esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Constrained Weighted Least-Squares  
In this section, the CwLS algorithm is developed for the considered passive target localization problem. Therefore, the nonlinear TDOA equations can be transformed into a set of linear equations, by introducing the variable \(R^{r}=\|x_{r}-x\|\), neglecting \(n_{i}^{2}\) and squaring the Equation (5) giving the following expression  
\[-2\big{(}\mathbf{x}_{r}-\mathbf{x}_{i}^{t}\big{)}^{T}\mathbf{x}-2\bar{r}_{i}R^ {r}+\bar{r}_{i}^{2}+\|\mathbf{x}_{r}\|^{2}-\big{\|}\mathbf{x}_{i}^{t}\big{\|}^{ 2}=2(\bar{r}_{i}-R^{r})n_{i},\quad\forall i\in\{1,2,...,N\}, \tag{12}\]  
If we write \(\boldsymbol{\theta}\), as  
\[\boldsymbol{\theta}=\big{[} \begin{array}{cc}\mathbf{x}&R^{r}\end{array}  \big{]}^{T}, \tag{13}\]  
then Equation (12) is converted to matrix form  
\[\mathbf{b}-\mathbf{A}\boldsymbol{\theta}=\mathbf{m}, \tag{14}\]  
where  
\[\mathbf{A}=2 \begin{bmatrix}x_{r}-x_{1}^{t}&y_{r}-y_{1}^{r}&\tilde{r}_{1}\\ x_{r}-x_{2}^{t}&y_{r}-y_{2}^{r}&\tilde{r}_{2}\\ \vdots&\vdots&\vdots\\ x_{r}-x_{N}^{t}&y_{r}-y_{N}^{r}&\tilde{r}_{N}\end{bmatrix} , \tag{15}\]  
\[\mathbf{b}= \begin{bmatrix}\bar{r}_{1}^{2}+x_{r}^{2}+y_{r}^{2}-\big{(}x_{1}^{t }\big{)}^{2}-\big{(}y_{1}^{t}\big{)}^{2}\\ \bar{r}_{2}^{2}+x_{r}^{2}+y_{r}^{2}-\big{(}x_{2}^{t}\big{)}^{2}-\big{(}y_{2}^{t }\big{)}^{2}\\ \vdots\\ \bar{r}_{N}^{2}+x_{r}^{2}+y_{r}^{2}-\big{(}x_{N}^{t}\big{)}^{2}-\big{(}y_{N}^{ t}\big{)}^{2}\end{bmatrix} , \tag{16}\]  
Figure 2: The plot of the considered ML objective function \(J_{ML}(\mathbf{x})\). and  
\[\mathbf{m}=2 \begin{bmatrix}(\tilde{r}_{1}-R^{r})n_{1}\\ (\tilde{r}_{2}-R^{r})n_{2}\\ \vdots\\ (\tilde{r}_{N}-R^{r})n_{N}\end{bmatrix} . \tag{17}\]  
The following constrained optimization problem can be used to estimate the coordinates of the target in the presence of measurement errors  
\[\min_{\mathbf{\theta}}J(\mathbf{\theta})=\min_{\mathbf{\theta}}{(\mathbf{b}- \mathbf{A}\mathbf{\theta})^{T}\mathbf{W}(\mathbf{b}-\mathbf{A}\mathbf{\theta})} \tag{18}\] \[s.t.\qquad\mathbf{\theta}^{T}\mathbf{S}\mathbf{\theta}=0, \tag{19}\]  
where \(\mathbf{W}\in R^{N\times N}\) is a matrix of weights that is symmetric, \(\mathbf{S}=\text{diag}\{1,1,-1\}\) is a diagonal and orthonormal matrix. It is possible to approximatively determine the elements of matrix of weights under conditions of sufficiently low measurement noise, as  
\[\mathbf{W}=\left[E\Big{\{}\mathbf{mm}^{T}\Big{\}}\right]^{-1}=\Big{(}\mathbf{ D}^{T}\mathbf{C}\mathbf{D}\Big{)}^{-1}, \tag{20}\]  
where  
\[\mathbf{D}=\text{diag}\{2(\tilde{r}_{1}-R^{r}),2(\tilde{r}_{2}-R^{r}),\dots,2 (\tilde{r}_{N}-R^{r})\}, \tag{21}\]  
The optimization problem (18) is a quadratically constrained quadratic program (QCQP), which can be solved using the Lagrange multiplier method. Therefore, the Lagrangian function of the optimization problem (18) is given by  
\[L(\mathbf{\theta},\lambda)=(\mathbf{b}-\mathbf{A}\mathbf{\theta})^{T}W(\mathbf{b}- \mathbf{A}\mathbf{\theta})+\lambda\mathbf{\theta}^{T}\mathbf{S}\mathbf{\theta}, \tag{22}\]  
where \(\lambda\) is the Lagrange multiplier.
