esa-sceva/satcom-chunk-collection huggingface dataset:
# Control Chart Concurrent Pattern Classification Using Multi-Label Convolutional Neural Networks
## 3 Experimental Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric\(\backslash\)Algorithm** & **RF** & **SVC** & **CNN** \\ \hline Accuracy & 0.7652 (0.0039) * & 0.9100 & 0.9406 (0.0031) \\ Recall & 0.7945 (0.0026) & 0.9273 & 0.9557 (0.0043) \\ Precision & 0.8131 (0.0031) & 0.9287 & 0.9546 (0.0041) \\ \(F_{1}\) & 0.8005 (0.0029) & 0.9259 & 0.9539 (0.0037) \\ \(F_{2}\) & 0.7964 (0.0027) & 0.9262 & 0.9546 (0.0039) \\ Hamming loss & 0.0481 (0.0011) & 0.0210 & 0.0159 (0.0013) \\ Jaccard\_score & 0.8143 (0.0036) & 0.9185 & 0.9383 (0.0050) \\ \hline \hline \end{tabular}  
* Numbers in parentheses are standard deviations.  
\end{table} 
Table 6: Classification performance in experiment 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric\(\backslash\)Algorithm** & **RF** & **SVC** & **CNN** \\ \hline Accuracy & 0.7574 (0.0058) * & 0.8640 & 0.9232 (0.0019) \\ Recall & 0.7981 (0.0049) & 0.9110 & 0.9564 (0.0050) \\ Precision & 0.8112 (0.0049) & 0.8960 & 0.9461 (0.0025) \\ \(F_{1}\) & 0.7997 (0.0050) & 0.8994 & 0.9486 (0.0032) \\ \(F_{2}\) & 0.7977 (0.0049) & 0.9049 & 0.9523 (0.0041) \\ Hamming loss & 0.0509 (0.0016) & 0.0307 & 0.0175 (0.0008) \\ Jaccard\_score & 0.8052 (0.0055) & 0.8840 & 0.9324 (0.0029) \\ \hline \hline \end{tabular}  
* Numbers in parentheses are standard deviations.  
\end{table} 
Table 8: Classification performance in experiment 4 after swapping the training and test sets.
# Telemedicine: A Survey of Telecommunication Technologies, Developments, and Challenges
## 4 Evolution of Communications Technologies for Telemedicine
### Classification of Communication Technologies in Telemedicine  
Communication technologies for telemedicine can be broadly classified into short-range communications such as Bluetooth, Wireless Fidelity (Wi-Fi), Zigbee, and Ultra-wideband (UWB), long-range communications such as satellite-based, internet-based, and mobile cellular network, and Wide Area Network (WAN), as shown in Figure 10.
## 3 Results
### Initial Characteristics
#### 3.2.1 Plasma TAC  
The results reveal that the experimental sauces significantly affected plasma TAC (\(p\) = 0.01) throughout the trial periods (group \(\times\) time interaction), despite the absence of any group or time effects (\(p\) > 0.05). Under within-group analysis, habitual consumption of the biofunctional miso-type sauce, enhanced with biocarotenoids, significantly increased plasma TAC (\(p\) = 0.04, MD = 0.07). On the contrary, after 30 days of consuming the control sauce, the plasma TAC of participants experienced a significant downward trend (\(p\) = 0.03, MD = \(-\)0.12) (Figure 2g). It is noteworthy that the baseline mean value in the control group was higher than the respective miso group concentration (\(p\) = 0.06, MD = 0.14). Even so, at  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Mean \(\pm\) SD** & \(p\)**Value 1 ** \\ \hline Body Water (kg) & 53.85 \(\pm\) 8.79 & 0.27 \\ Bone Mass (kg) & 2.78 \(\pm\) 0.60 & 0.01 2  \\ Waist/Hip Circumference Ratio (index) & 0.68 \(\pm\) 0.22 & 0.08 \\ Biochemical Characteristics & & \\ Total Cholesterol (mg/dL) & 143.70 \(\pm\) 21.12 & 0.62 \\ Glucose (mg/dL) & 75.70 \(\pm\) 12.84 & 0.93 \\ HDL Cholesterol (mg/dL) & 45.37 \(\pm\) 9.36 & 0.08 \\ LDL Cholesterol (mg/dL) & 81.64 \(\pm\) 33.32 & 0.96 \\ Triglycerides (mg/dL) & 61.20 \(\pm\) 21.38 & 0.58 \\ Uric Acid (mg/dL) & 4.30 \(\pm\) 1.34 & 0.69 \\ TAC (mmol/L) & 0.27 \(\pm\) 0.09 & 0.53 \\ \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **30-Day** & \(p\)**-Value 1 ** & **\(p\)-Value 1 ** & **\(p\)-Value 1 ** \\ \hline
