esa-sceva/satcom-chunk-collection huggingface dataset:
# Application of Riemannian Seismic Ray Path Tracing in Salt Dome Prospecting
[43] to the theory of seismic rays, where the main postulate will be that a seismic ray follows a geodesic curve (i.e., of minimum length) in an intrinsically curved \"seismic space\". In equivalence to the optical refractive index, the curvature of such space will be determined by the specific inhomogeneities of the elastic propagation medium, for which purpose the inverse of the propagation speed of P waves in geological media is proposed as \"refractive index of seismic rays\". For this purpose, Section 2 presents the elements of differential geometry required to develop this work, while in Section 3.1 it is applied to construct the Riemannian seismic ray theory. In order to summarise, Section 3.2 presents the methodology to be followed to apply this theory, while Section 4 presents several relevant applications in geophysics, such as a stratum change at a certain depth, simplified modelling of the speed of P-wave in the mantle, as well as an example of the modelling of irregular interfaces between two strata of constant wave propagation velocity. These simple examples show that the theory presented here reproduces the expected results. It should be noted that the last example shows the application of the theory to a realistic model of the subsoil with speeds of great interest in geophysical exploration, which contains a salt dome. In this case, it can be clearly seen that the seismic rays are refracted in the salt dome due to their high contrast with respect to their surroundings, which is consistent with the shadow generated by these objects in exploration and geophysical simulation. Finally, Section 5 presents an extensive discussion of the results and some interesting concluding observations are provided in Section 6.
# Inverse Multiscale Discrete Radon Transform by Filtered Backprojection
## 1 Introduction
### Multiscale DRT
With that definition it is possible to account for all the discrete lines of length 4, if we have previously computed all the lines of length 2. And so on. The definition of partial transform up to stage \(m\) emerges:  
\[\widetilde{f}^{m}(\overbrace{s_{n-m},\,\widetilde{s_{n-m+1}},\,\ldots,\,s_{n -1}}^{s})\mid\overbrace{v_{m},\,\ldots,\,\,v_{n-1}}^{\mathbf{v}}\mid d)= \sum_{\mathbf{u}\in\mathbb{Z}_{2}^{n}}f(\lambda(\mathbf{u},\mathbf{v})|l_{ \lambda(\mathbf{s})}^{m}(\mathbf{u})+d) \tag{4}\]  
The integration variable, \(\mathbf{u}\) (x if what we are considering are the horizontal lines), is now split in two, since we are transforming bits that go from being considered'vertical bands', \(\mathbf{v}\), to being considered'slopes', \(s\). See Figure 1.  
And finally, we arrive to the core equation that becomes the algorithm of the forward multiscale DRT, the equation that maps values from one stage to its consecutive:  
\[\widetilde{f}^{m+1}(\underbrace{s_{n-m-1},\overbrace{s_{n-m},\,\ldots,\,s_{n -1}}^{s\cdot m+1\,\,bits}}_{n\,\,bits}\mid\overbrace{v_{m+1},\,\ldots,\,v_{n- 1}}^{\mathbf{v}\cdot n-m-1\,\,bits}}_{n\,\,bits}\mid d)=\widetilde{f}^{m}( \mathbf{\sigma}\,|\,0,\mathbf{v}\,|\,d)+\ \widetilde{f}^{m}(\mathbf{\sigma}\,|\,1,\mathbf{v}\,|\,d+s_{n-m-1}+\lambda(\mathbf{ \sigma})) \tag{5}\]  
Notice that single comma () is used to separate binary indexes, and vertical bar () is used to separate different parameters. This latter equation, surrounded by a for \(m=0\) to \(log_{2}(N)\) loop, and the adequate loops traversing variables \(d,s\), and \(\mathbf{v}\) is basically the forward DRT algorithm. It can be seen that it is performing just two sums to compute a new datum. The described outer loops account for the computational complexity: \(O(N^{2}\log N)\). Notice also that the number of bits in partial stages is varying and depends on \(m\), the current stage. When \(m=0\), the array \(\widetilde{f}^{0}(s|v|d)\) is really bidimensional, as variable \(s\) is still empty, so \(\widetilde{f}^{0}(-|v|d)\) maps directly to \(f(x|y)\). And when \(m=n\), the last stage,  
Figure 1: Depiction of partial transforms of multiscale DRT. As the stage increases, the vertical bands decrease, and the slopes become more numerous. variable \(v\) will be emptied, and so \(\widetilde{f}^{n}(s|-|d)\) is the desired result \(\mathfrak{N}f(s|d)\). That can also be appreciated by evaluating the definition of partial transform, Equation (4), for stage \(m=n\): \(\mathfrak{N}f(s|-|d)=\)\(\widetilde{f}^{n}(s_{0},\,\ldots,\,s_{n-1}\,|-|\,d)=\sum_{u=0}^{N-1}f(u\,|\,l_{ \lambda(s)}^{n}(u)+d).\) This last equation is none other than the discrete version of Radon transform as expressed in Equation (2) with multiplication with the slope substituted by discrete line interaction between \(u\) and \(s\) at binary level. More details on the formulation of the discrete Radon transform can be found on a previous work [8].
