esa-sceva/satcom-chunk-collection huggingface dataset:
###### Abstract  
This study combines Visible Light Communication (VLC) and Artificial Intelligence (AI) to optimize traffic signal control, reduce congestion, and enhance safety. Utilizing existing road infrastructure, VLC technology transmits real-time data on vehicle and pedestrian positions, speeds, and queues. AI agents, powered by Deep Reinforcement Learning (DRL), process these data to manage traffic flows dynamically, applying anti-bottlenecking and rerouting techniques. A global agent coordinates local agents, enabling indirect communication and a unified DRL model that adjusts traffic light phases in real time using a queue/request/response system. A key focus of this work is the design of reward functions for standard and rerouting scenarios. In standard scenarios, the reward function prioritizes wide green bands for vehicles while penalizing pedestrian rule violations, balancing efficiency and safety. In rerouting scenarios, it dynamically prevents queuing spillovers at neighboring intersections, mitigating cascading congestion and ensuring safe, timely pedestrian crossings. Simulation experiments in the SUMO urban mobility simulator and real-world trials validate the system across diverse intersection types, including four-way crossings, T-intersections, and roundabouts. Results show significant reductions in vehicle and pedestrian waiting times, particularly in rerouting scenarios, demonstrating the system's scalability and adaptability. By integrating VLC technology and AI-driven adaptive control, this approach achieves efficient, safe, and flexible traffic management. The proposed system addresses urban mobility challenges effectively, offering a robust solution to modern traffic demands while improving the travel experience for all road users.  
Visible Light Communication (VLC); Artificial Intelligence (AI); Deep Reinforcement Learning (DRL); traffic signal control; traffic management; reward functions; rerouting scenarios; pedestrian safety; congestion reduction; urban mobility; adaptive traffic control +
Footnote †: journal: Applied sciences  
Article
## 3 Data Processing
### Ship Classification
#### 3.4.1 Parameters retrieval  
In this block, the following main steps are required, namely:  
* **Signature isolation**. Ship signature is isolated from the surrounding sea by applying the same method used for land masking. Now, clusters with higher reflectivity pertain to the ship signature, instead of being land. Some morphological constraints are applied to erase clusters of pixels with no relation to the ship signature. The most important ones are the analysis of the relative distance among the different clusters and the checking of the reflectivity values.
* **Heading retrieval**. Ship heading is estimated via the Radon Transform [7]. Qualitatively, this mathematical tool permits the projection of the image into a set of oriented lines and the calculation of the related correlation coefficient (see Figure 5). Therefore, the lines providing the highest correlation values indicate the tentative orientation of the linear features included in  
Figure 4: Snapshots of ship detection performed by SIDECAR for two sections of an ENVISAT image of the Strait of Gibraltar.  
the image. The angular step between successive reference lines is user-fixed and depends on the requested accuracy. A value of one degree is fairly normal.
* **Dimensions retrieval**. Ship dimensions are estimated by counting the number of pixels along the bow-stern (length) and port-starboard (breadth) axis. For making this process easier, the ship signature is rotated so that the bow-stern axis is vertical.
* **Signature division**. In order to evaluate the RCS of the ship signature, the isolated feature is divided into three sections with approximately the same area: bow, middle and stern (see Figure 5). For each one, a mean value is retrieved, which is normalized to the maximum value of the signature. Fuzzy logic is then applied to find which category from the reference ones best fits the reflective and geometrical characteristics of the isolated target. See Table 1 for a summary of the reference categories, which are defined according to official classifications.
## 2 System Description  
Figure 1 shows the two-slot dual-media hybrid communication system considered in this work. In the first time slot, the source (\(S\)) uses the transmit power \(P_{\text{S}}\) to communicate wirelessly with the relay (\(R\)). In the second time slot, \(R\) amplifies and forwards the received data and transmits these to the terminal (\(D\)) through the power line by power \(P_{\text{R}}\).  
The source \(S\) in Figure 1 refers to power equipment or independent smart meters or sensors, such as smart meters in buildings and homes, wireless sensor nodes in underground substations, non-contact infrared temperature cameras in substations, mobile Radio Frequency Identification card readers, etc. This system model combines the advantages of wireless and PLC technologies to provide consumers with the last kilometer access scheme, thereby effectively solving the distance limitation problem of the traditional wireless communication system. It likewise provides the infrastructure for many old buildings and residences that cannot achieve smart home conditions and effectively reduces cost. This system can also connect to the Internet in any room with weak wireless signals and expand network coverage. The system model uses mobile access and dual-hop relay technologies, which meet the practical requirements of flexible access and long-distance reliable transmission in smart grid communication.