**Total cholesterol (mg/dL)** & Control & 137.70 \(\pm\) 25.90 & 195.60 \(\pm\) 42.10 & & \\  & Miso & 141.80 \(\pm\) 28.20 & 183.60 \(\pm\) 37.08 & 0.80 & \textless{}0.001 2  & 0.25 \\
**Glucose (mg/dL)** & Control & 70.80 \(\pm\) 11.69 & 83.75 \(\pm\) 9.08 & & \\  & Miso & 81.30 \(\pm\) 10.40 & 110.00 \(\pm\) 53.69 & 0.08 & 0.04 2  & 0.39 \\ HDL cholesterol (mg/dL) & Control & 46.00 \(\pm\) 3.53 & 58.25 \(\pm\) 1.75 & & \\  & Miso & 55.37 \(\pm\) 4.77 & 59.50 \(\pm\) 4.22 & 0.27 & 0.002 2  & 0.18 \\ LDL cholesterol (mg/dL) & Control & 74.75 \(\pm\) 26.69 & 119.05 \(\pm\) 45.68 & & \\  & Miso & 86.27 \(\pm\) 37.68 & 101.17 \(\pm\) 33.30 & 0.75 & \textless{}0.001 2  & 0.03 2  \\
**Triglycerides (mg/dL)** & Control & 58.97 \(\pm\) 6.76 & 73.70 \(\pm\) 16.60 & 0.49 & 0.41 & 0.03 2  \\
**Uric Acid (mg/dL)** & Control & 4.30 \(\pm\) 1.34 & 5.01 \(\pm\) 1.20 & & \\  & Miso & 4.86 \(\pm\) 0.82 & 5.36 \(\pm\) 0.54 & 0.33 & 0.001 2  & 0.47 \\  & Control & 0.33 \(\pm\) 0.15 & 0.20 \(\pm\) 0.15 & & \\ TAC (mmol/L) & Miso & 0.18 \(\pm\) 0.09 & 0.26 \(\pm\) 0.12 & 0.50 & 0.001 2  & 0.01 2  & \\ \hline \end{tabular}
\end{table}
Table 3: Baseline and 30-day follow-up values of biochemical and antioxidant parameters of participants.  
the endpoint, the plasma TAC was nonsignificantly higher in the miso group compared with the control (\(p\) = 0.46, MD = 0.05) (Figure 2g).
# Experimental Research on the Effects of Suction Ports on Twin Screw Expander Performance
## 5 Conclusions  
With different rotation speeds, suction pressures and discharge pressures, an experimental investigation into the performance of a twin screw expander was carried out. The pressure loss value, the ratio of pressure loss to suction pressure, and the suction coefficient were used to evaluate the influence of the suction port. Conclusions are as follows.  
Lower rotation speeds decreased the pressure loss and increased the suction coefficient. With constant suction and discharge pressure, increasing the rotation speed increases the pressure loss value and pressure loss ratio. With a rotation speed of 1600 rpm, the pressure loss value and pressure loss ratio were 62.8 kPa and 0.142, respectively. The suction coefficient decreased from 0.965 to 0.912 when the rotation speed increased from 1400 rpm to 1600 rpm.  
Higher suction pressure increases the pressure loss value with a constant suction port. With a constant rotation speed and discharge pressure, increasing the suction pressure increases the pressure loss value but decreases the pressure loss ratio and the suction coefficient.  
With a constant rotation speed and suction pressure, discharge pressure variations did not change the suction process. The pressure loss value and the ratio of pressure loss to suction pressure had constant values. The suction coefficient showed small variations with the discharge pressure.  
The results and conclusions in this paper are given based on a specific twin screw expander with a constant suction area. The pressure loss value cannot be used directly in other twin screw expanders. Further research should be carried out to guide future expander designs.  