# Cell-Based Target Localization and Tracking with an Active Camera
###### Abstract  
This paper proposes a new method of target localization and tracking. The method consists of four parts. The first part is to divide the scene into multiple cells based on the camera's parameters and calibrate the position and error of each vertex. The second part mainly uses the bounding box detection algorithm, YOLOv4, based on deep learning to detect and recognize the scene image sequence and obtain the type, length, width, and position of the target to be tracked. The third part is to match each vertex of the cell in the image and the cell in the scene, generate a homography matrix, and then use the PnP model to calculate the precise world coordinates of the target in the image. In this process, a cell-based accuracy positioning method is proposed for the first time. The fourth part uses the proposed PTH model to convert the obtained world coordinates into \(P\), \(T\), and \(H\) values for the purpose of actively tracking and observing the target in the scene with a PTZ camera. The proposed method achieved precise target positioning and tracking in a 50 cm \(*\) 250 cm horizontal channel and a vertical channel. The experimental results show that the method can accurately identify the target to be tracked in the scene, can actively track the moving target in the observation scene, and can obtain a clear image and accurate trajectory of the target. It is verified that the maximum positioning error of the proposed cell-based positioning method is 2.31 cm, and the average positioning error is 1.245 cm. The maximum error of the proposed tracking method based on the PTZ camera is 1.78 degrees, and the average error is 0.656 degrees.  
target tracking; YOLOv4; PTZ camera; PnP model; PTH model +
Footnote †: journal: Applied  
Article
## 3 A Proposed Approach
### Path Planning Approach
#### 3.3.1 Trajectory Prediction of OS and TS  
The trajectory prediction of OS is based on the assumption that OS travels along the path at a constant speed. It should be noted that the path points are parameterized with arc length from the start point [26]. Then, a path can be denoted with \(P(s)\), where \(P(s)\) is a  
Figure 4: The representation of a dynamic obstacle with different configurations. (**a**) \(r_{2}=1.0\) and \(d_{2}=50\) m, (**b**) \(r_{2}=1.5\) and \(d_{2}=75\) m.  
Figure 3: The speed function of the FM method designed for dynamic obstacles.  
point on the path and the corresponding \(s\) is the arc length of the path between the current and the start points. Hence, the trajectory of OS can be characterized as follows:  
\[\mathbf{p_{os}}(t)=P(v_{os}t), \tag{4}\]  
where \(\mathbf{p_{os}}(t)\) is the predicted position of OS at time \(t\), and \(v_{os}\) indicates the velocity of OS. When \(t=0\), \(\mathbf{p_{os}}(0)\) equals \(P(0)\), which means that the OS is located at the start point of the current path.  
In addition, the trajectory prediction of TS is also significant for collision avoidance [27, 28]. The most basic and widely used method for predicting the trajectory of TS is based on the premise that the TS maintains its velocity and ignores external environmental disturbances [27]. In this work, such a trajectory prediction method is adopted. Therefore, the trajectory of TS based on the position of TS at time \(t_{1}\) can be defined as follows:  
\[\mathbf{p_{ts}}(t)=\mathbf{p_{ts}}(t_{1})+v_{ts}(t-t_{1}), \tag{5}\]  
where \(\mathbf{p_{ts}}(t)\) denotes the predicted position of TS at time \(t\), and \(\mathbf{p_{ts}}(t_{1})\) indicates the known position of TS at time \(t_{1}\). \(v_{ts}\) is the velocity of TS.  
