esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Performance Evaluation
In Figure 12, the estimated instantaneous frequency of the interference is used to down-convert the sweep interfering signal, where the \(C/N_{0}\) value is set to be 35 dB-Hz, the JNR value is set to be 10 dB when the sweep interference is present in the received GPS L1 signal, and the coherent integration time is set to be 2 ms in the acquisition process by using the parallel acquisition scheme in the time domain [20, 21]. In the simulation, two typical disturbing signal cases are considered: the all-time interference present in the received GPS L1 signal and the time-varying interference alternately appearing in one GPS C/Acode period (1 ms) and disappearing in the other GPS C/A code period, since the coherent integration time is chosen as 2 ms in the acquisition process. From Figure 12, it is easy to find that the ROC curve in absence of interference shows ideal acquisition performance; when no interference mitigation approach is applied, the presence of the sweep interference in the received GPS L1 signal results in serious acquisition performance degradation, and in detail, as expected, the acquisition performance obtained in the case of all-time interference is clearly worse than that achieved in the time-varying interference case. Recently, Chien developed a notch IIR filter with a lattice structure to mitigate the interfering signal for GNSS receivers [25]. This algorithm suggested using the second-order statistical value of the notch frequency-related parameter \(\beta\) to detect the interfering signal. In our proposed interference detection and mitigation method, the interfering signal is detected by the reassigned spectrogram and then mitigated by the notch IIR filter for GNSS receivers. In order to evaluate the interference detection and mitigation capability, our proposed method is compared to the state-of-the-art Chien's notch filter. In the interference mitigation performance comparison, we assume that the sweep interference is always present in the received GPS L1 signal. As shown in Figure 12, enhanced acquisition performance can be obtained by using Chien's notch filter when compared to the aforementioned two cases of no interference rejection. On the other hand, Figure 12 indicates that our proposed method provides much improved  
Figure 11: Reassigned Spectrogram of the GPS L1 signal with sweep interference. \(C/N_{0}\) = 46 dB-Hz and JNR = \(-\)2 dB. (**a**) Reassigned Spectrogram; (**b**) Contour of Reassigned Spectrogram. acquisition performance in comparison to Chien's notch filter, which further verifies the validity and effectiveness of the proposed anti-interference algorithm for GNSS receivers in jamming environments.
## 2 Problem Setting  
In this study, the training data were constructed assuming the condition of the low-speed wind tunnel and the anechoic cart in Japan Aerospace Exploration Agency (JAXA), as shown in Figure 1. Figure 1(a) shows a schematic diagram of the problem setting. A single monopole sound source is assumed to be placed in the center of an open-jet wind tunnel with a cross-sectional area of 2 m \(\times\) 2 m. The size of the sound source localization area is 1 m \(\times\) 1 m on the \(X_{n}-Z_{n}\) plane with the origin located at the sound source position, and the 200 \(\times\) 200 points source grid is defined in the sound source localization area. The wind tunnel flow only has the \(X_{n}\) direction component, and the velocity components in the \(Y_{n}\) and \(Z_{n}\) directions are zero. The shear layer is assumed to be located at \(Y_{n}=\pm\)1 m and it develops uniformly in the \(X_{n}-Z_{n}\) plane with a thickness of zero. Here, one microphone is installed at a given position within the 4 m \(\times\) 0.8 m \(\times\) 4 m area that is shown by the gray box in Figure 1(a). In the source localization, the steering vector that consists of the propagation time and attenuation rate from the source to the microphone are required at each grid point in the source grid. In other words, the propagation time and attenuation rate at 40,000 points should be calculated for each flow velocity in the wind tunnel and a microphone position. The exhaustive calculation of all those grid points is time-consuming and, therefore, the acceleration is required, as discussed in Section 1. Table 1 shows the parameters and the range of their values that we considered.  
_Appl. Sci._**2021**, _11_, 4216  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Range** \\ \hline Flow velocity (Mach number) & 0–0.2 \\ \hline \(X_{n}\)-axis : \(-\)2.0–2.0 m \\ Microphone placement & \(Y_{n}\)-axis: 1.2–2.0 m \\ \(Z_{n}\)-axis: \(-\)2.0–2.0 m \\ \hline \end{tabular}
\end{table}
Table 1: The flow velocity and the microphone placement area to be analyzed.  