## 3 The Proposed Scheme
### Cell Head Election  
In CBDAS, each node maintains a table to keep its own geographic location, cell ID, and the current cell head. Initially, each sensor node computes itself which cell it belongs to using Equation (1). Each sensor node \(s\) will then compete for being a cell head by broadcasting a _Head_electing_ message with its location after waiting for a certain period of time \(t(s)\), which is determined as follows:  
\[t(s)=K\,/\,energy(s) \tag{2}\]  
where \(K\) is a constant set at network initialization stage and \(energy(s)\) is the residual energy of node \(s\). Hence, a node with more residual energy has a higher probability of becoming a cell head. Once a node in the same cell receives _Head_electing_, it will give up its attempt since its residual energy is less. When there are multiple announcements, the node with the smallest location will win the competition. Location \(L_{1}(x_{1},\,y_{1})\) is smaller than \(L_{2}(x_{2},\,y_{2})\) if \(x_{1}\) is smaller than \(x_{2}\) or both \(x_{1}\) and \(x_{2}\) are equal but \(y_{1}\) is smaller than \(y_{2}\). Subsequently, the cell head will broadcast a _Head_confirming_ message with its location to announce its leadership. The ordinary nodes update their own table with the location of the new cell head. As a result, there is one cell head in each cell after election. Since a cell head node consumes much more energy than an ordinary node, our goal is to try to evenly distribute the energy load among the nodes in the network so that no overly used nodes will exhaust energy before the others.
# The Importance of Modeling Path Choice Behavior in the Vehicle Routing Problem
## 3 Path Choice Problem and Assignment (Behavioral Constraint)
### Models
#### 3.2.2 Behavioral Constraint
For this reason, the choice rate (\(p_{k}\)) is a function of the flow vector \(\mathbf{f}\):  
\[p_{k}(t)=v_{uv}(\mathbf{f}(t)) \tag{12}\]  
Given the nodes \(u\) and \(v\) connected by the path \(k\), the PCP defines a perceived set \(I_{uv}\) of alternatives and for each alternative belonging to \(I_{uv}\), a choice rate \(p_{k}\) is evaluated. Considering all the perceived path \(k\) between all nodes \(u\) and \(v\), the rate choice vector (\(\mathbf{p}=[\ \ldots\ \text{,}\text{p}_{uv}\ \text{,}\ldots\ ]^{\prime}\)) is defined, depending on the link flow vector:  
\[\mathbf{p}(t)=v(\mathbf{f}(t)) \tag{13}\]  
More details on the PCP are given in Section 3.2.1. Path cost-demand  
The demand \(d_{uvz}\) is the flow of passenger and freight between \(u\) and \(v\) for the homogeneous class \(z\). The demand model depends on the users' choice (purpose and time of departure and/or arrival, origin and destination, mode and route). The vehicles considered in the VRP are included in the demand. The demand is also evaluated with the discrete choice and utility theory described for the PCP. The travel demand \(d\), like \(p\), also depends on a set of attributes, including the path cost \(g\). Demand-flow  
The flow on each link \(l\) is given by the weighed sum (with weight \(\beta_{n}\)) of the demand flow through the link, considering all the origins \(u\), all the destinations \(v\) and all classes \(z\) of users:  
\[f_{l}(t)=\Sigma_{z}\;\Sigma_{u}\;\Sigma_{v}\;\Sigma_{k,\text{containing\_l}}\; \beta_{z}\bullet p_{k}(t)\bullet d_{uvz} \tag{14}\]  
Note that in \(p_{k}\), the user class must be considered, but it is omitted here for simplicity. Behavioral constraints can be described by the circular dependency between link flows (\(f\)), link costs (\(c\)), path cost (\(g\)), path choice (\(p\)) and demand (\(d\)) that generate the flows (\(f\)). In a dynamic context, within-day and/or day-to-day dynamic approaches can be adopted [27; 36], and the flow vector has a time dependency:  
\[f(t)=\zeta(f(t)) \tag{15}\]  
where \(\zeta(0)\) is the function that describes the dynamic dependency on time. Note that, as already reported for the costs, in the dynamic models, the flow is often considered as the weighted sum of the flow obtained at the same instant \(t\), and the flow obtained in a previous interval \(t\)-\(\tau\). In this specific case, a function further specified below should be adopted: \(\zeta(f(t),f(t\)-\(\tau),t,t\)-\(\tau)\). In the static context, the solution derives from a fixed-point model [27] and \(\zeta(0)\) is the loading flow function.