It is worth noting that the external environmental disturbances and the collision avoidance intentions are not included in the present trajectory prediction methods. However, once a new trajectory prediction method is achieved, it can directly replace the current method without any additional effort.
## 2 Materials and Methods
### Inversion Model Construction, Accuracy Verification, and Salinity Visualization
#### 2.8.1 Plsr  
Partial least squares regression (PLSR) is a statistical method used to model the linear relationship between two datasets, especially useful when both datasets contain multiple variables and multicollinearity exist among the variables. PLSR builds a model by extracting latent components from the two sets of variables (predictor set and response set, which can maximize the covariance structure between the predictors and responses. This method not only addresses the issue of multicollinearity among predictors but also allows for effective prediction when complex relationships exist between predictor matrix \(\mathbf{X}\) and response matrix \(\mathbf{Y}\)) [35]. The general multivariate basic equation is as follows:  
\[\mathbf{X}=\mathbf{TP}^{\mathbf{T}}+\mathbf{E}\]  
\[\mathbf{Y}=\mathbf{UQ}^{\mathbf{T}}+\mathbf{F}\]  
where \(\mathbf{Y}\) is the \(\mathbf{n}\times\mathbf{p}\) response matrix; \(\mathbf{X}\) is the \(\mathbf{n}\times\mathbf{m}\) modeling matrix; \(\mathbf{T}\) is the projection of \(\mathbf{X}\), also known as the factor matrix; \(\mathbf{U}\) is the projection of \(\mathbf{Y}\); \(\mathbf{P}\) and \(\mathbf{Q}\) are orthogonal loading matrices; and \(\mathbf{E}\) and \(\mathbf{F}\) represent errors. Based on the estimated factors \(\mathbf{T}\) and \(\mathbf{U}\) and loading matrices \(\mathbf{P}\) and \(\mathbf{Q}\), a linear model between \(\mathbf{Y}\) and \(\mathbf{X}\) can be established using the PLSR model. The equation is as follows:  
\[\mathbf{Y}=\mathbf{X}\mathbf{b}+\mathbf{e}\]  
where \(\mathbf{b}\) is the coefficient of the PLSR model, and \(\mathbf{e}\) is the error vector. This study explores the feasibility of establishing a quantitative relationship between soil salinity content and influencing factors using the PLSR model. In this study, GridSearchCV was used to tune the parameters for the PLSR model, searching for the number of principal components in the range of 0 to 10. Then, the model was trained using the optimal number of principal components.
## 4 Experimental Results and Discussion
### Efficiency Comparison between Concentrating and Nonconcentrating PV Systems
\begin{table}
\begin{tabular}{c c c c} \hline  & **Cities** & \
\begin{tabular}{c} **Optimum Tilt Angle** \\ (\({}^{\circ}\)) \\ \end{tabular} &
\begin{tabular}{c} \(H_{NCPV}\) (kWh) \\ \end{tabular} \\ \hline
1 & Medellin (Colombia) & 4.5 & 950.39 \\
2 & Bangkok (Thailand) & 13.2 & 1002.58 \\
3 & Morelia (Mexico) & 19.9 & 1198.87 \\
4 & Karachi (Pakistan) & 23.6 & 1265.54 \\
5 & Cairo (Egypt) & 24.2 & 1293.05 \\
6 & Almeria (Spain) & 30.3 & 1264.38 \\ \hline \end{tabular}
\end{table} 
Table 6: Results obtained for the NCPV system. Figure 23: Solar irradiation gain incident on the photovoltaic cells. is 10.03 (m/s), the \(NCPV\) systems perform much better. The energy gain of \(NCPV\) systems decreases considerably with increasing latitude.
