esa-sceva/satcom-chunk-collection huggingface dataset:
# A Multiscale Approach to the Numerical Simulation of the Solid Oxide Fuel Cell
## 3 Microstructure Analysis and Quantification
### Quantification of the Microstructure
#### 3.3.1 Volume Fraction and Mean Particle Diameter  
The volume fraction \(\psi\) was calculated by counting off the voxels which belong to each phase. The percentage of the voxels which belong to the phase of interest to the total number of voxels was computed [36; 41]. The mean diameters of the solid particles and pores \(\bar{d}\) were evaluated using the three-dimensional version of the line intercept method (see [48] for the details of the procedure). The results are shown in Table 5.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{3}{c}{**Sample Size [\(\mu\)m]**} & \multicolumn{3}{c}{**Voxel Size [nm]**} \\ \cline{2-7}  & \(x\) & \(y\) & \(z\) & \(x\) & \(y\) & \(z\) \\ \hline
**anode** & 10.04 & 10.04 & 10.43 & 26.98 & 26.98 & 70.00 \\ \hline
**cathode** & 10.33 & 10.33 & 10.92 & 38.54 & 38.54 & 70.00 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Sample sizes and voxel sizes.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & \multicolumn{3}{c}{**Anode**} \\ \hline
**phase** & Ni & YSZ & pore \\
**volume fraction**\(\psi\) & 0.33 & 0.41 & 0.26 \\
**mean diameter**\(\bar{d}\) [\(\mu\)m] & 0.77 & 0.81 & 0.71 \\ \hline \hline \multicolumn{4}{c}{**Cathode**} \\ \hline
**phase** & LSCF & GDC & pore \\
**volume fraction**\(\psi\) & 0.34 & 0.27 & 0.39 \\
**mean diameter**\(\bar{d}\) [\(\mu\)m] & 1.00 & 1.30 & 1.02 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Volume fractions and mean particle diameters of each phase.  
Figure 7: Three-dimensional reconstruction of the anode and cathode.
# Automated Control of the Fresh State of Industrial Concrete Behaviour by Rheometer Test Adjustment
## 7 Rheometer Test Adjustment
### Advantages and Disadvantages  
The use of a rheometer to obtain absolute measurements allowing users to compare the results with other devices is complex. Therefore, the use of these devices in relative units were proposed to simplify the process, although it limits the possibility for comparison. Furthermore, the relative parameters provide information regarding concrete workability and allow the comparison of different concretes when the same device is used. If necessary, the absolute parameters (yield stress and plastic viscosity) can be obtained with a post-process analysis.  
The need to adjust the rheological tests in advance is also a disadvantage. In addition to adjusting the concrete mix and statistically obtaining the compressive strength during previous tests, it would also be necessary to adjust the rheological tests following the flow chart provided in this study. Once they are fitted, the relative rheometer can evaluate the behaviour of concrete mixes in the fresh state, resulting in both a faster and automated production.  
Another aspect that can be easily captured with a rheometer is the tendency of the mixtures to segregate. If the concrete exhibits this issue, the rheometer produces odd results that would trigger corrective steps. This type of device also provides information regarding homogeneity and can detect the defects in certain batches during concrete production.  
The automation provided by this device is also a powerful tool. First, its use eliminates the need for operator intervention (most industrial tests are operator sensitive). Second, the information can be automatically stored, and it is possible to create databases that can be analysed in a post-process step to obtain rheography [32], or the relationships between the mixing parameters or raw material properties, and the rheological parameters. This can help engineers learn about concrete behaviour in concrete plants and enable faster and better adjustments of concrete mixes.  
The use of a rheometer would imply a decrease in the labour costs owing to the reduction in the manual testing of concrete. At this point, the cost of advanced industrial testing is needed for novel concretes, such as spread and T500, J-Ring, V-funnel, and L-Box, which must be performed when self-compacting concrete is being used. However, when the rheometer device is included in the production chain, it can be used to ensure a 100% automatic control of the concrete.  
