 48 & 1 & 384 & 256 \\
2 & 32 & 1 & 256 & 128 \\
3 & 16 & 1 & 128 & 128 \\
4 & 14 & 1 & 112 & 32 \\
5 & 8 & 1 & 64 & 16 \\
6 & 4 & 1 & 32 & 16 \\
7 & 2 & 1 & 16 & 16 \\
8 & 2 & 1 & 16 & 0 \\
9 & 2 & 0.5 & 8 & 0 \\
10 & 2 & 0.25 & 4 & 0 \\
11 & 2 & 0.125 & 2 & 0 \\
12 & 1 & 0.125 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Redundancy arrangement in this design.  
Figure 12: The comparator input voltage with/without a kickback cancellation circuit.  
redundancy range is arranged for the MSB decision steps. The unit capacitor is a high-density and highly matched MOM capacitor provided by the foundry. The total sampling capacitance is 410 fF, where the capacitance in the main DAC is about 340 fF and the parasitic capacitance is 70 fF.
# FedCrow: Federated-Learning-Based Data Privacy Preservation in Crowd Sensing
## 4 Evaluation
### Experimental Environment and Parameter Settings  
**The crowd-sensing environment**: adopted a constructed crowd-sensing federated-learning framework and simulated the distribution of crowd-sensing devices with 100 randomly generated coordinate nodes. On average, each client had 200 sample data points.  
**Federated-learning environment**: An artificial intelligence model, which was built using Keras, consisted of four fully connected layers to form a neural network model. The data features consisted of 30 attributes, hence the input x was of size 30. The four-layer neural network was composed of 32, 16, 8, and 1 neurons. The data used in this experiment were from the Credit Card Fraud Detection dataset (from Kaggle), which contains records of credit card transactions made by European cardholders over two days in September 2013. The dataset consists of 285,299 entries, with 284,807 transactions and 492 suspected cases of fraud. The machine learning model in this experiment was built using Keras, and employed four fully connected layers to construct the neural network model structure illustrated in Figure 3.  
Figure 3: The neural network model composed of four fully connected layers.  
**Server environment:** processor, AMD 5800H (Asus, Kowloon, Hong Kong, China); graphics card, NVIDIA RTX 3060 (NVIDIA, Santa Clara, CA, USA); 16 GB RAM; and 1 TB hard drive.  
**Client environment:** The client utilized both a Lenovo Legion laptop (Lenovo, Beijing, China) and a mobile emulator. The mobile emulator was operated using a Nox App Player (Nox Limited, Hong Kong, China), with an Android version of 7.1.2, 4 GB of RAM, and 128 GB of storage capacity. Within the Android environment, Python runtime was implemented using qpython3. The QPython 3.9.1 software had a size of 23.1 MB. Communication was established using IP addresses and port numbers.  
**Encryption parameters and algorithm:** with a dataset size of 285,299 entries, which is relatively large, this experiment utilized differential privacy algorithms to encrypt the data during transmission.  
**Simulated attack types:** data poisoning [38], model attacks [39], and inference attacks [40; 41].  
**User types:** this included normal users, unreliable users, and malicious users.
## 3 Results and Discussion
### Evaluation of the Hole Quality  
#### 3.2.1 Analyses of Drilled-Hole Images  
In this study, the quality of holes in terms of burrs was examined using a digital optical microscope with a scale of 1 mm. These burrs on the entrance and exit side of holes under selected drilling parameters using uncoated and coated drills, i.e., TiN and TiN, are shown in Figures 3-5.  
Figure 3: Hole images from uncoated carbide drills [18].  
Figure 4: Hole images from TiN coated carbide drills.  
The visual and microscopic inspections of hole quality showed that more burrs were generated at the entrance of holes compared to the exit side, irrespective of the coatings of the drills. Furthermore, the burrs at both sides of the holes increased with the increase in spindle speed and feed. However, the feed was found to be the dominant factor in increasing the burrs while the increase in spindle speed did not produce any considerable burrs. This is likely expected due to the effect of the thrust force where the feed was found to be more influential compared to the spindle speed. Figures 3-5 also show that the uncoated drill produces holes with less burr formation compared with the TiN and TiN coated drills. However, in comparison to TiN, the burrs formed by the TiN coated drill were found to be less.
## 5 Experimental Verification
### Analysis of the Data Transfer Rate  
Equation (20) shows that in order to increase the data transfer rate, we can either increase the conventional data transfer rate or the conduction duty cycle of \(S_{d}\). Figure 14a shows the case by increasing the conventional data transfer rate, while Figure 14b indicates the case by increasing the conduction duty cycle of \(S_{d}\).  
Figure 14: Increasing of the data transfer rate by: (**a**) increasing the conventional data transfer rate; (**b**) increasing conduction duty cycle of \(S_{d}\).  
Figure 13: Comparison between the proposed and traditional data transfer: (**a**) proposed method; (**b**) traditional circuit.  