###### Abstract  
Patients who are suffering from neuromuscular disorders or injuries that impair motor control need to undergo rehabilitation to regain mobility. Gait training is commonly prescribed to patients to regain muscle memory. Automated-walking training devices were created to aid this process; while these devices establish accurate ankle-path trajectories, the knee and hip movements are inaccurate. In this work, a redesign of the leg assembly in a multi-purpose rehabilitation robotic device (RoboREHAB) was explored to improve hip- and knee-movement accuracy by adding an extra link and rollers to the assembly. Motion analysis was employed to test feasibility, reinforcement learning was utilized to train the new leg assembly to walk, and the joint motions achieved with the redesign were compared to those achieved by motion-capture (mocap) data. As a key result, the motion analysis showed an improvement in the knee- and hip-path trajectories due to the added roller/joint segment. The redesigned leg assembly, under the reinforcement-learning policy, showed a 5% deviation from the motion-capture joint trajectories with a maximum deviation of 51.177 mm but maintained a similar profile to the mocap trajectory data. This is an improvement over the original two-segment design, which achieved a maximum deviation of 72.084 mm. These results in the knee- and hip-joint movements more closely reflect the mocap and motion-analysis results, validating the redesign and opening it up to further experimentation and technical improvement.  
gait motion; leg-assembly design; motion capture (mocap); reinforcement learning; multi-purpose rehabilitation robotic device (RoboREHAB); feasibility analysis +
Footnote †: journal: Applied Sciences
# Application of the Residue Method in Steam Superheater Fault Detection
## 2 Methods of Fault Detection
### Fault Detection Using the Residual Generator  
The primary residual \(r(s)\) is defined as the difference between the process output \(yr(s)\) and the model output \(ym(s)\). Ideally, the residuals may be affected by defects. Often,  
Figure 2: Additive (**a**) and multiplicative (**b**) faults.  
disturbances, noise, or modeling errors will cause specific components of the residual vector r(s) to become non-zero, which will be used in fault detection.  
The residual generator must be designed to be unaffected by variations caused by disturbances, noise, or modeling errors defined in the literature as problem inputs, making it robust against them.  
It must have robust detection properties and be so designed as to ensure fault location. Localization, however, always requires a set of residuals. The residue set must have distinctive properties and unique characteristics of particular defects to facilitate defect localization.  
The design of residue sets for this purpose considers intensified residues. There are two higher fundamental approaches to residuals: structured and directional residuals.  
Structured residuals. Structured residues are set up so that each residue corresponds to a different subset of defects and is independent of the others; when a defect occurs, some residues may respond, and others may not.  