The time required for rheological testing differs depending on the adjustment. In the flow chart proposed in this study, the time required to breakdown the mixture and reach a shear stress plateau was limited to 90 s. Thus, the total time to develop the FCT would always be less than 120 s.  
Although not covered in this study, the rheometer can be adjusted as an indicator for mixed thixotropy. This requires specific tests and a post-process analysis of the measured results [33].
## 4 Dataset
### Data Acquisition  
We utilized a synthetic dataset specifically crafted to mimic real-world insider threat scenarios, allowing for adjustments aligned with various organizational cybersecurity objectives. Generating synthetic data addresses the security and privacy concerns that make it challenging to access real organizational datasets. The dataset comprises 10,000 records representing the activities of 500 employees over 4 weeks (expanded to 23,483 after resampling) with 22 features, including Personally Identifiable Information (PII) such as users' names, email addresses, Social Security Numbers (SSNs), Dates of Birth (DoB), and employee numbers, as well as 17 distinct anomalous activity types detailed in Table 2.  
To ensure that the synthetic dataset can accurately reflect real-world scenarios, we incorporated several key characteristics. First, the dataset predominantly comprises normal employee behaviors, mirroring the typical distribution observed in real-world organizations. Additionally, time-related features were included in order to capture the temporal dynamics of employee activities, specifically the timing of the most common abnormal behaviors. Furthermore, the distribution of abnormal behaviors in the dataset was constructed to avoid being skewed toward specific types of anomalies, ensuring a representative range  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Study**} & **Instantaneous** & **Real-Time** & **Real-Time User** & **Non-** & **Continuous** & **Adjustability** & **Detection** & **Classification** \\  & **Data** & **Analysis** & **Classification** & **Interactive** & **Continuous** & **Adjustability** & **Time** & **Classification** \\ \hline
[48] & ✓ & ✓ & ✗ & ✓ & ✓ & ✗ & ✗ & ✗ \\ \hline
[49] & ✓ & ✓ & ✗ & ✓ & ✓ & ✗ & ✓ & ✗ \\ \hline
[50] & ✓ & ✗ & ✗ & ✓ & ✓ & N/D & ✗ & ✗ \\ \hline
[51  
of potential threats. Finally, the dataset contains a sufficient amount of data points to effectively capture the complexity of employee behavior patterns. Weights were assigned to each anomalous activity type based on its severity. To ensure a meaningful and manageable scale for assessing the relative risk associated with different types of anomalous activities, weights were assigned on a scale from 4 to 10. Higher weights were assigned to activities with a greater potential impact on security, ensuring that the system effectively reflects organizational priorities. For example, previous incidents of security violations were assigned a weight of 10, as such incidents strongly suggest severe abnormal behavior. In contrast, logging in outside business hours was
## 2 Materials and Methods
### Antenna I  
In this design, the first order of the Hilbert method is used to miniaturize the antenna for the first resonant frequency. By adding more vertices to the geometry of the antenna and bending the antenna's shape in a quasi-periodic pattern, we were able to miniaturize the antenna's dimensions. The effective length of the antenna does not decrease, but the required area is smaller since the length of the antenna is distributed more evenly on the surface. Then, this idea was combined with the inverted F method so that the input impedance of the antenna could be tuned for the impedance matching by moving the location of the input port and also have the effective length of the antenna \(\lambda/4\). After the main body and dimensions of the antenna are determined for 400 MHz resonance frequency and the current distribution is observed by the simulation, other branches are added to the high-current nodes of the antenna to achieve the other resonant frequencies at 2.45 GHz and 5.63 GHz bands. Adding the branches to the high-current nodes also increases the capacitance between the lines, which also helps to further decrease the antenna size to 1.4 mm \(\times\) 10 mm \(\times\) 10 mm.