Conceptualization, Y.H. and Z.X.; validation, Y.Z.; investigation, H.W.; data curation, T.J.; writing--original draft preparation, Y.H. and Y.Z.; writing--review and editing, Z.X.; All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (No. 51976148) and the Scientific and Technological Project of Henan Province (No.222102320269).  
Not applicable.  
We have no conflicts of interest to declare.  
Figure 10: \(\eta_{\text{s}}\) variations with discharge pressure.
## 3 System under Consideration  
Block diagram of the system under consideration for performance evaluation of the proposed incremental conductance-based particle swarm optimization (ICPSO) algorithm is detailed in Figure 2. An ideal photo-voltaic cell is comprised of a single diode connected in parallel with a light current source, which is connected to the single-phase converter and controlled by the proposed ICPSO based global maximum MPPT algorithm. An electrical equivalent circuit of a solar cell can be represented by a single or double diode model [38]. Single diode equivalent model is found simple with accurate efficiency [39]. The single diode equivalent circuit is as illustrated in Figure 3. In this circuit, the relation between output voltage (V) and current (I) of the solar cell can be expressed by the following relation where the symbols are defined as \(I_{ph}\): current of the solar cell, \(I_{0}\): saturation current, A: curve fitting factor, \(R_{sh}\): shunt resistance, \(R_{s}\): series resistance, q: electronic charge, and k: Boltzmann constant [40]. Data of the solar PV system used for the study are available in Appendix A.  
\[I=I_{ph}-I_{0}\left\{exp\left[\frac{q(V+IR_{s})}{AKT}\right]-1\right\}-\left( \frac{V+IR_{s}}{R_{sh}}\right) \tag{1}\]  
Figure 1: Characteristics of Solar-PV under different irradiance and temperature levels.
# Design and Numerical Study of Induction-Heating Graphitization Furnace Based on Graphene Coils
## 2 Numerical Model  
### Structure of Induction-Heating Graphitization Furnace  
This paper presents a study on an original IHGF, as shown in Figure 1a. The furnace has a radius of 0.9 m and a height of 2.1 m, and its main components are the furnace shell, coil, graphite heater, and insulation. The vacuum environment of the furnace, with a pressure of less than 0.5 Pa, prevents the oxidation of the graphite heater and charge at high temperatures. The carbon-black and carbon-felt insulation does not react with the graphite heater, even when in contact with it at high temperatures. The copper tube coil is located in the corundum insulation layer, and cooling water with a pressure of 0.2 MPa is passed inside the copper tube. By applying an alternating current with a frequency of 1500 Hz to the coil, eddy currents are induced in the graphite heater. This, in turn, heats the heater through the Joule effect. The temperature at control point A (0, 1.5) was measured throughout the manufacturing process.  
The graphene-coil IHGF is shown in Figure 1b. The insulation layer contains a 30 mm radius graphene coil to which an alternating current is applied. The ultra-high-heat performance of the graphene material in a vacuum environment eliminates the need for cooling water to pass through the coil. The heat generated by the coil is used to heat the graphite heater or insulation. Compared to original furnaces, the graphene-coil furnace makes more efficient use of the ohmic heat on the coils, resulting in higher energy efficiency. In addition, the proximity of the graphene coil to the graphite heater ensures higher electrical efficiency.  
The furnace charge is made of graphite products, the furnace insulation is made of carbon black and carbon felt, and the furnace wall is made of cement. The specific material parameters were obtained from the literature [35; 36; 37; 38] and are expressed as polynomials or interpolated functions due to the significant variation in the material properties during the heating process. The study simplified the heat transfer process in the furnace by unifying and simplifying the convection, radiation, and heat transfer to solid heat transfer. The  
Figure 1: Geometric modeling of IHGF: (**a**) original IHGF; (**b**) graphene-coil IHGF.  
material parameters for the graphene coil were chosen based on the macroscopic graphene film prepared by our group. The conductivity of the coil was measured to be \(1.1\times 10^{6}\) S/m using the four-probe method. The parameters of coils are shown in Table 1.