## 3 Distributed PV Storage Virtual Synchronous Generator System
### Bidirectional PV Storage Converter
#### 3.4.2 Improved PQ Control  
In this subsection, an improved PQ control strategy with active regulation characteristics is proposed. The control block diagram is shown in Figure 13.  
where, \(f_{0}\), \(U_{0}\) are the reference frequency and voltage, respectively. \(f\) and \(U\) are the frequency and voltage at steady state operation, respectively. \(R_{P}\), \(R_{Q}\) are the inverter active and reactive droop coefficient, respectively. Actually, they are the magnitude of the slope of the power-frequency characteristic and voltage-droop characteristic of power supply. The power reference of the control strategy consists of the initial reference value and the correction. The expressions are shown in Equations (22)-(25).  
\[P_{\text{ref}}\ =\ P_{\text{ref0}}+\Delta P \tag{22}\]  
\[Q_{\text{ref}}\ =\ Q_{\text{ref0}}+\Delta Q \tag{23}\]  
\[\Delta P\ =\ \frac{1}{R_{P}}\cdot(f_{0}-f) \tag{24}\]  
\[\Delta Q\ =\ \frac{1}{R_{Q}}\cdot(U_{0}-U) \tag{25}\]  
In the steady state, the inverter outputs active power and reactive power, according to the power reference values. The frequency and voltage satisfy \(f\) = \(f_{0}\), \(U\) = \(U_{0}\) so the correction amount \(\Delta P\) and \(\Delta Q\) is zero, which results in \(P_{\text{ref}}\ =\ P_{\text{ref0}}\), \(Q_{\text{ref}}\ =\ Q_{\text{ref0}}\) and means the inverter can output constant power as a PQ source. In transient process, the inverter can take the initiative to participate in frequency regulation process. When the load is increased, the frequency of the power grid is reduced,\(f\) < \(f_{0}\), \(\Delta P\) is positive, and \(P_{\text{ref}}\) increases. The inverter increases the power according to the increased new reference value to supply the load for the purpose of reducing the decline process of frequency. On the contrary, when the load drops, the grid frequency rise, \(f\) > \(f_{0}\), \(\Delta P\) is negative, and \(P_{\text{ref}}\) decreases. The inverter reduces the power output, according to the reduced power reference value to slow down the rise of frequency. In this way, when the frequency is fluctuating, the PV storage system can participate in the frequency regulation process, which is consistent with the requirements of the autonomous power system [14].  
Figure 13: Improved PQ control strategy.
## 2 Materials and Methods
### Spectral Measurements  
An auto-observation spectra system was installed on the 5 m tower-based platform (Bergsun Inc., Beijing, China). Over the course of the growing period of winter wheat, canopy spectra were continuously monitored by an Ocean Optics QE65 pro spectrometer (QE65 pro; Ocean Optics, Dunedin, FL, USA). The observation system covers a spectral range of 645-805 nm at a resolution of \(-0.34\) nm. The Ocean Optics QE65 pro spectrometer samples at an interval of about 0.17 nm and has a high signal-to-noise ratio (SNR) greater than 1000 [35], which allows for better extraction of the fluorescence information. A cosine corrector (CC3-3-UV-S; Ocean Optics, Inc., Dunedin, FL, USA) and a conical fore-optic (bare fiber) were used to capture the downwelling incident radiance (\(E(\lambda)\)) and upwelling radiance (\(L(\lambda)\)), respectively. The former has a large field of view (FOV) of 180\({}^{\circ}\), and the latter can make measurements within a small FOV of about 25\({}^{\circ}\). In order to avoid the influence of the tower, the upwelling radiance was measured off-nadir with a view zenith angle of 25\({}^{\circ}\). The ground instantaneous field of view (GIFOV) was close to 2.2 m. The GIFOV was used to describe the ground size observed by sensors (\(GIFOV=2*\tan(FOV/2)*H\)). In addition, the spectrometer uses a'sandwich' type (the downwelling solar irradiance was first collected, the upwelling irradiance was then measured, and the downwelling solar irradiance was finally collected again by alternately opening the up and down channels) to reduce the influence of rapidly changing light conditions [36]. Moreover, the integration time can automatically be optimized depending on the light conditions. More details about the spectra observation system can be found in [PERSON] et al. [35]. The sowing date was 25 September 2020, and the harvest date was 5 June 2021. Finally, we gathered spectral data for the entire winter wheat growth cycle, from DOY 272 in 2020 to DOY 157 in 2021, for a total of 272 days.