## 4 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Image**} & \multicolumn{6}{c}{**Baboon**} & \multicolumn{6}{c}{**F16**} \\ \hline \multicolumn{2}{c}{**Prediction Method**} & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**2**} & \multicolumn{2}{c}{**3**} & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**2**} & \multicolumn{2}{c}{**3**} \\ \hline \multicolumn{2}{c}{**Metrics**} & **EC** & **PSNR** & **EC** & **PSNR** & **EC** & **PSNR** & **EC** & **PSNR** & **EC** & **PSNR** & **EC** & **PSNR** \\ \hline \multirow{3}{*}{\(t_{g}=1t_{w}=1\)} & 106,143 & 32.52 & 117,132 & 31.15 & 111,459 & 31.64 & 210,873 & 32.67 & 221,529 & 32.47 & 215,176 & 32.52 \\  & (1, \(-\)1) & 203,076 & 31.91 & 172,179 & 30.59 & 163,764 & 31.09 & 318,078 & 31.43 & 324,075 & 31.11 & 316,520 & 31.23 \\ \hline \multirow{3}{*}{\(t_{g}=3t_{w}=3\)} & 186,306 & 31.63 & 198,483 & 30.35 & 190,475 & 30.84 & 371,144 & 30.93 & 371,924 & 30.58 & 364,017 & 30.72 \\  & (1, \(-\)1) & 203,015 & 31.5 & 211,894 & 30.24 & 202,242 & 30.72 & 398,247 & 30.7 & 396,637 & 30.34 & 387,276 & 30.5 \\ \hline \multirow{3}{*}{\(t_{g}=5t_{w}=5\)} & 207,407 & 31.44 & 218,109 & 30.19 & 208,425 & 30.67 & 411,064 & 30.59 & 407,421 & 30.23 & 398,069 & 30.39 \\The recursive parameters \(t_{g}\) and \(t_{w}\) can also be adjusted for help embedding in different ways. We experimented with \(t_{g}\in\{1,\,2,\,3,\,4,\,5\}\) and \(t_{w}\in\{1,\,2,\,3,\,4,\,5\}\), and after observing the experiment results, we found that the triple-RDH method we proposed is stable in terms of image quality PSNR and can maintain the image quality PSNR above 30 dB. Different combinations of \(t_{g}\) and \(t_{w}\) can help us make changes in different situations. Table 8 shows the performance results of our triple-RDH method in \(t_{g}\in\{1,\,2,\,3,\,4,\,5\}\) and \(t_{w}\in\{1,\,2,\,3,\,4,\,5\}\). We have observed that changing \(t_{g}\) and \(t_{w}\) can help us make finer adjustments to the embedding capacity and image quality, so that they can have more different embedding possibilities for various application needs.
## 8 Fuzzy Incremental-N State Model
\begin{split}\text{S}^{(i_{1}\dots i_{m})}\text{:}\text{ If }z_{1}(k)\text{ is }M^{i_{1}}_{1}\text{ and }\dots\text{ and }z_{m}(k)\text{ is }M^{i_{m}}_{m}\text{, then}\\ \left[\begin{array}{c}y(k+1)\\ \Delta x_{a^{N-1}}(k+1)\end{array}\right]&=\left[\begin{array}{cc}I&C_{a^{ N-1}}A^{(i_{1}\dots i_{m})}_{a^{N-1}}\\ 0&A^{(i_{1}\dots i_{m})}_{a^{N-1}}\end{array}\right]\left[\begin{array}{c}y(k )\\ \Delta x_{a^{N-1}}(k)\end{array}\right]+\left[\begin{array}{c}C_{a^{N-1}}B^{( i_{1}\dots i_{m})}_{a^{N-1}}\\ B^{(i_{1}\dots i_{m-1})}_{a^{N-1}}\end{array}\right]\Delta^{N}u(k)\\ y(k)&=\left[\begin{array}{cc}I&0\end{array}\right]\left[\begin{array}{c}y(k )\\ \Delta x_{a^{N-1}}(k)\end{array}\right]\end{split}  \tag{54}\]From this, we can express its matrix form using the T-S fuzzy model, taking Equation (47) as a reference:  
\[ \begin{split}\mathsf{S}^{(i_{1}\ldots i_{m})}:\text{ If }z_{1}(k)\text{ is }M_{1}^{i_{1}}\text{ and }\ \ldots\text{ and }z_{m}(k)\text{ is }M_{m}^{i_{m}},\text{ then}\\ x_{a^{N}}(k+1)&=A_{a^{N}}^{(i_{1}\ldots i_{m})}x_{a^{N }}(k)+B_{a^{N}}^{(i_{1}\ldots i_{m})}\Delta^{N}u(k)\\ y(k)&=C_{a^{N}}x_{a^{N}}(k)\end{split}  \tag{55}\]  