## 4 Experiments and Analysis
### Classification Accuracy Analysis  
To test the effectiveness of the areal settlement shape classification model, it is necessary to give a test set, use the model to predict each sample in the test set, and calculate an evaluation score on the basis of the results of the model's predicted classification. For classification problems, common evaluation criteria include accuracy, precision, recall, and F-measure values [26]. This paper uses accuracy to evaluate how well the model classifies all classes as a whole, and for each class, the performance estimates are evaluated using precision and recall. The accuracy of a class is the proportion of all samples predicted to be in that class that are predicted correctly. The recall of a class is the proportion of all samples truthfully labeled as being in that class that are predicted correctly. The result  
Figure 11: Test of the number of hidden layers and vector dimension.  
Figure 10: The validation accuracy of the model with training batches of different sizes; (**a**) batch 10, accuracy 0.9361, (**b**) batch 50, accuracy 0.9278, (**c**) batch 100, accuracy, 0.9222, and (**d**) batch 500, accuracy 0.9028.  
is shown in Table 1. The F-measure is the summed mean of the accuracy and recall and represents a metric given when both are equally important.  
\[\text{Accuracy rate}:\;\text{P}=\frac{Number\;of\;Correct\;Classifications}{Number\;of\; classifications\;in\;the\;Model} \tag{8}\]  
\[\text{Recall rate}:\;\text{R}=\frac{Number\;of\;correct\;classifications}{Artificial\;number\;of\;classifications} \tag{9}\]  
\[\text{Measurement values}:\;\text{F}=\frac{2\times P\times R}{P+R} \tag{10}\]
# Behaviour Investigation of SMA-Equipped Bar Hysteretic Dampers Using Machine Learning Techniques
## 5 Machine Learning Approaches
### Proposed GMDH Models  
Around 25% of the database (97 data out of 389 data) was arbitrarily put aside in GMDH-NN techniques, analogous to ANN models, in order to suggest more trustworthy closed-form equations. After many tests, using the GMDH-NN methods, Equations (24) and (25) were proposed to estimate the \(\beta\) and \(\alpha\) parameters, respectively. For the matter of brevity, further details of the GMDH-NN method are not included here; interested readers are encouraged to refer to the relevant published papers [85; 96; 97; 98; 99]. \[ \begin{array}{ll}GMDH&-NN(\beta)=-3.624+28.948N_{10}+41.850N_{10}\cdot N_{2} +8.402N_{10}\cdot N_{2}^{2}-72.915N_{10}^{2}\\ &-40.419N_{10}^{2}\cdot N_{2}+54.341N_{10}^{2}\cdot N_{2}89N_{2}-6.552N_{2}^{2} \\ &N_{2}=0.252+0.638E-2.068E\cdot N_{3}-0.131E\cdot N_{3}^{2}+2.642E^{2}\cdot N_{3 }-1.011E^{3}+1.291N_{3}^{2}-0.382N_{3}^{3}\\ &N_{3}=0.049+2.992N_{4}\cdot N_{5}-1.326N_{4}\cdot N_{2}^{2}-0.939N_{4}^{2}\cdot N _{5}\\ &N_{5}=-0.062-2.936E\cdot