## 3 Methodology
### Computation of Monthly Land-Water Masks with Data Gaps  
The computation of monthly land-water mask with remaining data gaps caused by clouds, cloud shadows, and snow/ice is divided into four processing steps. The first step is the pre-processing step in which the input data are downloaded. Afterwards, the data are homogenized by converting them to the same spatial resolution and image projection. In the second step, water indexes are computed followed by an automated classification which is finally used to create monthly land-water masks with remaining data gaps.
## 2 Materials and Methods
### Mix Design  
Pervious concrete is similar to ordinary concrete in composition, which is composed of cementitious material, aggregate, water and an admixture. The difference is the amount of fine aggregate in pervious concrete. The pervious concrete in this paper does not use fine aggregates. The mix design of pervious concrete is a decisive factor for determining the performance of pervious concrete. Usually, a target porosity is set first, and then the mass of the corresponding components are calculated by the following equations.  
\[W_{A}=\alpha\cdot\rho_{A} \tag{1}\]  
\[V_{CM}=1-\alpha\cdot(1-\varphi_{A})-\varphi_{TP} \tag{2}\]  
\[W_{C}=\frac{\rho_{C}\rho_{W}V_{CM}}{\rho_{C}R_{w/c}+\rho_{W}} \tag{3}\]  
\[W_{w}=W_{c}\cdot R_{w/c} \tag{4}\]  
\[W_{wr}=\delta\cdot W_{C} \tag{5}\]  
\[W_{MA}=\left(V_{CM}-\frac{W_{W}}{\rho_{W}}-\frac{W_{c}(1-\beta)}{\rho_{C}} \right)\rho_{MA} \tag{6}\]  
where: \(W_{A}\) is the mass of the aggregate of pervious concrete measured in unit volume, kg/m\({}^{3}\). \(\alpha\) is the correction coefficient of the aggregate usage, taking 0.98. \(\rho_{A}\) is the bulk density of the aggregates, kg/m\({}^{3}\). \(V_{CM}\) is the paste volume of the cementitious materials, m\({}^{3}\)/m\({}^{3}\). \(\varphi_{A}\) is the packed porosity of the aggregates, %. \(\varphi_{TP}\) is the target porosity of the pervious concrete, %. \(W_{C}\) is the mass of the cement in unit volume, kg/m\({}^{3}\). \(R_{w/c}\) is the ratio of the water to the cementitious materials. \(\rho_{C}\) is the true density of the cement, taking 3150 kg/m\({}^{3}\). \(W_{w}\) is the mass of the water in unit volume, kg/m\({}^{3}\). \(W_{wr}\) is the mass of the water reducer in unit volume, kg/m\({}^{3}\). \(\delta\) is the ratio of the water reducer to the cementitious materials. \(W_{MA}\) is the mass of the mineral admixture in unit volume, kg/m\({}^{3}\). \(\rho_{W}\) is the true density of water at 20 \({}^{\circ}\)C, taking 1000 kg/m\({}^{3}\). \(\rho_{MA}\) is the true density of the mineral admixture, kg/m\({}^{3}\).  
In this paper, different target porosities (8%-30%) were selected to prepare pervious concrete using iron tailings as the coarse aggregates. At the same time, the water-cement ratio, silica fume-cement ratio, and water reducer-cement ratio were 0.23%, 6%, and 0.2%, respectively. For clarity, the mix proportions of different pervious concrete mixture are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Category**} & **Particle Size** & **Specific Gravity** & **Bulk Density** & **Void Ratio** \\  & **(mm)** & **(kg\(\cdot\)m\({}^{3}\))** & **(kg\(\cdot\)m\({}^{3}\))** & **(\%)** \\ \hline Iron tailing & 4.75–9.5 & 2750 & 1500 & 45 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Basic properties of the coarse aggregate of iron tailings.
# Differential Privacy in Federated Learning: An Evolutionary Game Analysis
## 5 Numerical Results
### Stability Analysis  
In this section, we conduct a comprehensive stability analysis to verify the theoretical results presented in the previous section. Through numerical simulations, we examine the stability of the system under different scenarios, including two-strategy, four-strategy, and eight-strategy cases. The goal is to demonstrate that the system converges to an ESS under various initial conditions and parameter settings.  