Figure 1: JAXA’s 2 m \(\times\) 2 m low-speed wind tunnel and an anechoic cart.
# Stimulation Montage Achieves Balanced Focality and Intensity
## 4 Discussion  
### Electrode Configuration  
The electrode configuration for all studies clearly shows that MI always uses four electrodes, where two are used for stimulation and the other two are for current return. The two stimulation electrodes deliver most of the current to the targets to increase the intensity. However, with the safety constraint on the total amount of injected current, no spare electrodes can be used to neutralize the effects in non-target regions. This is why MI usually has poor locality and large target error. In contrast, CLS needs more electrodes than any of the other methods. These electrodes counteract each other to eliminate effects at non-target areas, which explains the good focality and small target error in all CLS results. The large number of electrodes also contributes to low intensity since each electrode can only deliver a small current to meet the safety constraint on total current. Therefore, the strategy is to keep the number of electrodes neither too large nor too small, which is the unique approach of SBFI. In a sense, some electrodes deliver enough current to ensure the desired intensity, while others are used to decrease the unwanted effects at non-target brain regions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Tissue** & \(\sigma\) **(S/m)** & **Max Focality (mm)** & **Min Focality (mm)** & **Rate ((mm)/(S/m))** \\ \hline Scalp & 0.2-0.6 & 22.808 & 22.007 & 2.002 \\ Skull & 0.001–0.04 & 62.773 & 21.635 & 1054.8 \\ CSF & 1.20–2.01 & 22.598 & 22.102 & 0.612 \\ Cortex & 0.05–0.71 & 33.227 & 21.522 & 17.736 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Focality results of the robustness test.  
Figure 7: **(A)** Maximum focality deviation from the expected value due to the conductivity uncertainty. **Left**: single target. **Right**: synthetic multiple targets, from top to bottom are the results for target 1, 2, and 3, respectively. (Note: \(y\)-axis is log scale in the right column.) The effects on locality in general: skull \(>\) cortex \(>\) CSF \(\approx\) scalp. (**B**) Example of the focality changes. (Note: the \(y\)-axis starts at 20 mm.) No clear tendency of the focality changes. Most focality changes happen when the skull conductivity is small.
# Similarity Analysis for Time Series-Based 2D Temperature Measurement of Engine Exhaust Gas in TDLAT
## 4 Statistical-Based Mean Difference Test and Similarity Analysis
### [Step 2] Similarity Analysis
#### 4.2.3 Time-Based Mahalanobis Distance (TMD)  
MD was introduced by [PERSON] in 1936 to measure distance between a point P and distribution D. It is a multi-dimensional generalization of the idea for measuring the amount of standard deviations P is away from the mean of D [30]. Among various methods for measuring distance (i.e., Euclidean distance, Manhattan distance, etc.), MD is used as it has the advantage of calculating the distance by considering weight according to the magnitude of covariance between variables [31]. Thus, MD is a method that is used to assess similarities between two groups. In this study, TMD analysis is performed to analyze similarities between \(T_{Thc}\) and \(\overline{T}_{Rec}\) by reference time. The closer the TMD value is to zero, the more likely \(T_{Thc}\) and \(\overline{T}_{Rec}\) are to be similar. The calculation of TMD procedure is as follows:[Stage 1] Calculate the covariance matrix (S) and TMD using the following formula (14) and (15).  
\[S=\left[\begin{array}{cc}Var\Big{[}T_{Thc(i)}\Big{]}&Cov\Big{[}T_{Thc(i)},\ \overline{T}_{Rec(i,j)}\Big{]}\\ Cov\Big{[}\overline{T}_{Rec(i,j)},\ T_{Thc(i)}\Big{]}&Var\Big{[}\overline{T}_{ Rec(i,j)}\Big{]}\end{array}\right], \tag{14}\]  
\[MD=\sqrt{\left(X_{i}-\overline{X}\right)^{T}S^{-1}\big{(}X_{i}-\overline{X} \big{)}}, \tag{15}\]  
\[\left(X_{i}-\overline{X}\right)=\left(\begin{array}{c}T_{Thc(i)}-\overline{ T}_{Thc}\\ \overline{T}_{Rec(i,j)}-\overline{\overline{T}}_{Rec(i,j)}\end{array}\right) \tag{16}\]  
where, \(\overline{T}_{Thc}\) denotes the geometric mean of all \(T_{Thc(i)}\), \(i=1.0,\ 1.1,\ 1.2,\ \cdots,\ 9.9\). \(\overline{\overline{T}}_{Rec(i,j)}\) denotes the geometric mean of all \(\overline{T}_{Rec(i,j)}\) in \(j\)th cycles. \(S^{-1}\) denotes inverse covariance matrix. \(T\) indicates that the vector should be transposed.  
