esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Results  
### Trends in Vertical and Horizontal Ground Deformation  
The trends in vertical and horizontal ground deformation occurring on land in 2016-2021 are shown in the EGMS Ortho Vertical and EGMS Ortho East/West datasets (Figures 9 and 10). The ground deformation patterns referring to the 2016-2021 period show that the eastern sector of Campi Flegrei is characterized by eastward horizontal movements, whereas the western sector is characterized by westward horizontal movements with maximum values in the caldera central area of about 2 km to the west and east outside Pozzuoli (Figure 9). As we are considering only the E-W component of horizontal movements, the velocity values strongly decreased along the N-S linear axis crossing through the center of the caldera deformation, which is located near Pozzuoli city center. Along this axis, the N-S component of the horizontal movements is very high, and the E-W component is almost null due to the radial geometry of ground deformation. For this reason, considering the SAR acquisition geometry, the spatial pattern of horizontal velocity looks larger in the E to W direction.  
The central area with negligible east-west displacement is characterized by maximum uplift rates (Figures 9 and 10). The vertical ground deformation of Campi Flegrei during 2016-2021 period is mainly spatially symmetrical with a radial pattern (Figure 10), with annual velocity varying from + 90 mm/yr in the central sector to zero in an annular strip between 6 and 7 km away from the center of deformation. The areas external to the caldera rim, beyond 7-8 km from the center (Figure 10), are also characterized by small subsidence rates (\(-1\) to \(-3\) mm/year) that may only locally show lower rates of up to \(-14\) mm/yr due to local subsidence due to underground cavities or landslide processes. The ground uplift is confined within a circle of about 7 km in diameter, roughly corresponding to the caldera  
Figure 8: Location of the GPS station of the INGV network; GPS location by [PERSON] et al. (2016).  
rim, and is further amplified in the resurgent block [54; 77; 109] due to the control of the ring faults, bounding both the caldera and the resurgent block, over the ground deformation.  
Figure 10: Vertical component of ground deformation at Campi Flegrei during 2015–2021 derived from the ortho-vertical EGMS dataset [110].  
Figure 9: E-W horizontal component of ground deformation at Campi Flegrei during 2015–2021 derived from the EGMS Ortho East/West dataset [110]. Class limits were obtained using the Natural Break (Jerkins) method.
# Fibre Wireless Distributed Antenna Systems for 5G and 6G Services
## 1 Introduction
The suggested design and method of operation would remain effective and useful, even if the 6G THz wireless system is utilized for point-to-point communication. In this case, we experimentally broadcast the single-carrier modulation 6G signal using 256-QAM modulation and a 5G new radio signal across a single mode fibre optic link. 3. The experimental trial is assessed in terms of error vector magnitude (EVM) and Carrier Suppression Ratio (CSR). The remainder of the paper is divided into the following sections. Section 2 discusses the Industrial Distributed Antenna System assisting 5G and 6G services followed by Section 3 which explains the experimental setup and realization. Section 4 will provide the results. Section 5 discusses the future prospects and challenges, while Section 6 concludes the paper.
## 2 Background
### Code-Based GNSS Inter-User Ranging Techniques
#### 2.1.5 Single Differences Ranging  
Also based on the exchange of the set of pseudorange measurements from the aiding to the _aided user_, this technique exploits a set of differential quantities known as Single Differences (SD). It was introduced in [53; 54]. A generic SD can be defined between two GNSS receivers, \(i\) and \(j\) tracking a common satellite \(s\) as the difference between synchronous pseudorange measurements:  
\[\begin{split} S^{s}_{ij,k}&=\rho^{s}_{j,k}-\rho^{s}_{ i,k}\\ &=\Delta r^{s}_{ij,k}+\Delta b_{ij,k}+\Delta e_{ij,k},\end{split} \tag{9}\]  