where \(A_{a^{N}}^{(i_{1}\ldots i_{m})}\in\Re^{((Nq+n)\times(Nq+n))}\), \(B_{a^{N}}^{(i_{1}\ldots i_{m})}\in\Re^{((Nq+n)\times p)}\) and \(C_{a^{N}}\in\Re^{(q\times(Nq+n))}\), and they are calculated using the iterative method presented in Equations (44) and (45). Then, a discrete LQR controller is used, the calculation of which will use the state matrices \(A_{a}^{N}\) and \(B_{a}^{N}\), as well as the matrices \(Q\in\Re^{((Nq+n)\times(Nq+n))}\) and \(R\in\Re^{(p\times p)}\). For this reason, to obtain the controller and the control action, we start from Equation (50), to which the T-S fuzzy model is applied. In this way, the following is obtained:  
\[ \begin{split}\mathsf{S}^{(i_{1}\ldots i_{m})}:\text{ If }z_{1}(k)\text{ is }M_{1}^{i_{1}}\text{ and }\ \ldots\text{ and }z_{m}(k)\text{ is }M_{m}^{i_{m}},\text{ then}\\ \Delta^{N}u(k)&=K^{(i_{1}\ldots i_{m})}(x_{a^{N}}-x_ {a^{N}}(k))\\ \Delta^{(N-1)}u(k)&=\Delta^{(N-1)}u(k-1)+\Delta^{N} u(k)\\ \Delta^{(N-2)}u(k)&=\Delta^{(N-2)}u(k-1)+\Delta^{(N- 1)}u(k)\\ &\quad\vdots\\ \Delta u(k)&=\Delta u(k-1)+\Delta^{2}u(k)\\ u(k)&=u(k-1)+\Delta u(k)\end{split}  \tag{56}\]  
Finally, a fuzzy state observer is used because the state \(\Delta^{N}x(k)\) is not accessible. This observer is obtained by applying the T-S fuzzy model to Equation (52):  
\[ \begin{split}\mathsf{S}^{(i_{1}\ldots i_{m})}:\text{ If }z_{1}(k)\text{ is }M_{1}^{i_{1}}\text{ and }\ \ldots\text{ and }z_{m}(k)\text{ is }M_{m}^{i_{m}},\text{ then}\\ \Delta^{N}x_{e}(k+1)&=A^{(i_{1}\ldots i_{m})}\Delta ^{N}x_{e}(k)+B^{(i_{1}\ldots i_{m})}\Delta^{N}u(k)\\ &+H^{(i_{1}\ldots i_{m})}\Big{(}\Delta^{(N-1)}y(k)-\Delta^{(N-1)} y(k-1)-C\Delta^{N}x_{e}(k)\Big{)}\end{split}  \tag{57}\]  
where \(H^{(i_{1}\ldots i_{m})}\) is calculated using the Equation (34).
## 2 Methodology
### Model Design and Architecture
Its updated equations are  
\[m_{t}=\beta_{1}\cdot m_{t-1}+(1-\beta_{1})\cdot g_{t}, \tag{5}\]  
\[v_{t}=\beta_{2}\cdot v_{t-1}+(1-\beta_{2})\cdot g_{t}^{2}, \tag{6}\]  
\[\theta_{t}=\theta_{t-1}-\alpha\cdot\frac{m_{t}}{\sqrt{v_{t}}+\epsilon} \tag{7}\]  
where \(\theta\) represents the model parameters, \(g_{t}\) is the gradient at time step \(t\), \(m_{t}\) and \(v_{t}\) are the first and second moment estimates, respectively (which are weighted averages of past gradients), \(\beta_{1}\) and \(\beta_{2}\) are exponential decay rates for moment estimates, \(\alpha\) is the learning rate, and \(\epsilon\) is a small constant (typically \(10^{-8}\)) to prevent division by zero, ensuring numerical stability. The command rmsprop uses a moving average of squared gradients, and sgd employs the standard stochastic gradient descent update rule. The choice of optimizer depends on factors like the specific characteristics of the dataset and the desired training efficiency [25]. The depth and width of the network, activation functions, number of epochs, optimizer choice, and mini-batch size collectively impact the ability of the model to capture patterns and its training efficiency [14]. These parameters not only influence accuracy but also significantly impact the training time. In this work, three methods for choosing LSTM architectures are proposed: population-specific, patient-specific, and category-specific.