## 4 Results
### Performance Measurements and Predictions
#### 4.1.1 Isolated Rotor  
Rotor performance values are calculated as the mean over the tenth, and final, rotor revolution. The isolated rotor performance results of this paper are compared with other available data for the APC 8x4.5-MR rotor in the literature and in industry. Experiments conducted by [PERSON] et al. at the University of Alabama, referred to as UA in this paper, measured thrust and torque using the RC Benchmark Series 1580 Dynamometer [64]. The rotor was also tested, using the Cobra CM-2206/30 Motor. The thrust data are available on the Innovative Designs website [65]. This work will be referred to as Cobra data. Only thrust was measured. Finally, we also include the manufacturer-reported performance data available on the APC that are computed using vortex theory [66].  
The thrust coefficient \(C_{\rm T}=T/(\rho\pi R^{4}\Omega^{2})\), where \(T\) is the thrust, \(\rho\) is the air density, \(R\) is the rotor radius, and \(\Omega\) is the rotor rotation rate and the torque coefficient \(C_{Q}=Q/(\rho\pi R^{5}\Omega^{2})\), where \(Q\) is the torque are plotted in Figure 7. The CFD results are in reasonable agreement with the experimental data. However, the scatter in the experimental data further highlights the difficulty of characterizing a rotor's performance. While the UA thrust values were obtained using an industry standard benchmark measurement device, they seem quite low. This is also confirmed by initial thrust measurements of the same rotor at BU performed using a JR3 Multi-Axis Force/Torque Sensor, which are closer to the Cobra and Helios results. The low value could be due to a calibration issue in the experiment. Even given all of these challenges faced when attempting validation, one can draw some  
Figure 5: The acoustic spectra of a dual rotor case at an above-plane mic measured in the experiments.  
Figure 6: The acoustic spectra of a dual rotor case at an above-plane mic predicted by Helios/PSUWOPWOP, UCD-Quietffy, and a combination of both.  
general conclusions. Both the CFD and the experiments show an overall increasing trend with RPM for both thrust and torque coefficient values, which is not present in the APC inviscid calculation. This points to a Reynolds number effect that can only be captured with CFD.  
The rotor figure of merit is a measure of hovering efficiency defined as \(\eta=C_{T}^{3/2}/(\sqrt{2}C_{Q})\)[67]. A comparison of experimental and computed values for the APC rotor is plotted in Figure 8. The Helios results compare well with APC, even though the APC vortex theory predicted higher thrust and torque coefficients than Helios. When compared to UA, the computed FOM is higher, due to the low thrust value recorded by UA. Previous CFD results using fully-turbulent turbulence models have shown low figure of merit predictions, due to failure to capture boundary layer transition and separation [23; 39]. The current results would, therefore, indicate that the flow is largely turbulent over this rotor, which allows the simulation to give a good prediction of FOM.
# Sliding Mode Control of Electro-Hydraulic Position Servo System Based on Adaptive Reaching Law
## 3 Design of Sliding Mode Controller Based on Adaptive Reaching Law
### Controller Design  
Step 1: Designing a suitable controller can make the sliding points outside the sliding mode switching surface reach the sliding mode switching surface within a certain period of time, that is to say, the following conditional expression is satisfied  
\[\dot{s}=0 \tag{30}\]  
The equivalent control part can be derived from Equation (27) to obtain  
\[\begin{array}{rl}\dot{s}&=c_{1}\dot{e}_{1}+c_{2}\dot{e}_{2}+\dot{e}_{3}\\ &=c_{1}\dot{e}_{1}+c_{2}\dot{e}_{2}-\  
where  
\[\text{sgn}(s)=\left\{\begin{array}{ll}1&s>0\\ -1&s<0\end{array}\right. \tag{34}\]  
Combining (31) and (33) we get  
\[\dot{s}=c_{1}e_{2}+c_{2}e_{3}+\dot{e}_{3}=-\zeta\text{sgn}(s)-\zeta s \tag{35}\]  
Substituting into (31) we get  
\[\begin{array}{ll}\dot{s}&=c_{1}e_{2}+c_{2}e_{3}-{\omega_{h}}^{2}e_{2}-2\xi_{ h}\omega_{h}e_{3}-K_{sys}{\omega_{h}}^{2}u+{\omega_{h}}^{2}\dot{r}+2\xi_{h} \omega_{h}\ddot{r}+\dddot{r}\\ &=-\zeta\text{sgn}(s)-\zeta s\end{array} \tag{36}\]  
The exponential reaching law SMC control law \(u\) is designed as:  
\[u=\frac{1}{K_{sys}{\omega_{h}}^{2}}\bigg{[}\begin{array}{c}(c_{1}-{\omega_{ h}}^{2})e_{2}+(c_{2}-2\xi_{h}\omega_{h})e_{3}+{\omega_{h}}^{2}\dot{r}+2\xi_{h} \omega_{h}\ddot{r}\\ +\dddot{r}+\zeta\text{sgn}(s)+\zeta s\end{array}\bigg{]} \tag{37}\]  
If \(\xi\) is too small, the approach velocity will be very slow, and the adjustment process will be too slow; on the contrary, if \(\xi\) is too large, the system velocity will be large, and the jitter will be large when the system reaches the switching surface.  