Two-Strategy Scenario  
We begin with a two-strategy scenario, where the system's stability is analyzed under varying Gaussian noise powers. The parameters are set as follows: \(I=80,000\), \(N=2\), \(\sigma_{1}=0.1\), \(E_{1}=100\), \(\sigma_{2}=1.1\), \(E_{2}=695\), \(\eta=0.0002\), and \(A=5\). Additional parameters  
Figure 4: Utilities for different scenarios: (**a**) Two-strategy scenario. (**b**) Four-strategy scenario.  
include \(a=0.02\), \(b_{1}=0.008\), \(b_{2}=0.004\), and initial shares \([0.4,0.6]\). The evolution of shares and utilities is shown in Figure 5.  
The Jacobian matrix satisfies Equation (23), indicating that it is negative definite. The equilibrium point is calculated as \(x^{*}=[0.7181,0.2813]\). This implies that regardless of the initial shares, the system will eventually converge to this ESS. As shown in Figure 5, when the initial conditions satisfy Equation (23), the simulation results are consistent with the analytical results, thereby confirming the correctness of our previous analysis. From the right figure of Figure 5, we observe that when the system converges to the ESS, the utilities no longer change.  
To further validate the stability analysis, we conducted a simulation for the second case where Equation (24) is satisfied. The number of clients is still set as \(I=80,000\). For Strategy \(S_{1}\), the Gaussian noise is set to \(\sigma_{1}=0.4\) with \(E_{1}=1265\) iterations. For Strategy \(S_{2}\), the Gaussian noise is \(\sigma_{2}=1.1\) with \(E_{2}=778\) iterations. The learning rate is \(\eta=0.0002\), and the basic incentive for training is still set as \(A=5\). Other parameters are set as \(a=0.1\), \(b_{1}=0.2\), and \(b_{2}=0.01\). The initial shares for selecting strategies were set to \([0.4,0.6]\). In this scenario, the Jacobian matrix satisfies Equation (24), indicating that it is negative definite. Through computation, we obtained the equilibrium point \(x^{*}=[0.2180,0.7820]\).  
As shown in the left figure of Figure 6, when the initial conditions satisfy Equation (24), the simulation results are consistent with the computed results, thereby verifying our analysis. From the right figure of Figure 6, it is evident that when the system converges to the ESS, the utilities no longer change.  
Figure 5: Population shares and utilities for two-strategy scenario (Equation (23) holds): (**a**) Population shares. (**b**) Utilities.
# Novel Approach in Vegetation Detection Using Multi-Scale Convolutional Neural Network
## 2 Materials and Methods
### Proposed Architecture
#### 2.1.1 Convolution Layers  
These layers facilitate hierarchical learning that captures complex patterns within images. Organized in stacked configurations, the earlier layers focus on detecting simple features, while the deeper layers are responsible for identifying more complex patterns. The feature map \(F\) resulting from passing an image \(I\) through a convolutional layer can be expressed mathematically as follows [21]:  
\[F=\delta(I*K+b) \tag{1}\]  
where \(K\) denotes the kernel or filter, \(*\) denotes the convolution operation, \(b\) is a bias term, and \(\delta(.)\) is the (Rectified Linear Unit) ReLU activation function. This process captures local spatial relationships in the data. The ReLU activation function introduces nonlinearity, enabling the model to learn complex relationships.  
A detailed overview of each convolutional layer, along with its corresponding kernel sizes, is presented in Table 1.
## 2 Cars, Media, Mobiles
Google Maps is also a leading instance of what has been termed the \"geospatial web\" (or \"geoweb\"), the merging of geographical information with web browsers, and the collaborative tools that are layered on top of these [44]. Location and mapping technologies--including satnavs, Google Maps, geoweb, and what is now being called geomedia [45]--represent a highly significant stage in the complex intermingling of automobiles, mobiles, and media. Debate is underway about the new kinds of relationships between public and private spaces such mobile media entail, and what kinds of mobilities and immobilities, inclusion and exclusion, and new possibilities for connection these entail.