[Stage 2] The obtained TMD values are calculated using the following formula for each time (s) interval.  
\[T_{MD}=\ (MD_{1}\times MD_{2}\times\cdots\times MD_{n})^{\frac{1}{n}},\ n=1,2, \cdots m. \tag{17}\]
## 4 Experimental Results and Analysis
### IGVMD Decomposition  
To address the problem of premature convergence and falling into the local optimum of the GWO algorithm, three adjustment strategies are introduced in the GWO algorithm to obtain the IGVMD algorithm. The number of IGVMD algorithm population was set to 30, the maximum number of iterations was 30, the range of \(K\) values was set as [1; 15], and the range of \(\alpha\) values was set as [500, 4000][11]. In the process of optimizing the VMD model, the fitness convergence curves obtained using four different optimization algorithms are shown in Figure 9. GWO represents the standard GWO; IGWO-1 represents the GWO algorithm that introduces a non-linear convergence factor adjustment strategy on top of GWO; and IGWO-2 represents the GWO algorithm that introduces a levy flight adjustment strategy on top of IGWO-1.  
The curves in Figure 9 show that the fitness value of GWO converges too early; compared with GWO, IGWO-1 and IGWO-2 algorithms have the ability to jump out of the local optimum but converge more slowly; IGVMD not only has a good ability to avoid falling into the local optimum but also has faster convergence performance compared with the first three optimization algorithms. It is verified that the improved strategy proposed in this paper can effectively improve the global search performance of GWO and has a strong search capability in optimizing this model problem.  
Taking Fault 1 as an example, optimal [\(K\),\(\alpha\)] combinations are obtained by the IGVMD algorithm: \(K\) = 4, \(\alpha\) = 791, and fault signals are decomposed into four IMF components. Time and frequency domain waveforms of each modal component obtained after the signal decomposition are shown in Figure 10.  
For comparison, the Fault 1 signal is decomposed using EMD and conventional VMD. EMD is decomposed into 11 IMF components, and the first 6 IMF components are analyzed for ease of observation. The time-frequency diagrams of IMF1-IMF6 are shown in Figure 11. According to the spectrum after EMD, it is obvious that IMF5 and IMF6 showed the modal mixing phenomenon. A traditional VMD reference [38] empirically sets [K = 4, \(\alpha\) = 2000]. Figure 12 shows the IMF component time-frequency diagram of traditional VMD, which is carefully compared with the improved VMD, and the IMF component period pulse pattern of the improved VMD, are more obvious.  
Figure 9: Fitness value curves for each algorithm.  
Experimental results showed that, compared with the EMD method and the traditional VMD method, the IGVMD method effectively avoids modal confusion and endpoint effects generated by EMD; this solves the problem of adaptive VMD solution and avoids the influence of the traditional VMD method on the experimental results due to improper signal decomposition caused by human factors.  
Figure 11: Time domain and frequency domain diagrams of IMF components decomposed by EMD.  
Figure 12: Time domain and frequency domain diagrams of IMF components decomposed by traditional VMD.  
Figure 10: Time domain and frequency domain diagrams of IMF components decomposed by IGVMD.
# A Study on the Maximum Reliability of Multi-UAV Cooperation Relay Systems
## 5 Conclusions  
This paper studied the problem of maximizing the reliability of static and mobile UAVs in a multi-source, multi-destination, and multi-hop communication model, in which the UAV provides wireless services for remote users without direct communication links on the ground as a CC relay. The goal was to minimize the total BER by jointly optimizing the variable and, at the same time, the total path loss was minimized and the ground communication coverage was maximized. The simulation results validated the superiority of the proposed joint optimization iteration algorithm and showed that the optimal height of different reliability measures is slightly different, and when using the mobility of UAVs, the outage performance of the mobile UAV is better than that of the static UAV and can improve the reliability of communication performance.  