###### Abstract  
The aim of the study was to determine the correct movement patterns of fencing techniques in wheelchair fencers. Through a comprehensive analysis, the key muscles in the kinematic chain exposed to potential injuries were identified. The study participants were 16 wheelchair fencers, divided into two groups representing two categories of disability: Group A (N = 7) comprising fencers with mild paraplegia, having freedom of movement of the trunk and arms; and Group B (N = 9) comprising fencers with a spinal cord injury and partial paresis of the arms. EMG and an accelerometer were used as the main research tools. The EMG electrodes were placed on the muscles of the sword arm as well as on the left and right sides of the abdomen and torso. The EMG signal was transformed using wavelet analysis, and the muscle activation time and co-activation index (CI) were determined. In Group A fencers, first the back and abdominal muscles were activated, while in Group B, it was the deltoid muscle. The wavelet coherence analysis revealed intermuscular synchronization at 8-20 Hz for Group A fencers and at 5-15 Hz for Group B fencers. In Group A fencers, the co-activation index was 50.94 for the right-side back and abdominal muscles, 50.75 for the ECR-FCR, and 47.99 for the TRI-BC pairs of upper limb muscles. In contrast, Group B fencers demonstrated higher CI values (50.54) only for the postural left-side muscle pairs. Many overload injuries of the shoulder girdle, elbow, postural muscles, spine, and neck have been found to be preventable through modification of current training programs dominated by specialist exercises. Modern wheelchair fencing training should involve neuromuscular coordination and psychomotor exercises. This will facilitate the individualization of training depending on the fencer's degree of disability and training experience.  
wheelchair fencing; EMG; wavelet analysis; muscle co-activation Article
# Joint Optimization of Relay Communication Rates in Clustered Drones under Interference Conditions
## 2 System Model
### Power Transmission Model and Energy Model  
Transmission power is closely related to the communication rate, ensuring reliable data transmission across varying distances and environments, while also being significant for optimizing energy consumption. Hence, a power transmission model is introduced to achieve precise measurement. The corresponding calculation expression is given by the following:  
\[P_{TX}^{uav}=P_{RX}^{uav}-L^{uav}+G_{r}^{uav}+G_{l}^{uav} \tag{10}\]  
In this context, \(P_{RX}^{uav}\) denotes the received signal power, \(P_{TX}^{uav}\) represents the transmitted signal power, \(L^{uav}\) indicates the path loss, \(G_{r}^{uav}\) signifies the receiver antenna gain, and \(G_{t}^{uav}\) signifies the transmitter antenna gain. In a drone cluster relay communication system, the system energy consumption primarily comprises the flight energy consumption and communication energy consumption of the drones. The calculation expression for flight energy consumption is given by the following:  
\[E_{fly}^{uav}=\sum_{k=1}^{K}\frac{mg}{2}(v(k))^{2}\delta_{T} \tag{11}\]  
In this context, \(p^{F/R}(k)\) represents the transmission power of the drone, while the calculation expression for communication energy consumption is given by the following:  
\[E_{c}^{uav}=\sum_{k=1}^{K}P^{F/R}(k)\delta_{T} \tag{12}\]  
In this context, \(v(k)\) represents the drone's flight speed at time \(k\). In summary, the total system energy consumption, \(E^{s}\), can be expressed as follows:  
\[E^{s}=E_{fly}^{uav}+E_{c}^{uav} \tag{13}\]