We define the primary residues \(r(s)=y_{m}(s)-y_{r}(s)\) and the structured residues \(R(s)=W(s)\times r(s)\) as:  
\[r(s)=\begin{bmatrix}r_{1}(s)\\ r_{2}(s)\end{bmatrix},\ R(s)=\begin{bmatrix}R_{1}(s)\\ R_{2}(s)\end{bmatrix}. \tag{14}\]  
The primary residual \(R(s)\) is obtained by multiplying the primary residual \(r(s)\) by a weighting matrix \(W(s)\) that provides decoupling concerning the defects. The new residual \(R(s)\) will be of the form  
\[\text{R(s)}=\text{W(s)}r(s)=Z(s)\text{H}_{\text{d}}(s), \tag{15}\]  
where Z(s) is a diagonal matrix of the form:  
\[Z(s)=\begin{bmatrix}Z_{11}(s)&0\\ 0&Z_{22}(s)\end{bmatrix}, \tag{16}\]  
and the weighting matrix W(s) is of the form:  
\[\text{W(s)}=Z(s)[\text{H}_{\text{d}}(s)]^{-1}. \tag{17}\]  
Directional residues. Directional residuals are designed such that, in response to a particular fault, the residual vector is confined to a fault-specific straight line at any time, including the transient regime.  
With directional residuals, fault localization determines which predefined fault direction the observed residual vector is attached. A set in which each residual corresponds to a single defect is structured and directional. Such sets are essential in locating multiple defects and can serve as a common basis for structural or directional design. These residuals are also called diagonal residuals or primary residuals.
# Optimal Strategy to Select Load Identification Features by Using a Particle Resampling Algorithm
## 3 Experiments and Results
### Validated on \(Redd\)
#### 3.2.1 Event Detection  
This part presents the performance of the proposed bilateral CUSUM event detection method and makes a comparison with the original CUSUM method over the REDD. In this work, the confusion matrix-based metrics are taken as the evaluation metric [25]. So, the detection events were divided into four categories: true positive (TP), true negative (TN), false positive (PF), and false negative (FN). Only TP, FP, and FN are considered in event detection performance evaluation because TN is usually infinite. On the basis of the confusion matrix, the evaluation can be carried out by using the following measurements, as seen in Table 8.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Event** & **Induction Cooker** & **Kettle** & **Rice Cooker** & **Air Conditioner** & **Microwave Oven** \\ \hline A & 3 & 4 & 6 & 8.69 & 4.43 \\ B & 8.17 & 6.06 & 3.78 & 3.01 & 4.30 \\ C & 5.48 & 8.24 & 5.50 & 4 & 5.5 \\ D & 5 & 5.5 & 5.22 & 5.5 & 7.57 \\ E & 5.70 & 4.64 & 6.92 & 4.85 & 3.5 \\ F & 5.57 & 7.46 & 5.42 & 4.13 & 5.63 \\ G & 8.72 & 6.02 & 3.59 & 3 & 4.10 \\ H & 4.89 & 6.5 & 4.5 & 5.34 & 7 \\ I & 4.18 & 6.16 & 8.95 & 5.82 & 3.68 \\ J & 3.5 & 4 & 6.54 & 8.25 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The value of 2-D fuzzy membership about each event.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbols** & **Math Equation** & **Description** \\ \hline TPR & \(TPR=\frac{TP}{TP+TN}\in[0,1]\) & True positive rate: This is the ratio that is correctly judged to be positive in all samples that are actually positive. \\ FPR & \(FPR=\frac{TP}{TP+TN}\in[0,1]\) & False positive rate: The ratio that is erroneously judged to be positive in all samples that are actually negative. \\ Acc & \(Acc=\frac{TP+TN}{TP+TN+TP+TN}\) & Accuracy: The ratio of the number of correct decisions to the total output of the system is used to measure the frequency of correct decisions made by the system. \\ Score & \(Score=\frac{TP}{TP+TP+TN}\) & Score: This definition is meaningless in event detection as there is no available TN count. To solve this problem, [PERSON] [26] proposed the definition of score.  