N_{5}+3.492N_{4}\cdot N_{5}^{2}-3.424E^{2}+1.887N_{2} ^{2}\\ &N_{7}=21.914E\cdot N_{4}\cdot N_{4}+839.35N_{10}\cdot N_{10}^{2}-563.851\cdot N _{10}^{2}+185.822L^{2}-226.389L^{2}\cdot N_{10}\\ &-42.135L^{3}-893.032N_{10}+172.570N_{10}^{2}-609.221N_{10}^{2}\\ &N_{4}=-1.401+6.141N_{6}+22.290N_{6}\cdot N_{5}^{2}-11.104N_{6}^{2}-24.236N_{6} ^{2}\cdot N_{9}+15.5168N_{6}^{3}+4.181N_{9}-8.881N_{2}^{2}\\ &N_{9}=29.662-198.001N_{10}+216.561N_{10}\cdot N_{13}+254.998N_{10}^{2}-200.840N_{ 10}^{2}\cdot N_{13}-85.519N_{10}^{3}-50.323N_{13}^{2}\\ &N_{13}=0.572-0.068F_{3}^{3}\\ &N_{6}=181.620-20.824L+658.575L\cdot N_{11}-516.201L\cdot N_{11}^{2}+60.644L^{2 }-120.965L^{2}\cdot N_{11}\\ &-844.64N_{11}+1286.790N_{11}^{2}-643.663N_{11}^{3}\\ &N_{11}=0.878-0.726L-0.668L\cdot N+1.069L^{2}\cdot N\\ &N_{10}=0.850+0.214D-1.203L+0.669L^{3}\\ &\\ GMDH&-NN(\alpha)=0.017+0.936N_{17}+21.868N_{17}\cdot N_{3}+36.544N_{17}\cdot N _{3}^{2}-13.872N_{17}^{2}\\ &-78.697N_{17}^{2}\cdot N_{3}+42.287N_{17}^{2}-0.868N_{2}^{2}\\ &N_{3}=0.203-2.336N_{39}-6.5868N_{39}\cdot N_{3}+6.709N_{3}^{2}-1.216N_{39}^{3} +2.054N_{3}+2.176N_{7}^{2}\\ &N_{7}=-0.007+1.17N_{14}+1.986N_{14}\cdot N_{16}-1.583N_{12}^{2}-0.174N_{16}-0. 378N_{16}^{3}\\ &N_{16}=-0.443+0.409D-4.486D\cdot N_{20}+3.206D\cdot N_{20}^{2}+0.434D^{2}+3. 350N_{20}-1.521N_{20}^{3}\\ &N_{14}=0.051+0.052E+0.631E\cdot N_{19}-8.49E\cdot N_{19}^{2}+0.124E^{2}\cdot N _{19}-0.288E^{3}+0.675N_{19}\\ &+0.419N_{19}^{2}\\ &N_{19}=2.128-2.779L+28.021L\cdot N_{37}-19.2193L\cdot N_{37}^{2}-3.247L^{2}-23. 794L^{2}\cdot N_{37}+7.899L^{3}\\ &-15.099N_{37}+24.820N_{27}^{2}\\ &N_{37}=0.021-1.336D+57.68D\cdot L-6.182D\cdot L^{2}+3.512L-10.896L^{2}+10.483L ^{3}\\ &N_{37}=-0.159+0.412N_{99}-0.437N_{49}\cdot N_{12}^{2}+1107N_{20}\\ &N_{20}=0.233+10.41L-18.342L\cdot N_{29}^{2}+158.349L^{2}\cdot N_{39}-45.763L^{3 }-0.982N_{39}+70.831N_{39}^{3}\\ &N_{39}=-0.082+2.429L-0.703L\cdot F_{3}^{2}-50.53L^{2}+0.744L^{2}\cdot F_{3}+3 7.378L^{3}+0.106F_{y}\\ &N_{49}=0.204+0.188N+0.056N^{2}\cdot F_{y}+0.227F_{y}+0.005F_{y}^{2}-0.301F_{y}^{3} \\ \end{array}
# Efficient Tensor Sensing for RF Tomographic Imaging on GPUs
## 5 Experiment Methodology
### Testing Data  
In the experiment, we used both IKEA model and synthetic data in the evaluation. For IKEA model data, we used the IKEA 3D data [1] that generated a ground truth tensors of size \(60\times 60\times 15\) with rank 6. Each 3D model was placed in the middle of the \"tensor\" and occupied a part of the space. In this task, we mainly focused on the location and outline information, while the texture and color information were ignored. The synthetic data were generated according to the compressed sensing model [1]. The synthetic data did not correspond to a specific physical model. We used them to demonstrate the performance of our approach for different data sizes.