Investigation: N.N. and S.Z.; methodology: N.N. and S.Z.; software, N.N.; writing--original draft: N.N.; writing--review and editing: S.Z., W.B. and X.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.
## 3 Results  
Based on the information available, all the experts have been compared against each other according to particular criteria. In this way, the weight of each expert has been calculated. The results are recorded in the table below (Table 6). These values will subsequently be used in the product selection process.  
In the same way, the weight of each selected criterion of the scanners has been calculated. Pairwise comparison by members of the evaluation team at this level of hierarchy structure should reflect their personal preferences, according to which they will give priority to a specific product. The results are shown in the following table (Table 7).  
The last step in the analysis is to process the matrices of pairwise comparisons, in which every product is assessed according to each criterion for product assessment  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Criterion** & **Weight** & **Quality Manager** & **Technician** & **Economist** & **Engineer** \\ \hline Education degree & 0.0383 & 0.3535 & 0.0855 & 0.4103 & 0.1507 \\ Practical experiences with RE systems & 0.5635 & 0.5083 & 0.3612 & 0.0376 & 0.0928 \\ Theoretical knowledge from quality inspection & 0.2736 & 0.5525 & 0.298 & 0.0362 & 0.1133 \\ Economic knowledge & 0.1246 & 0.1458 & 0.0892 & 0.7067 & 0.0583 \\ Weighted sum & & 0.4693 & 0.2995 & 0.1349 & 0.0963 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Weights of particular experts.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Expert** & **Weight** & \(f_{1}\) & \(f_{2}\) & \(f_{3}\) & \(f_{4}\) & \(f_{5}\) & \(f_{6}\) & \(f_{7}\) \\ \hline Quality manager & 0.4693 & 0.0228 & 0.4286 & 0.1083 & 0.1293 & 0.1582 & 0.1170 & 0.0358 \\ Technician & 0.2995 & 0.0232 & 0.4391 & 0.1958 & 0.0718 & 0.0597 & 0.1299 & 0.0805 \\ Economist & 0.1349 & 0.3375 & 0.2646 & 0.0352 & 0.0667 & 0.0887 & 0.1499 & 0.0574 \\ Engineer & 0.0963 & 0.0245 & 0.4574 & 0.1734 & 0.0943 & 0.0806 & 0.1170 & 0.0528 \\ Weighted sum: & & 0.0655 & 0.4124 & 0.1309 & 0.1003 & 0.1118 & 0.1253 & 0.0537 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Weight of product assessment criteria.  
(Table 8). The considered variants are as follows: MetraSCAN 70 (\(a_{1}\)), MetraSCAN 70-R (\(a_{2}\)), HandyPROBE (\(a_{3}\)), Nikon XC65 Dx (\(a_{4}\)), Nikon LC60 Dx (\(a_{5}\)), Nikon LC15 Dx (\(a_{6}\)), Metronor DUO (\(a_{7}\)), and ATOS Triple Scan (\(a_{8}\)).  
As can be observed in the table above, the ATOS Triple Scan corresponds best to all the stated criteria, and slightly worse is the Nikon LC15 Dx. In this case, the best solution is not the cheapest, for these two machines are more expensive than the others. Using this method, and by engaging staff in the process, a company can prevent many mistakes before buying and implementing any equipment under consideration. Before choosing one of the solutions, the firm can perform an additional analysis of the profitability of an investment, so that they can select the best option.
## 3 Proposed Coordination Inertia Control Strategy
### Coordination Inertia Control Strategy of Wind Farms
Considering that the offshore MMC frequency variation range is small, the DC-side voltage will also be kept within the acceptable range. In addition to the original control, the inertia transfer link is also introduced to utilize the energy of the wind turbine. The reason for the introduction of this link can be intuitively reflected in Equation (7). We find that the inertia provided by the grid-connected system of the PMSG depends on the inherent inertia of the capacitor. Its inertia is small compared with the wind turbine grid-connected system as a whole. So, it is necessary to introduce the inertia transmission link on the machine side. After introducing the inertia transfer link, as shown in Figure 4, and ignoring the influence of the first-order inertia link and the control delay, the expression of the active power \(P_{m}\) on the machine side is:  
\[P_{m}=P_{opt}-K_{C}\frac{dv_{dc}}{dt} \tag{11}\]  
Then, combine Equation (11) with Equation (8)  
\[(2H_{C}v_{dc0}+K_{C})\frac{dv_{dc}}{dt}=P_{opt}-P_{g} \tag{12}\]  
where \(K_{C}\) is the inertia transfer coefficient, and \(P_{opt}\) is the maximum wind power tracking output command value, which can be ignored in the analysis process and considered as a constant. It is not difficult to see from Equation (12) that the overall inertia of the grid-connected system of wind turbines at this time not only depends on the inherent inertia of the DC capacitor but also increases the inertia by adjusting the inertia transfer coefficient \(K_{C}\).