where \(\Delta r^{s}_{ij,k}\) is the difference between the ranges from the i-th and j-th users to satellite \(s\), \(\Delta b_{ij,k}\) is the difference between the clock biases of the two users and \(\Delta e_{ij,k}\) is a noise term that aggregates all the non-correlated errors. In fact, provided that all the measurements are synchronous, SDs allow canceling satellite clock errors as well as the part of the satellite orbital errors common to both users and the other correlated bias terms affecting pseudorange measurements. Besides the cancellation of correlated error terms, the variance in the uncorrelated errors, such as thermal noise, is increased. These noise contributions are hence aggregated in \(\Delta e_{ij,k}\). Assuming a minimum of four visible GNSS satellites common to both users, the computation of the baseline vector based on SD is performed through:  
\[\begin{bmatrix}S^{1}_{ij,k}\\ S^{2}_{ij,k}\\ \vdots\\ S^{s}_{ij,k}\end{bmatrix}\simeq-\begin{bmatrix}\mathbf{h}^{1}_{\mathbf{z},k}&1 \\ \mathbf{h}^{2}_{\mathbf{z},k}&1\\ \vdots&\vdots\\ \mathbf{h}^{5}_{\mathbf{z},k}&1\end{bmatrix}\begin{bmatrix}\mathbf{d}_{ijk}\\ \Delta b_{ij,k}\\ \Delta b_{ij,k}\end{bmatrix} \tag{10}\]  
where \(*\) represents the point chosen as the origin for the unit steering vector, which could be the SPP estimate of the _aided user_, _aiding user_, or a higher quality estimation from one of the user's positions. By means of this approach, the exchange of the estimated position is not necessary since it can be computed autonomously at the aided receiver. The current contribution presents, therefore, a comparison of the different cases to understand the impact of the linearization point accuracy on the final ISR estimation. The Section 4 shows an assessment of the baseline estimation quality as a function of this chosen point. This technique will be named SD Haiding and SD Haided when the _aiding user_ and the _aided user_, respectively, are used as origins of the steering vectors in the results presented in Section 4.
# A Deep Reinforcement Learning Approach for Active SLAM
## Appendix A Proof of the Monotonicity Property of the Robot's Pose Uncertainty
### Uncertainty Propagation  
Let's now consider two noisy poses, \(T_{AB}\) and \(T_{BC}\), both contained in \(\text{SE}(3)\) with their associated \"small\" perturbation errors \(d_{A}\) and \(d_{B}\). The composed pose, \(T_{AC}\), can be estimated by the matrix product,  
\[T_{AC}=T_{AB}\;T_{BC}=\exp(\hat{d}_{A})\bar{T}_{AB}\exp(\hat{d}_{B})\bar{T}_{BC} \tag{10}\]  
Using the following definition of the adjoint,  
\[\exp\left(Ad_{X}Y\right)\triangleq X\exp\left(Y\right)X^{-1} \tag{11}\]  
or, equivalently,  
\[\exp\left(Y\right)=X^{-1}\exp\left(Ad_{X}Y\right)X \tag{12}\]  
and setting \(Y=\hat{d}_{B}\) and \(X=\bar{T}_{AB}\), Equation (10) results in,  
\[T_{AC} =\exp\left(\hat{d}_{A}\right)\exp\left(Ad_{T_{AB}}\hat{d}_{B} \right)\bar{T}_{AB}\bar{T}_{BC} \tag{13}\] \[=\exp\left(\hat{d}_{A}\right)\exp\left(Ad_{T_{AB}}\hat{d}_{B} \right)\bar{T}_{AC} \tag{14}\]  
Finally, using the first-order approximation [45, 46, 47] of the Baker-Campbell-Haussdorf formula for the product of the exponential maps, it can be inferred that,  
\[T_{AC}\simeq\exp\left(\hat{d}_{A}+Ad_{T_{AB}}\hat{d}_{B}\right)\bar{T}_{AC} \tag{15}\]  
Thus, the perturbation of the composed pose \(T_{AC}\) will be:  
\[\hat{d}^{\;\prime}_{A}\simeq\hat{d}_{A}+Ad_{T_{AB}}\hat{d}_{B} \tag{16}\]  
Assuming that the perturbation errors \(d_{A}\) and \(d_{B}\) are uncorrelated with one another, the uncertainty of \(\hat{d}^{\;\prime}_{A}\) is,  
\[\Sigma^{\prime}_{A}\simeq\Sigma_{A}+Ad_{T_{AB}}\Sigma_{B}Ad^{\mathcal{T}}_{T_{ AB}} \tag{17}\]  
where \(Ad_{T_{AB}}\) is the adjoint representation of transformation \(\bar{T}_{AB}\), defined, in \(\text{SE}(2)\) and \(\text{SE}(3)\) respectively, as,  
\[Ad^{2D}_{T_{AB}}=\left(\begin{array}{ccc}\cos\phi_{AB}&-\sin\phi_{AB}&y_{AB} \\ \sin\phi_{AB}&\cos\phi_{AB}&-x_{AB}\\ 0&0&1\end{array}\right) \tag{18}\]  
\[Ad^{3D}_{T_{AB}}=\left(\begin{array}{ccc}R_{AB}&D_{AB}R_{AB}\\ 0&R_{AB}\end{array}\right) \tag{19}\]  
where \(R_{AB}\) is an orthogonal rotation matrix and \(D_{AB}\) is the \(3\times 3\) skew symmetric matrix related to the translational part of \(\bar{T}_{AB}\).