## 3 Results
### Verification of Cage Prototype Performance  
Static compression test results in comparison of the composite cage with the commercial PEEK cage and titanium cage showed 78% and 159% in Yield load, and 86% and 136% in stiffness, respectively. Static compression shear test results in comparison to the composite cage with the commercial PEEK and titanium cage showed 83% and 154% in yield load, and 81% and 207% in stiffness, respectively. Static torsion test results in comparison to the composite cage with the commercial PEEK and titanium cage showed 66% and 138% in yield torque, and 76% and 169% in stiffness, respectively (Figure 9). Static subsidence test results in comparison to the composite cage with the commercial PEEK and titanium cage showed 103% and 61% in yield torque, and 95% and 61% in stiffness, respectively (Figure 10).  
Figure 8: Load distribution of spine bone in the various motions  
Figure 9: Comparison of subsidence likelihood in each motion.  
The dynamic compression test of the composite fusion cage confirmed the collapse of the titanium grains in the porous cover at 51,000 cycles at a load of 12,000 N and 2,401,500 cycles at a load of 8000 N. However, no change was observed in the porous composite cage after 5,000,000 cycles at a load of 6000 N.
## 3 Methodology
### Training Process  
Algorithm 1 presents the self-training procedure of our GeoCWS framework. Specifically, in every iteration stage, we generate the pseudo-labels \(P\) for unlabeled data \(U\) using the teacher model \(f^{W}\), except for the first epoch stage, where we fine-tune the model only using the labeled data \(L\). Then, we use the model's confidence and certainty to select reliable pseudo-labels in each sentence and update the parameters of the student model \(f^{W}\) using them together with the labeled data by modifying the loss \(L_{st}\). Finally, the model \(f^{W^{*}}\) is replaced with the trained student model \(f^{W}\), and the aforementioned procedures are repeated until model convergence.  
```
1:Neural model \(f^{W_{0}}\), labeled data \(L\), unlabeled data \(U\).
2:Initialize a teacher mode \(f^{W^{*}}=f^{W_{0}}\);
3:Fine-tune the teacher model \(f^{W^{*}}\) over the labeled data \(L\);
4:while not converged do
5:Pseudo annotate each unlabeled sentence \(X_{i}\in U\). by Equation (8) to obtain the hard labels \(\widetilde{Y}\);
6:for\(X_{i}\in U\)do
7: Obtain the confidence score \(score_{i}^{cf}\) for \(x_{i}\in X_{i}\) by Equation (11);
8: Obtain the certainty score \(score_{i}^{uc}\) for \(x_{i}\in X_{i}\) by Equation (12);
9: Sample reliable pseudo-labels by the sampling weight in Equation (13), and generate a masked matrix \(G_{i}\);
10:endfor
11: Initialize a student model \(f^{W}=f^{W_{0}}\);
12: Train the student model \(f^{W}\) by reduce \(L_{st}\) in Equation (15);
13: Update the teacher model \(f^{W^{*}}=f^{W}\);
14:endwhile
15:return The teacher model \(f^{W^{*}}\).