Taking data from House3 in the REDD as an example, Table 9 illustrates the main metrics using the bilateral CUSUM, original CUSUM, and BIC (Bayesian information criterion) detector [27]. This is a day-of-event detection statistics. From the results, it can be seen that the bilateral CUSUM had the highest Score. The original CUSUM event detection method had the highest true positive rate (TPR), but it often had multiple FPs. The BIC detector had the lowest TPR and Score. By comparison, the bilateral CUSUM method performed better than the other two methods.
# How Resilient Are Kolmogorov-Arnold Networks in Classification Tasks? A Robustness Investigation
## 4 Methodology
### KAN-Convolution and Convolution Layer  
In this section, we investigate the effectiveness of KANs and CNN for traffic sign classification. We implemented and compared four different architectures, ConvNet_MLP, ConvNet_KAN, KANConv_MLP, and KANConv_KAN, based on the research by [21; 22]. All models were trained using a batch size of 512 over 100 epochs, leveraging the Adam optimizer with a learning rate of 0.001 and employing cross-entropy loss as the primary loss function.  
The ConvNet_MLP model is the baseline architecture combining standard convolutional layers with a fully connected MLP. It consists of four convolutional layers: two with 32 filters and a kernel size of 5 \(\times\) 5, followed by two with 64 filters and a kernel size of 3 \(\times\) 3. These layers are interspersed with ReLU activations and 2 \(\times\) 2 max-pooling layers, leading to fully connected layers with 256 neurons for class output.  
The ConvNet_KAN model builds on this by replacing the fully connected layers with a KAN linear layer, using a 10 \(\times\) 10 grid and a spline order of 3 to model complex nonlinear relationships. This architecture retains the initial convolutional layers from the ConvNet_MLP model but introduces the KAN layer after flattening the feature maps to capture more sophisticated patterns in the data.  
Figure 5: Architectures of KAN-Mixer and MLP-Mixer illustrate the differences in their token and channel-mixing approaches, with KAN-Mixer utilizing KAN layers instead of MLP layers.  
The KANConv_MLP model further explores the potential of a KAN by incorporating it directly into the convolutional layers. It employs two KAN-based convolutional layers, with each consisting of five independent 3 \(\times\) 3 convolutions, followed by max-pooling. These KAN layers aim to enhance the model's feature extraction capabilities by leveraging the adaptive spline functions of the KAN during convolution. The output of these KAN-based convolutions is then passed through fully connected layers--similar to those in the ConvNet_MLP model.  
Finally, the KANConv_KAN model fully integrates the KAN into the convolutional and fully connected layers using KAN-based layers throughout the network. It applies two KAN convolutional layers, similar to those in KANConv_MLP, and follows them with a KAN linear layer for classification. This model is designed to fully leverage the KAN's nonlinear, adaptive properties to potentially achieve better performance in recognizing traffic signs, especially under adversarial conditions.  
The architecture depicted in Figure 6 showcases the combination of convolutional layers with KAN components to improve robustness in classification tasks.
## 3 Data-Driven Solutions Applied for the Detection of NTLs
### Supervised Methods
#### 3.1.1 Nearest Neighbors  
The K nearest neighbors (K-NN) algorithm allows for the classification of samples based on training data. This technique calculates the distances from the new sample to all the data and selects the K nearest elements. The sample that is most repeated among the K elements will be the classification of the new element. In other words, this algorithm for categorization seeks out examples that are \"very similar\" to the new sample and classifies them according to this similarity [27, 28, 30, 89].  
It is the simplest and easiest-to-implement supervised algorithm, and it is often used to make comparisons with other algorithms [16]. While the most commonly used distance function is the Euclidean (Equation (1)), there are also the Manhattan and cosine distances [26].  
\[d(x_{i},x_{j})=\sqrt{\sum_{r=1}^{p}(x_{ri}-x_{rj})^{2}} \tag{1}\]  
where \(d\) is the distance between two points in a metric space, \((x_{i},x_{j})\) are the points whose coordinates are given in an \(n\)-dimensional space, and \((x_{ri},x_{rj})\) are the coordinates of \((x_{i},x_{j})\) in dimension \(i\).  