# Fed-Hetero: A Self-Evaluating Federated Learning Framework for Data Heterogeneity
## 3 Notations and Preliminaries
### Metrics to Measure Data Heterogeneity
#### 3.3.4 Structural Similarity Index  
The Structural Similarity Index (SSIM) [26] is a measure used to compare and quantify the similarity between two images. It evaluates differences in structural details, factoring in elements such as brightness, contrast, and overall structure. The SSIM index is calculated using the following formula as defined in [26].  
\[SSIM(y,z)=\frac{(2\mu_{y}\mu_{z}+C_{1})(2\sigma_{yz}+C_{2})}{(\mu_{y}^{2}+\mu_ {z}^{2}+C_{1})(\sigma_{y}^{2}+\sigma_{z}^{2}+C_{2})} \tag{8}\]  
where the variables used in Equation (8) as defined in [27] are the following:  
* \(\mu_{y},\mu_{z}\) are the average values of the images \(y\) and \(z\).
* \(\sigma_{y}^{2},\sigma_{z}^{2}\) are the variances of the images \(y\) and \(z\).
* \(\sigma_{yz}\) is the covariance of \(y\) and \(z\).
* \(C_{1}\) and \(C_{2}\) are small constants.  
The similarity range is shown in Table 3.  
An SSIM value of 1 indicates perfect similarity (identical images), 0 means no similarity, and values closer to 1 indicate greater similarity. The threshold values are specific to the dataset used in the study to identify clients with close similarity and details are mentioned in the Experiment Setup section in Section 5.
# Transient Time Reduction in Time-Varying Digital Filters via Second-Order Section Optimization
## 5 Discussion  
In this study, we found that introducing time-varying coefficients into only one second-order section can substantially shorten the overall transient time, offering a clear advantage over a fully time-invariant design. At the same time, the computational overhead remains relatively modest, since the method requires storing just a limited set of coefficients within a user-defined horizon rather than adapting the entire filter for the time-varying concept. These optimized coefficients, derived through a nonlinear routine that carefully balances settling speed and stability, cannot be readily approximated by a simple mathematical function or curve, so the most reliable approach is to store them directly. Although this adds some memory usage--particularly in low-power or embedded contexts--its footprint is still far smaller than that of a fully time-varying filter architecture. By confining the mechanism to one SOS, the structure preserves the benefits of time-varying behavior exactly where it is most needed, while leaving the rest of the filter in a low-complexity, stationary form. Moreover, empirical tests confirm that this targeted approach preserves steady-state performance across a range of signal and noise conditions. Thus, it provides a practical middle ground, allowing significant transient improvements in return for only a slight increase in storage and computational effort.  
Although the approach of using time-varying coefficients in one second-order section has demonstrated notable benefits, it is not universally advantageous across all filter structures or use cases. For instance, Butterworth filters, with their relatively low selectivity, gain much less from this technique, suggesting that filters offering sharper roll-offs or more complex pole-zero placements stand to benefit most. Additionally, while the coefficient adaptation process proves straightforward under a \"cold start,\" where the filter begins with zero initial conditions, the performance in a \"hot start\" scenario--when the filter is already operating--requires further investigation. Another critical concern is determining the precise moment at which to initiate time-varying behavior; if it is triggered too early or too late, the potential gains can be diminished or overshadowed by unnecessary overhead. Likewise, rapid changes in the input signal, such as narrow \"stairs,\" can disrupt the predefined horizon if the filter coefficients are only optimized for a single transient event. These issues underscore the method's current limitations and highlight areas where additional research--on trigger mechanisms, adaptive horizons, and robust designs for rapidly shifting signals--remains necessary.