Both Figure 14a,b show the output voltage is controlled to be around 16 V. In addition, the data transfer rate can be increased through these two methods, i.e. by increasing the conventional data transfer rate or increasing the conduction duty cycle of \(S_{d}\).
# In-Situ Monitoring and Analysis of the Fitting Corrosion of Carbon Steel by Acoustic Emission
## Materials and Methods
### Electrochemical Measurements and Corrosion Morphology Observations  
Open circuit potential (OCP) was measured by a CHI4 electrochemical workstation of Wuhan Corrtest Instruments Corp. LTD in China. Specimens of Q235 carbon steel were used as the work electrodes. A saturated calomel electrode (SCE) was used as the reference electrode. The corrosion morphologies were recorded by an industrial digital camera (Yilong Electronic Technology Co., Ltd., Shenzhen, China, 5 mega-pixel) during the experiment and a scanning electron microscope (SEM, ZEISS, EVO, MA 15) after the experiments. The OCP and AE measurements were carried out and recorded simultaneously.
## Appendix A  
In this appendix we present the basic steps needed for obtaining an analytical expression for \(\sigma^{(1)}(\omega,\tau)\) [Equation (12)]. First, we require the functions \(f^{mn}_{fxy0}(t)\) introduced in Equation (18). Neglecting initial-state dressing, they are given in Table 1 for the dressing pulse in Equation (19).  
Here, we made the choice \(t_{0}\rightarrow-\infty\) when evaluating Equation (10) using Equations (13) and (17). The energy differences \(\Delta^{(n)}_{x\pm}\) appearing in Table 1 are \[\Delta_{x}^{(0)} = E_{x}-E_{0}; \tag{10}\] \[\Delta_{x\pm}^{(1)} = E_{x}-E_{0}\pm\omega_{d};\] (11) \[\Delta_{x\pm}^{(2)} = E_{x}-E_{0}\pm 2\omega_{d}. \tag{12}\]  
The other quantities used in Table 11 are listed in the following:  
\[B_{1} = \frac{A_{d}}{2}\frac{1}{i(E_{f}-E_{x}+\omega_{d})}; \tag{13}\] \[B_{2} = \frac{A_{d}}{2}\frac{1}{i(E_{f}-E_{x}-\omega_{d})}; \tag{14}\]  
\[A(t)=\frac{A_{d}}{2}f_{1}(E_{f}-E_{x},\omega_{d},t), \tag{15}\]  
where  
\[f_{1}(x,\omega,t)=\frac{\mathrm{e}^{i(x+\omega)t}}{i(x+\omega)}-\frac{\mathrm{ e}^{i(x-\omega)t}}{i(x-\omega)}; \tag{16}\]  
\[D_{1}=-\frac{A_{d}^{2}}{4}\frac{1}{(E_{f}-E_{x}+\omega_{d})(E_{f}-E_{y}+2 \omega_{d})}; \tag{17}\]  
\[D_{2}=-\frac{A_{d}^{2}}{4}\Bigg{(}\frac{1}{(E_{f}-E_{x}+\omega_{d})(E_{f}-E_{ y})}+\frac{1}{(E_{f}-E_{x}-\omega_{d})(E_{f}-E_{y})}\Bigg{)}; \tag{18}\]  
\[D_{3}=-\frac{A_{d}^{2}}{4}\frac{1}{(E_{f}-E_{x}-\omega_{d})(E_{f}-E_{y}-2 \omega_{d})}; \tag{19}\]  
\[D_{4} = \frac{A_{d}^{2}}{4}\frac{f_{1}(E_{f}-E_{x},\omega_{d},t_{1})}{i(E _{x}-E_{y}+\omega_{d})}; \tag{20}\] \[D_{5} = \frac{A_{d}^{2}}{4}\frac{f_{1}(E_{f}-E_{x},\omega_{d},t_{1})}{i(E _{x}-E_{y}-\omega_{d})}; \tag{21}\]  
\[C(t)=\ D_{1}e^{i(E_{f}-E_{y}+2\omega_{d})t}-D_{2}e^{i(E_{f}-E_{y})t}+D_{3}e^{ i(E_{f}-E_{y}-2\omega_{d})t}-\frac{A_{d}^{2}}{4}f_{1}(E_{f}-E_{x},\omega_{d},t )f_{1}(E_{x}-E_{y},\omega_{d},t). \tag{22}\]  
To construct the XUV one-photon cross-section [Equation (20)], we further require \(\tilde{F}_{0f}(\omega,\tau)\) [Equation (21)]. From Section 2.2 we may conclude that the perturbative expansion of \(F_{0f}(t)\) is given by  