A better adaptive reaching law for reducing system jitter is adopted below. The constructed adaptive reaching law is  
\[\dot{s}=-\xi|s|^{2}\text{sgn}(s)-\zeta\frac{1-e^{-|x|}}{1+e^{-|x|}}\text{sgn}(s) \tag{38}\]  
Combining Equations (31) and (38), we obtain  
\[\dot{s}=c_{1}e_{2}+c_{2}e_{3}+\dot{e}_{3}=-\xi|s|^{2}\text{sgn}(s)-\zeta\frac {1-e^{-|x|}}{1+e^{-|x|}}\text{sgn}(s) \tag{39}\]  
Substituting into Equation (31) yields:  
\[\begin{array}{ll}\dot{s}&=c_{1}e_{2}+c_{2}e_{3}-{\omega_{h}}^{2}e_{2}-2\xi_ {h}\omega_{h}e_{3}-K_{sys}{\omega_{h}}^{2}u\\ &+{\omega_{h}}^{2}\dot{r}+2\xi_{h}\omega_{h}\ddot{r}+\dddot{r}\\ &=-\xi|s|^{2}\text{sgn}(s)-\zeta\frac{1-e^{-|x|}}{1+e^{-|x|}}\text{sgn}(s) \end{array} \tag{40}\]  
The SMC actual control law \(u\) is designed as  
\[u=\frac{1}{K_{sys}{\omega_{h}}^{2}}\left[\begin{array}{c}(c_{1}-{\omega_{h }}^{2})e_{2}+(c_{2}-2\xi_{h}\omega_{h})e_{3}+{\omega_{h}}^{2}\dot{r}+2\xi_{h} \omega_{h}\ddot{r}\\ +\dddot{r}+\xi|s|^{2}\text{sgn}(s)+\zeta\frac{1-e^{-|x|}}{1+e^{-|x|}}\text{ sgn}(s)\end{array}\right] \tag{41}\]  
where \(\xi\) and \(\zeta\) are the adaptive reaching law parameters, and \(\xi>0,\zeta>0\).
###### Abstract  
This study presents an active noise control (ANC) algorithm using long short-term memory (LSTM) layers as a type of recurrent neural network. The filtered least-mean-square (FxLMS) algorithm is a widely used ANC algorithm, where the noise in a target area is reduced through a control signal generated from an adaptive filter. Artificial intelligence can enhance the reduction performance of ANC for specific applications. An LSTM is an artificial neural network for recognizing patterns in arbitrarily long sequence data. In this study, an ANC controller consisting of LSTM layers based on deep neural networks was designed for predicting a reference noise signal, which was used to generate the control signal to minimize the noise residue. The structure of the LSTM neural networks and procedure for training the LSTM controller for the ANC were determined. Simulations were conducted to compare the convergence time and performances of the ANC with the LSTM controller and those with a conventional FxLMS algorithm. The noise source adopted sounds from a single-cylinder diesel engine, while reference noises selected were single harmonics, superposed harmonics, and impulsive signals generated from the diesel engine. The characteristics of each algorithm were examined through a Fourier transform analysis of the ANC results. The simulation results demonstrated that the proposed ANC method with LSTM layers showed outstanding noise reduction capabilities in narrowband, broadband, and impulsive noise environments, without high computational cost and complexity relative to the conventional FxLMS algorithm.  
active noise control; long short-term memory; impulsive noise; diesel engine noise +
Footnote †: journal: Applied  
Acticle Noise Reduction with Filtered Least-Mean-Square Algorithm Improved by Long Short-Term Memory Models for Radiation Noise