```  
**Algorithm 1** Self-training Procedure of GeoCWS
## 4 The Yaw Tracking Control System
Combining with the sliding surface (47), a control law can be obtained to make the system states moving from the outside to the inside of the sliding surface, and finally, they remain inside the surface despite unknown parameters, model uncertainties, and external disturbances. Therefore, the control law in the proposed adaptive PI SMC is  
\[\delta_{a}=\delta_{p}-(\lambda_{1}\widetilde{\psi}+\lambda_{2}r)\hat{J}- \hat{\alpha}_{v}v-\hat{\alpha}_{r}r-\hat{\alpha}_{y}y-\tau_{0}s_{a}, \tag{48}\]  
where  
\[\delta_{p}=-\text{sgn}(s_{a})\hat{\Gamma}_{0}. \tag{49}\]  
The adaptive law is  
\[\left\{ \begin{array}{l}\dot{\hat{J}}=\frac{1}{p_{1}}s_{a}\big{(}\lambda_{1} \widetilde{\psi}+\lambda_{2}r\big{)},\\ \dot{\hat{\alpha}}_{v}=\frac{1}{p_{2}}s_{a}v,\ \ \dot{\alpha}_{r}=\frac{1}{p_{3}}s_{a}r,\ \ \dot{\alpha}_{y}=\frac{1}{p_{4}}s_{a}y,\\ \dot{\hat{\Gamma}}_{0}=\frac{1}{p_{5}}|s_{a}|.\end{array} \right. \tag{50}\]  
**Theorem 2**. : _Consider the steering system (46) with the sliding surface (47), the trajectory of the closed-loop system can be driven onto the sliding surface using the control law (48) with the adaptive law (49) and (50), the yaw tracking control system is GUAS and the stabilization objective \(\underset{t\rightarrow\infty}{\lim}\widetilde{\psi}=0\) can be achieved._  
Proof. : Given a Lyapunov function candidate  
\[V_{4}=\frac{1}{2}{s_{a}}^{2}+\frac{1}{2}p_{1}\widetilde{f}^{2}+\frac{1}{2}p_{2} \widetilde{\alpha}_{v}{}^{2}+\frac{1}{2}p_{3}\widetilde{\alpha}_{r}{}^{2}+ \frac{1}{2}p_{4}\widetilde{\alpha}_{y}{}^{2}+\frac{1}{2}p_{5}\widetilde{\Gamma }_{0}{}^{2}, \tag{51}\]  
where \(\widetilde{J}=J-\hat{J}\), \(\widetilde{\alpha}_{v}=\alpha_{v}-\hat{\alpha}_{v}\), \(\widetilde{\alpha}_{r}=\alpha_{r}-\hat{\alpha}_{r}\), \(\widetilde{\alpha}_{y}=\alpha_{y}-\hat{\alpha}_{y}\), \(\widetilde{\Gamma}_{0}=\Gamma_{0}-\hat{\Gamma}_{0}\). Taking the time derivative of \(V_{4}\):  
\[ \begin{array}{l}\dot{V}_{4}=s_{a}\big{(}J\lambda_{1}\widetilde{\psi}+J \lambda_{2}r+J\dot{r}\big{)}+p_{1}\widetilde{J}+p_{2}\widetilde{\alpha}_{v} \dot{\widetilde{\alpha}}_{v}+p_{3}\widetilde{\alpha}_{r}\dot{\widetilde{ \alpha}}_{r}+p_{4}\widetilde{\alpha}_{y}\dot{\widetilde{\alpha}}_{y}+p_{5} \widetilde{\Gamma}_{0}\dot{\widetilde{\Gamma}}_{0}\\ =s_{a}\big{(}J\lambda_{1}\widetilde{\psi}+J\lambda_{2}r+\alpha_{v}v+\alpha_{ r}r+\alpha_{y}y+\delta\big{)}+s_{a}\Gamma(\cdot)\\ \qquad\qquad\qquad-p_{1}\widetilde{J}-p_{2}\widetilde{\alpha}_{v}\dot{ \widetilde{\alpha}}_{v}-p_{3}\widetilde{\alpha}_{r}\dot{\widetilde{\alpha}}_{ r}-p_{4}\widetilde{\alpha}_{y}\dot{\widetilde{\alpha}}_{y}-p_{5}\widetilde{\Gamma}_{0} \hat{\Gamma}_{0}.\end{array}  \tag{52}\]  
Substituting Equations (48)-(50) into Equation (52) yields  
\[
# Robust Sampling Frequency Offset Estimation for OFDM over Frequency Selective Fading Channels
## 3 Conventional Estimation Scheme
### Conventional Scheme A  
The method in [12] is designed for real-time implementation in a DRM receiver, which utilizes the difference between two adjacent FRCs. In this scheme, the SFO is estimated in the form of  