\[F_{0f}(t) = \big{[}\,f_{0f}^{00}(t)\big{]}^{*}e^{-\frac{\Gamma_{f}}{2}t} \langle\Psi_{0}|\hat{Z}|\Psi_{f}\rangle\] \[+\sum_{x}\big{[}\,f_{f\times 0}^{10}(t)\big{]}^{*}e^{-\frac{ \Gamma_{f}}{2}t}\langle\Psi_{0}|\hat{Z}|\Psi_{x}\rangle\langle\Psi_{x}|\hat{Z }|\Psi_{f}\rangle\] \[+\sum_{xy}\big{[}\,f_{f\times 0}^{20}(t)\big{]}^{*}e^{-\frac{ \Gamma_{f}}{2}t}\langle\Psi_{0}|\hat{Z}|\Psi_{y}\rangle\langle\Psi_{y}|\hat{Z }|\Psi_{x}\rangle\langle\Psi_{x}|\hat{Z}|\Psi_{f}\rangle+...\]  
The function \(\tilde{F}_{0f}(\omega,\tau)\) has the same structure, but with the functions \(\big{[}\,f_{f\times 0}^{mn}(t)\big{]}^{*}e^{-\frac{\Gamma_{f}}{2}t}\) replaced with  
\[\tilde{f}_{0y\times f}^{nm}(\omega,\tau)=\int\limits_{\tau}^{\infty}dt\big{[} \,f_{f\times 0}^{mn}(t)\big{]}^{*}e^{-\frac{\Gamma_{f}}{2}t}e^{i\omega t}. \tag{23}\]
## 3 Heuristics Method to Calculate the Global Fitness of a Solution
### Computation of the Start Time of Observation  
According to Algorithm CNV, given the start time \(t_{gu}\) of the last target \(g_{u}\) in \(\mathbf{b}_{s}\) and a target \(h\
otin\mathbf{a}_{s}\setminus\mathbf{b}_{s}\), the feasible non-conflict VTWs \(\mathbf{V}_{sh}(\mathbf{b}_{s})\) can be obtained. Based on the idea of dichotomy, we develop Algorithm 2, namely _compute start-observing time_ (CST), to compute the start time \(t_{h}\) of the observation for \(h\) such that the VTW Constraints (11) and (12), as well as the transition time Constraint (13), are satisfied.  
In Algorithm CST, the Boolean variable \(Flag=\text{True}\) represents that we can find the start time \(t_{h}\) within one non-conflict VTW in \(\mathbf{V}_{sh}(\mathbf{b}_{s})\) while satisfying the Constraints (11)-(13). Initially, we set \(Flag\)alsease and \(t_{h}=0\). This algorithm first tries to find a VTW [\(\varpi\), \(\varphi\)] \(\in\mathbf{V}_{sh}(\mathbf{b}_{s})\) so that  
\[trans(t_{gu}\), \(-\varphi\) \(-\)\(d_{h})+t_{gu}+d_{gu}\leq-\varphi\) \(-\)\(d_{h}\)  
Satisfying the above inequity implies that the VTW and transition-time constraint are met if we set \(t_{h}=-\varphi\) \(-\)\(d_{h}\). In this case, let \(Flag=\text{True}\) and we execute a loop (Lines 10-21) to further find a sufficiently small number \(x\in[\varpi\), \(-\)\(\varphi\) \(-\)\(d_{h}]\) which satisfies the constraint \(trans(t_{gu}\), \(x)+t_{gu}+d_{gu}\leq x\) based on the dichotomy theory. Finally, if \(Flag=\text{True}\), let \(t_{h}=x\), otherwise \(t_{h}=0\).  
```
1:AEGOS \(s\), \(t_{gu}\), \(h\in\mathbf{a}_{s}\)\(\setminus\)\(\mathbf{b}_{s}\), and \(\mathbf{V}_{sh}(\mathbf{b}_{s})\);
2:\(t_{h}\);
3: Let \(Flag=\) False and \(t_{h}=0\);
4:for each VTW \([\alpha,\ \varphi]\in\mathbf{V}_{sh}(\mathbf{b}_{s})\)
5:if\(trans(t_{gu},\ -\varphi-d_{h})+t_{gu}+d_{gu}\leq-\varphi-d_{h}\)
6: Set \(x=-\varphi-d_{h}\), \(y=\varpi\);
7: Set \(x^{\prime}=(x+y)/2\);
8: Set Flag = True;
9:break;
10:end
11:while(Flag)
12:if\(trans(t_{gu},\ x^{\prime})+t_{gu}+d_{gu}\leq x^{\prime}\)
13:\(x=x^{\prime}\);
14:\(x^{\prime}=(x^{\prime}+y)/2\);
15:else
16:\(y=x^{\prime}\);
17:\(x^{\prime}=(x+y)/2\);
18:end
19:if\(-x-x^{\prime}\leq 0.1\);
20:break;
21:end
22:if\(Flag=\) True
23: Set \(t_{h}=x\);
24:end
25:Output \(t_{h}\);
```  
**Algorithm 2**Compute start-observing time (CST).