# Game-Based Resource Allocation Mechanism in B5G HetNets with Incomplete Information
## 5 Conclusions  
In this paper, a Stackelberg game-based resource allocation scheme with incomplete information is proposed to solve the competitions for the limited wireless resource in B5G HetNets. The dynamic interactions among networks and mobile users is modeled as a two-tier game framework, where both networks and mobile users have only partial information about others. To be practical, the follower game, which is the competition of limited bandwidth among mobile users, was analyzed as a non-cooperation dynamic Bayesian game, where the channel gain was the private information. A method of probability prediction and a distributed iteration algorithm ensured the feasibility of the Bayesian game. Given the price strategies made by network operators, the mobile users adjusted their bandwidth requesting strategies based on a distributed iteration algorithm to maximize their expected utility function and finally converge to equilibrium. The existence of the Bayesian Nash equilibrium is proved both by mathematical derivation and evolution, and we offer sufficient conditions to prove its uniqueness. When obtaining the BNE in the follower game, the networks in the leader game will correspondingly change their pricing strategies to satisfy their maximal profit. The iteration step for networks to adjust their pricing is based on its marginal utility. In the end, the two-tier Stackelberg game will converge its final equilibrium when the follower game obtains its BNE and the leader game gets its Nash equilibrium. Finally, the evolution results illustrate the theoretical analysis.  
Conceptualization, W.F. and X.L.; methodology, W.F. and X.L.; validation, X.L.; formal analysis, W.F. and X.L.; investigation, W.F. and X.L.; writing--original draft preparation, W.F. and X.L.; writing--review and editing, W.F. and X.L. All authors have read and agreed to the published version of the manuscript. This research is funded by the Natural Science Foundation of China (NSFC): 61602345; National Key Research and Development Plan: 2019 YFB2101900; Application Foundation and Advanced Technology Research Project of Tianjin (15 CQNJC01400). The authors declare no conflict of interest.
## 3 Results and Discussion
### Antioxidant Activity and Total Phenolic Content
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Sample**} & **CAOX DPPH \({}^{*}\)** & **CAOX ORAC \({}^{*}\)** & **Total Phenolic Content \({}^{*}\)** \\  & **IC\({}_{\text{50}}\) (\(\mu\)g/g)** & **(g Trolox/g of Sample)** & **(mg GAE/g Sample DW)** \\ \hline AL & 876 \(\pm\) 84 & 29.96 \(\pm\) 0.50 & 145.9 \(\pm\) 6.8 \\ CH & 824 \(\pm\) 82 & 27.34 \(\pm\) 0.50 & 167.2 \(\pm\) 10.2 \\ HU & 861 \(\pm\) 53 & 27.46 \(\pm\) 0.50 & 154.6 \(\pm\) 17.3 \\ LO\_S & 711 \(\pm\) 12 & 24.03 \(\pm\) 0.44 & 171.9 \(\pm\) 19.4 \\ LO\_N & 846 \(\pm\) 53 & 27.78 \(\pm\) 0.51 & 177.1 \(\pm\) 11.0 \\ LI & 1066 \(\pm\) 75 & 28.77 \(\pm\) 0.53 & 156.1 \(\pm\) 13.4 \\ PI & 1126 \(\pm\) 19 & 33.11 \(\pm\) 0.61 & 133.5 \(\pm\) 18.8 \\ TO & 922 \(\pm\) 116 & 30.43 \(\pm\) 0.56 & 146.9 \(\pm\) 13.0 \\ VE & 792 \(\pm\) 9 & 24.95 \(\pm\) 0.46 & 145.5 \(\pm\) 11.3 \\ \hline \end{tabular} \({}^{*}\)Three replicates of each sample were analysed. Results are expressed as mean \(\pm\) SD.  
\end{table} 
Table 3: Results of antioxidant capacity obtained by ORAC and DPPH methods and total phenolic content.
# Utilization of Quasi-Zenith Satellite System for Navigation of a Robot Combine Harvester
## 2 Materials and Methods
### Static Experiment
Therefore, to incorporate accuracy into the \(2 DRMS\) and \(CEP\) concept, it is necessary to include an additional accuracy estimator. To achieve this, the root mean square error (RMSE) was used to describe the accuracy by measuring the errors between the GNSS data and the actual position [21]. The actual position was chosen as the mean position recorded by the Trimble SPS855 GNSS modular receiver, which, as stated before, performs using the RTK positioning augmentation. The \(RMSE\) is given by Equation (3):  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(E_{i}-\overline{E}\right)^{2}} \tag{3}\]  
where \(E_{i}\) is the location of the i\({}_{\text{th}}\) measurement along the easting and northing directions, \(\overline{E}\) is the Mean of the measurements and \(n\) is the total number of measurements.