# Band Gap Properties in Metamaterial Beam with Spatially Varying Interval Uncertainties
## 2 The Model and Method
### Interval Field Finite Element Formulation  
In this subsection, the results of the interval field decomposition shown in Equation (12) are introduced into the finite element method, and the deterministic dynamic equation shown in Equation (3) is extended to the interval dynamic equation. As shown in Figure 3, a coordinate system is established along the direction of the basic beam. The origin is established at the left end of the metamaterial beam, while \(x_{n}\) represents the coordinate of the left end of the \(n\)th beam element. As we all know, density only affects the system mass matrix, and the interval mass matrix of the \(n\)th beam element \(\mathbf{m}^{(n)I}\) can be obtained by integration as follows:  
\[\mathbf{m}^{(n)I}=\int_{x_{n}}^{x_{n+1}}\rho^{I}(x)S\mathbf{N}^{(n)T}\mathbf{ N}^{(n)}dx \tag{14}\]  
Here, \(\mathbf{N}^{(n)}\) stands for the shape function matrix, and \(S=bh\) is the area of the cross-section. Substituting Equation (12) into Equation (14), \(\mathbf{m}^{(n)I}\) can be recast as:  
\[\mathbf{m}^{(n)I}=\mathbf{m}_{0}^{(n)}+\sum_{i=1}^{N}\mathbf{m}_{i}^{(n)}[ \varepsilon_{i}] \tag{15}\]  
Here, \(\mathbf{m}_{0}^{(n)}=\rho_{0}S\int_{x_{n}}^{x_{n+1}}\mathbf{N}^{(n)T}\mathbf{ N}^{(n)}dx\) and \(\mathbf{m}_{i}^{(n)}=\rho_{0}S\sqrt{\lambda_{i}}\int_{x_{n}}^{x_{n+1}}\psi_{i} (x)\mathbf{N}^{(n)T}\mathbf{N}^{(n)}dx\). After assembly, the interval global mass matrix of the basic beam \(\mathbf{M}_{\text{beam}}^{I}\) can be expressed in the following form:  
\[\mathbf{M}_{\text{beam}}^{I}=\mathbf{M}_{0}+\sum_{i=1}^{N}\mathbf{M}_{i}[ \varepsilon_{i}] \tag{16}\]  
where  
\[\mathbf{M}_{0}=\sum_{n=1}^{N_{u}N_{v}}\mathbf{L}^{(n)T}\mathbf{m}_{0}^{(n)} \mathbf{L}^{(n)};\mathbf{M}_{i}=\sum_{n=1}^{N_{u}N_{v}}\mathbf{L}^{(n)T} \mathbf{m}_{i}^{(n)}\mathbf{L}^{(n)} \tag{17}\]  
Here, \(\mathbf{L}^{(n)}\) is the connectivity matrix of the \(n\)th element. Furtherly, the interval dynamic equation of the metamaterial beam can be expressed as:  
\[\mathbf{D}^{I}\mathbf{U}^{I}=\mathbf{F} \tag{18}\]  
Figure 3: Coordinate diagram of the basic beam’s finite element meshing.  
where  
\[\begin{split}\mathbf{D}^{I}&=\mathbf{D}^{I}_{\text{beam}} \,+\mathbf{D}_{\mathbf{R}}=\mathbf{K}_{\text{beam}}\,-\omega^{2}\mathbf{M}^{I}_{ \text{beam}}\,+\mathbf{D}_{\mathbf{R}}\\ &=\mathbf{K}_{\text{beam}}\,-\omega^{2}\mathbf{M}_{0}+\mathbf{D} _{\mathbf{R}}-\omega^{2}\sum_{i=1}^{N}\mathbf{M}_{i}[\varepsilon_{i}]\\ &=\mathbf{D}_{0}-\omega^{2}\sum_{i=1}^{N}\mathbf{M}_{i}[ \varepsilon_{i}]\end{split} \tag{19}\]  
Here, \(\mathbf{D}^{I}\) represents the interval global dynamic stiffness matrix, and \(\mathbf{U}^{I}\) is the dynamic response interval vector. Similarly, in order to make \(u_{in}\) always equal to \(1\), \(\mathbf{D}_{0}(1,1)\) needs to be changed to \(10^{50}\), and \(\mathbf{M}_{i}(1,1)\) needs to be changed to \(0\). \(\mathbf{F}\) still represents the structural load vector, which is defined according to Equation (5). Hence, \(\mathbf{F}\) is not an interval vector.