In Figure 3, an example of how this algorithm works is presented. For the example case, four classes of geometric shapes are shown: Class A = circle (red color), Class B = triangle (purple color), Class C = square (blue color), and Class D = star (yellow color). The value of K = 5. As can be seen, the new sample is classified as a circle because, out of its five nearest neighbors, three are circles, one is a triangle, and one is a square. Therefore, by majority vote, it is classified as a circle.
# Broadband Generalized Sidelobe Canceler Beamforming Applied to Ultrasonic Imaging
## 2 Background  
The diagram of the traditional ultrasonic imaging beamforming method is shown in Figure 1. First, one single element is excited to transmit the ultrasonic, and all elements receive the echo signal. Delay-and-sum (DAS) is introduced to obtain a receiving focused echo image, with low lateral resolution [14]. Then, exciting each element in turn, N's receiving focused images will be achieved. Later, N's receiving focused images are summed together to form the final beamforming output. Synthetic aperture (SA) is a passive process using fixed, data-independent apodization weights. The phase-shift can be implemented as time-delay and space-delay, therefore, SA achieves both receiving and transmitting focused [15; 16]. The non-adaptive beamforming DAS and SA works for both narrowband and broadband signals.  
For narrowband signals, adaptive beamforming is simply an extension of the SA. The only difference is the choice of apodization weights. Instead of using predefined, data-independent apodization weights, the adaptive beamforming actively updates a set of new weights that are dependent on the received echo data.
## 3 Finite-Element Setup
### FE Error Estimates  
Discretization errors occur when continuous electromagnetic fields are approximated using finite-element meshes. These errors are influenced by the mesh density and refinement, especially in regions with steep field gradients, such as near conductors and insulation layers. Adaptive meshing mitigates these errors by prioritizing critical regions, enhancing accuracy without significantly increasing computational demands. In ANSYS, the EMAGERR macro is commonly used to compute maximum discretization error norms, providing error estimates for electromagnetic field quantities like magnetic flux density (\(B\)). The \(BN_{\text{ERR}}\) represents a normalized metric indicating the discrepancy in flux density (\(B\)) values. Table 2 and Figure 6 shows error values for each of the 14 twisted models at 0 Hz and 50 Hz.
# A Compact Sub-GHz Wide Tunable Antenna Design for IoT Applications
## 2 Design Details
### Antenna Geometry  
Figure 1 shows the proposed a meandered loop slot-line antenna design. The antenna was designed and fabricated using an RO4350 substrate with dimensions of 27 mm \(\times\) 60 mm \(\times\) 0.76 mm. The relative permittivity (\(\epsilon_{r}\)) of the substrate is 3.48 and its loss tangent (tan\(\delta\)) is 0.0036. The Rogers substrate can be replaced with FR-4 to obtain good resonance sweeps but with slightly lower radiation efficiency values. For the Rogers-4350 board, the temperature coefficient of the dielectric constant is among the lowest of any circuit board material. This makes it an ideal substrate for broadband applications. After optimizing the antenna design, the design is mainly composed of the following: an etched slot-line structure from the ground plane and a meandered-shaped rectangular slot-line used to increase the radiating structure's effective electrical length. The proposed antenna design dimensions are the following: \(l_{1}\) = 38, \(l_{2}\) = 36, \(l_{3}\) = 19, \(l_{4}\) = 11, \(l_{5}\) = 7.5, \(w_{1}\) = 5.5, \(w_{2}\) = 3.5, \(w_{3}\) = 6, \(w_{4}\) = 4.  