\[\hat{\Delta}_{s}=\frac{N}{4\pi DN_{u}}\sum_{m=2}^{3}\frac{\arg\left\{\hat{R}_ {l}(k_{m})\right\}-\arg\left\{\hat{R}_{l}(k_{1})\right\}}{k_{m}-k_{1}} \tag{4}\]  
with  
\[\hat{R}_{l}(k_{m})=b_{l}(k_{m})R_{l}^{*}(k_{m})R_{l+D}(k_{m}) \tag{5}\]  
where \((\cdot)^{*}\) is the complex conjugate operation, \(\arg\{x\}\) represents the argument of a complex number \(x\), \(D\) is the distance between two pilot symbols selected for the parameter estimation, and \(b_{l}(k_{m})=d_{l}(k_{m})/d_{l+D}(k_{m})\) is introduced to remove the polarity of the temporal correlation. In order to cope with the effects of noise when it is encountered with a relatively small difference of the rotated phases between two adjacent symbols, \(D\)-symbol delay estimation is employed in (5). By using \(D\)-symbol delay estimation, the MSE of (4) can be calculated by [13]  
\[E\left[|\hat{\Delta}_{s}-\Delta_{s}|^{2}\right]\approx\left(\frac{1}{\gamma}+ \frac{1}{2\gamma^{2}}\right)\frac{N^{2}}{8\pi^{2}D^{2}N_{u}^{2}}\left[\frac{1} {(k_{2}-k_{1})(k_{3}-k_{1})}+\sum_{m=2}^{3}\frac{1}{(k_{m}-k_{1})^{2}}\right] \tag{6}\]  
where \(\gamma=E_{X}/\sigma_{Z}^{2}\) stands for the signal-to-noise ratio (SNR).
# Exploiting Lunar Navigation Constellation for GNC Enhancement in Landing Missions
## 2 Simulation Environment
### User Navigation Equipment
#### 2.2.2 Accelerometer  
Concerning the accelerometers contained in the Inertial Measurement Unit (IMU), it is fundamental to recall that such sensors are insensitive to volume forces, such as all the gravitational effects included in the environment of our simulation.  
For this reason, they are particularly useful for obtaining an estimate of the real control acceleration provided by the thrusters, as well as the perturbations induced by the SRP.  
A high-fidelity model for an accelerometer typically includes misalignment and cross-axis sensitivity errors, sensor biases, and scale factor errors [29]. For the purpose of this work, the model has been simplified and all the errors have been collected into an additive Gaussian white noise, with a standard deviation that is representative of commercial high-fidelity accelerometers. As a consequence, the simulated sensor reading is defined as per Equation (14).  
\[\mathbf{\hat{a}}_{IMU,I}=\mathbf{a}_{SRP,I}+\mathbf{a}_{thr,I}+\epsilon_{ \mathbf{IMU}} \tag{14}\]  
It is also relevant to recall that the accelerations recorded by the IMU are usually expressed in the sensor frame, \(S\). However, since in this framework the attitude dynamics and kinematics are not taken into consideration, the spacecraft attitude is assumed perfectly known and the accelerations of the IMU are directly expressed in the inertial frame, \(I\).  
A consolidated practice to exploit such sensors in the orbital filters is the so-called _Dynamic Compensation Mode_[17]. The basic principle is not to use the accelerometer readings among the measurement vector, but to leverage them within the propagation step of the filter. This concept, also exploited with gyroscopes, is backed by the high accuracies that such sensors show. Moreover, some computation savings are thus achievable, avoiding the evaluation of the non-volume forces, which generally have quite complex mathematical formulations, e.g., a high-fidelity SRP or propulsive acceleration representation.