## 3 Results
### Hardness  
The macro-hardness values in HRC are given in Table 6. The AGI and QTGI specimens had similar macro-hardness in each test group. For AGI specimens, the macro-hardness decreased with increasing austempering temperature because there was more acicular ferrite and stable austenite with high carbon content produced in the matrix than martensite. Likewise, the macro-hardness of QTGI specimens decreased when the tempering temperature was increased due to the decomposition of martensite and growth of cementite phases. In Table 7, the micro-hardness of different regions in the matrix of LHAGI and LHQTGI specimens is reported. For LHAGI specimens, ledeburite in Zone 1 and martensite in Zone 2 had high hardness above 67 HRC. Since the acicular ferrite and stable austenite with high carbon content were tempered in Zone 3, it has a lower hardness than that of the substrate. For LHQTGI specimens, Zone 1 and Zone 2 were similar in hardness with the LHAGI specimens because of the formation of ledeburite and martensite. Since the solid-liquid-solid phase transformation in Zone 1 and solid-solid phase transformation in Zone 2 occurred during the laser-hardening process, the hardness of these two regions did not depend on the original heat treatment designs.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Group 1**} & \multicolumn{2}{c}{**Group 2**} & \multicolumn{2}{c}{**Group 3**} \\ \hline Austempering & \multirow{2}{*}{232 \({}^{\circ}\)C} & \multirow{2}{*}{288 \({}^{\circ}\)C} & \multirow{2}{*}{343 \({}^{\circ}\)C} \\ Temperature & & & & & \\ \hline Macro-Hardness (HRC) & \multirow{2}{*}{
\begin{tabular}{c} AVE \\ 41.6 \\ \end{tabular} } & SD & AVE & SD & AVE & SD \\
27.7 & 0.5 & & & & \\ \hline Tempering Temperature & \multicolumn{2}{c}{316 \({}^{\circ}\)C} & \multicolumn{2}{c}{399 \({}^{\circ}\)C} & \multicolumn{2}{c}{482 \({}^{\circ}\)C} \\ \hline Macro-Hardness (HRC) & \multirow{2}{*}{
\begin{tabular}{c} AVE \\ 41.2 \\ \end{tabular} } & SD & AVE & SD & AVE & SD \\
26.1 & 0.7 & & & & 26.1 & 0.7 \\ \hline \hline \end{tabular}  
* AVE: Average Hardness, SD: Standard Deviation.  
\end{table}
Table 6: Macro-Hardness of AGI and QTGI Specimens with Various Heat Treatment Designs.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature** & \multirow{2}{*}{\(\mathbf{W_{1}}\) (mm)} & \multirow{2}{*}{\(\mathbf{D_{1}}\) (mm)} & \multirow{2}{*}{\(\mathbf{W_{2}}\) (mm)} & \multirow{2}{*}{\(\mathbf{D_{2}}\) (mm)} \\
316 \({}^{\circ}\)C & 2.237 & 0.751 & 3.022 & 1.118 \\
399 \({}^{\circ}\)C & 2.216 & 0.735 & 3.062 & 1.089 \\
482 \({}^{\circ}\)C & 2.219 & 0.728 & 2.947 & 1.082 \\ \hline \hline \end{tabular}  
\end{table}
Table 5: Width and Depth of Laser-Hardened and Heat-Affected Zones for LHQTGI Specimens with Various Tempering Temperatures.
## 3 Effect of Error Sources on Antenna Gain
### The Influence of the Scanning Error on Antenna Gain
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(fld\) & **0.3** & **0.4** & **0.5** & **0.6** & **0.7** & **0.8** & **0.9** & **1.0** \\ \hline lateral offset & \(-\)0.819 & \(-\)0.248 & \(-\)0.086 & \(-\)0.034 & \(-\)0.015 & \(-\)0.007 & \(-\)0.004 & \(-\)0.002 \\ axial offset & \(-\)6.816 & \(-\)3.435 & \(-\)1.794 & \(-\)0.997 & \(-\)0.589 & \(-\)0.366 & \(-\)0.238 & \(-\)0.161 \\ \hline \end{tabular}
\end{table} 
Table 1: Relationships between feed offset error gain loss coefficients \(a_{gl}\) and focal diameter ratios. By fitting the feed offset error curve in Figure 9, the relationship equation between the scanning error and antenna gain loss is obtained as:  
\[\eta=s_{gl}\sigma^{2} \tag{14}\]  
where \(s_{gl}\) is the gain loss coefficient with the values shown in the Table 2 and \(\delta\) is the feed offset error. From Equation (14), it can be seen that the antenna gain loss is proportional to the square of the standard deviation of the scanning error, by which the antenna gain loss caused by the scanning error can be quickly calculated.