The proposed antenna top layer detailed view is shown in Figure 1a. It is composed of a matched 50 \(\Omega\) input impedance (\(Z_{in}\)), a microstrip feedline, and the biasing circuitry of the varactor diode. The varactor diode biasing circuit (\(Dv\)) consisted of a series of combinations of RF chokes (\(L_{1}\) and \(L_{2}\)) and current limiting resistors (\(R_{1}\) and \(R_{2}\)). Sorting posts (SP) were used to connect the bottom layer varactor diode to the biasing circuitry in the top layer. RF chokes were used to isolate the radiating structure from the power supply. The reverse-biased varactor diode acted as a DC blocking capacitor. Hence, the DC biasing part and the RF radiating structure are well isolated and have a very minimal effect on the antenna's performance. SMV 1233 varactor diode is used [37]. The varactor diode (SMV1233) maximum reverse bias current is 20 nA. From the maximum current specifications, the maximum biasing circuit power loss is \(-\)87.7 dBm.  
The ground plane detailed view is shown in Figure 1b. After optimization, the rectangular slot operates at below 1 GHz frequency band. After several parametric sweeps of the structure's length and width, the resultant structure is shown. The 1 mm wide uniform slot-line is used throughout the meandered structure. The final optimized antenna dimensions are shown in Figure 1b. The varactor diodes' exact positions and placements are critical as they help in achieving wide frequency band tuning. The LPKF S103 machine [38] was used to fabricate the antenna. The fabricated model top and bottom layers are shown in Figure 2a,b, respectively. The other antenna design dimensions are shown in Figure 1. An increase in the slot length will increase the electrical length of the antenna, and hence the antenna will resonate at a lower frequency band. On the other hand, any change in the slot width will result in poor matching. The given optimal slot width gave us the best Zin matching.
# Audio-Visual Action Recognition Using Transformer Fusion Network
## 1 Introduction
This powerful capability of self-attention can be harnessed to seamlessly integrate information from diverse modalities, like audio and visual data, by extending its application beyond a single modality. This enables the model to dynamically adjust its focus and allocate attention to the most relevant features from each modality, thereby facilitating the effective fusion of multi-modal information and enhancing the overall performance of tasks like action recognition. Our approach is centered on two innovative methodologies aimed at enhancing the effectiveness and precision of multi-modal feature learning and fusion for action recognition. Firstly, we introduce a transformer model designed to learn and extract features from multi-modal data, specifically audio and visual information. This model processes individual modalities independently, capturing intricate relationships and patterns within each modality. It is adept at extracting high-level semantic features from both audio and visual data, ensuring a comprehensive understanding of each modality's unique characteristics. Secondly, we present an attention transformer module that enables the effective integration of the extracted audio and visual features. This module is engineered to compute cross-modal attention between audio and visual elements, allowing the model to selectively emphasize the most relevant modality in a given context. Leveraging the attention mechanism, the model dynamically assigns importance weights to audio and visual features, leading to more robust and accurate action recognition by synthesizing the strengths of each modality.
## 2 Materials and Methods
### Global Digital Controller
#### 2.2.2 Serial Peripheral Interface Protocol  
A light that passed through the FPGA generated data on the transmitter side. A unique data packet was created for data transmission, consisting of a start bit that denoted the beginning of a new packet followed by a fixed 23-bit data address. This address identified the transmitted data type and confirmed that the data packet was received correctly. The 8-bit variable data were processed immediately as the header was validated. The stop bit, which also served as the parity bit, signified the end of the data packet. The data packet structure is depicted in Figure 3.  
The data packet comprises 32 bits. Furthermore, a simple verification protocol was implemented to transmit and verify 22-bit data packets. The 8-bit binary data were generated based on the light intensity, with a starting value of 0 and a maximum value of 127. As the light intensity varied, each data value modified the form and amplitude of the pulse pattern. Furthermore, the data provided patient control over the amplitude or form of pulses elicited by electrodes inside the human eye, depending on the intensity of light. Figure 3 shows the data packet structure. A 32-bit data packet was generated at the transmitter as parallel data using a 32-bit multiplexer. These data, along with the clock signal, were received by the receiver side. A verification protocol was applied to the serial data. This verification protocol checked for the header of each data packet, and the 8-bit data were sent to a digital controller that defines 128 different pulse patterns and amplitudes.