## 6 Conclusions  
In this paper, the idea of fast, bandwidth-efficient, and robust image communication required for 5G and 6G systems is presented by using a hybrid combination of massive MIMO and OFDM systems augmented with diverse transforms, i.e., FFT, FrFT and DWT. The analysis is presented for the Rayleigh fading channel for different levels of M-PSK modulation technique. It is very evident from the simulation outcome that the image  
Figure 23: SSIM variations for Massive MIMO incorporated FFT-OFDM, FRFT-OFDM and DWT-OFDM for various modulation levels and number of users over Rayleigh Channel. (**a**) \(n=10\); (**b**) \(n=20\); (**c**) \(n=50\).  
quality deteriorates when the number of users increases from 10 to 50 for a given value of SNR. However, if we increase the SNR, we can see an improvement in the received image quality. On comparing the received image quality of hybrid combination of massive MIMO and OFDM augmented with FFT, FrFT and DWT transforms, it is observed that the received image quality in the case of FrFT augmented OFDM is much better than the OFDM system augmented with FFT. However, if we replace the FrFT transform with DWT we can see a significant improvement in the received image quality. In addition to the visual inspection, the image quality enhancement also can be accessed by the reported values of PSNR and SSIM. Our analysis also revealed that the values of PSNR and SSIM for DWT augmented OFDM is better than the FrFT and FFT augmented OFDM. However, if the number of users keeps on increasing, there is a decrease in the PSNR and SSIM values for all the diverse modulation levels and transformation techniques.  
In the future, a hybrid combination of massive MIMO, generalized frequency division multiplexing (GFDM) and filter band multi-carrier (FBMC) techniques can be explored to support the multimedia application for 5G/6G users as no cyclic prefix is required in GFDM and FBMC. Additionally, the assessment of hybrid amalgamation of OFDM and massive MIMO can be evaluated for other signal detection techniques such as zero-forcing and mean squared error (MSE).  
Conceptualization, L.K., S.B., M.M.; methodology, S.B., R.M.; software, L.K., S.B.; validation, L.K., S.B. and M.M.; formal analysis, S.B., R.M.; investigation, R.D., K.R. and R.M.; resources, M.M., S.B. and L.K.; data analysis, L.K. and S.B.; writing--original draft preparation, L.K., S.B., M.M. and R.M.; writing--review and editing, R.M., R.D. and K.R.; visualization, R.M., R.D. and K.R.; supervision, R.M.; project administration, R.M. and S.B.; funding acquisition, R.D. All authors have read and agreed to the published version of the manuscript.  
Fundacao para a Ciencia e Tecnologia.  
**Data Availability Statement:** All data that support the findings of this study are included within the article.  
**Acknowledgments:** This work was supported by FCT/MCTES through national funds and when applicable co-funded EU funds under the project MASSIVE5G (PTDC/EEI-TEL/30588/2017), Copelabs (UIDB/04111/2020), and Instituto de Telecomunicacoes (UIDB/50008/2020).  
**Conflicts of Interest:** The authors declare no conflict of interest.
## 7 Stability and Support Polygons
While the Directed Angular Restitution (DAR) method provides precise control over the angular orientation of the legs, it is the closed-loop trajectory design that plays a fundamental role in ensuring stability. Traditional approaches, such as those described in [13], focus on predefined gait patterns, which may not dynamically adjust to changes in the robot's environment. In contrast, the trajectory design approach, as discussed in [6, 15], allows for continuous adaptation to varying terrains, ensuring that the CoM remains within the support polygons even under challenging conditions. In summary, the stability of the hexopod robot is ensured by the proper application of support polygon principles in combination with the careful design of the closed-loop trajectory. This design ensures that the CoM remains within the support polygons, avoiding collisions and ensuring robust locomotion. This approach, as supported by [8, 13], and others, is essential for achieving stable and adaptable walking in dynamic environments.
# Comparing Sentinel-2 and Landsat 8 for Burn Severity Mapping in Western North America
###### Abstract  
Accurate assessment of burn severity is a critical need for an improved understanding of fire behavior and ecology and effective post-fire management. Although NASA Landsat satellites have a long history of use for remotely sensed mapping of burn severity, the recently launched (2015 and 2017) European Space Agency Sentinel-2 satellite constellation offers increased temporal and spatial resolution with global coverage, combined with free data access. Evaluations of burn severity derived from Landsat and Sentinel generally show comparable results, but these studies only assessed a small number of fires with limited field data. We used 912 ground calibration plots from 26 fires that burned between 2016 and 2019 in western North America to compare Sentinel- and Landsat-derived burn severity estimates with the field-based composite burn index. We mapped burn severity using two methods; the well-established paired scene approach, in which a single pre- and post-fire scene are selected for each fire, and also a mean image compositing approach that automatically integrates multiple scenes using the cloud-based remote sensing platform Google Earth Engine. We found that Sentinel generally performed as well or better than Landsat for four spectral indices of burn severity, particularly when using atmospherically corrected Sentinel imagery. Additionally, we tested the effects of mapping burn severity at Sentinel's finer spatial resolution (10 m) on estimates of the spatial complexity of stand-replacing fire, resulting in a 5% average reduction per-fire in area mapped as high-severity patch interiors (24,273 ha total) compared to mapping at the resolution of Landsat (30 m). These findings suggest Sentinel may improve ecological discrimination of fine-scale fire effects, but also warrant caution when comparing estimates of burn severity spatial patterns derived at different resolutions. Overall, these results indicate that burn severity mapping will benefit substantially from the integration of Sentinel imagery through increased imagery availability, and that Sentinel's higher spatial resolution improves opportunities for examining finer-scale fire effects across ecosystems.  
f
# Diagnosing the Machine Set Rotor Using Its Relative Vibrations
## 4 Measurements of Relative Vibration
### Measurements of the Displacement of Rotors' Relative Vibration  
The measurement of the relative vibration displacement means that the distance change is measured between the vibration points of the item's element and the point of the reference item, and the measured signal has constant and variable components.  
Non-contact sensors of vibration displacement suitable for measurements of relative rotor vibration displacement include the eddy current, inductive and capacitive sensors. Eddy current sensors are characterized by:  
* a sufficiently large linear range of the distance-voltage characteristic;
* vibrating element can be made of any electric conductor material, which allows the measurement of vibration without installing additional elements on the rotor.  
In the case of eddy current sensors, the distance-voltage characteristic has to be made for a given pair consisting of sensor and vibrating element. Inhomogeneity in the chemical composition of the vibrating material, discontinuities of material macrostructure, errors of shape and position of the vibrating element produce runout signals. The elimination of runout signals requires special procedures, such as processing of journal surface or appropriate processing of the measured signals [57].  
Figure 11: Synchronously averaged spectrum of the torsional vibration acceleration amplitude. Frequency range: 1–500 Hz.  
Figure 12: Synchronously averaged spectrum: compressor torsional vibration acceleration. Harmonic order: 1–14 orders.
# Model-Based Real-Time Motion Tracking Using Dynamical Inverse Kinematics
## 1 Introduction
The absence of iterations makes the _dynamical optimization_ approach faster, therefore suitable for solving whole-body inverse kinematics of complex models in time-critical motion tracking applications. In literature, dynamical inverse kinematics has been successfully applied in real-time applications involving human or humanoid models [29; 30]. This article presents a scheme for real-time motion tracking of highly articulate human, or humanoid, models. The tracking is achieved at a high frequency through a dynamic inverse kinematics optimization approach. The main contributions of this work are the application of a dynamical inverse kinematics strategy using rotation matrix parametrization for the rotation targets of the floating base human model, proving the convergence of the method using Lyapunov theory, and presenting a constrained inverse differential kinematic strategy to enforce model kinematic constraints. The implementation of the proposed scheme is tested for both human and humanoid models. The tests are preformed during different tasks involving both static posture and dynamic motions such as shown in Figure 1. The performances obtained using the dynamical inverse kinematics scheme are compared to the results obtained using instantaneous optimization methods. Further tests are performed using a real humanoid robot, controlling it in real-time using input sensors measurements and output of the humanoid model inverse kinematics. The paper is organized as follows: Section 2 introduces the notation, human modeling, formulation of motion tracking as an inverse kinematics problem, and the dynamical optimization scheme. Section 3 presents the proposed implementation of the dynamical inverse kinematics with rotation matrix parametrization and constrained inverse differential kinematics. In Section 4 the experimental details lay, and in Section 5 the performances are discussed and compared to instantaneous optimization. Conclusions follow in Section 6.