esa-sceva/satcom-chunk-collection huggingface dataset:
# Error Averaging Effect in Parallel Mechanism Coordinate Measuring Machine
## 5 Conclusions  
This study analyzed the error averaging effect on the parallel mechanism. Although this issue had not been fully explored, we have found solid evidence from theoretical analysis and experimental results that this effect is mainly dependent on the symmetry of structure. The input motion error, angle errors, and straightness errors of each slider can be averaged and reduced at the probe position through parallel links rods. In the 3-PUU PCMM, the precision linear gu  
Figure 10: Variation of error caused by straightness motion error.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Selected Points/mm** & \multicolumn{3}{c}{**Corresponding Slider Position/mm**} & \multicolumn{3}{c}{**Error Value/\(\mu\)m**} \\ \hline \((X,\,Y,\,Z)\) & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(\xi_{xS}\) & \(\xi_{yS}\) & \(\xi_{zS}\) \\ \hline
750, 150, 200 & 193.58 & 1167.44 & 1319.58 & 3 & 8 & \(-8\) \\
750, 150, 300 & 240.49 & 1047.23 & 1285.55 & \(-7\) & 5 & 17 \\
750, 150, 400 & 314.56 & 1074.49 & 1211.45 & 6 & 2 & \(-9\) \\
750, 300, 200 & 257.96 & 1357.98 & 1468.03 & \(-3\) & \(-4\) & 4 \\
750, 300, 300 & 311.70 & 1308.28 & 1414.32 & 3 & \(-1\) & 9 \\
750, 300, 400 & 400.57 & 1228.27 & 1325.46 & \(-5\) & \(-10\) & \(-25\) \\
750, 450, 200 & 390.01 & 1371.35 & 1486.67 & \(-1\) & 1 & 3 \\
750, 450, 300 & 467.86 & 1310.48 & 1458.19 & \(-2\) & 13 & \(-13\) \\
750, 450, 400 & 652.02 & 1203.11 & 1374.04 & 2 & \(-8\) & 14 \\
1000, 150, 200 & 443.58 & 1403.64 & 1582.45 & 4 & 8 & 6 \\
1000, 150, 300 & 490.49 & 1397.26 & 1735.50 & 3 & \(-9\) & \(-22\) \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\
1250, 450, 200 & 890.00 & 1671.33 & 1836.56 & 1 & 10 & 18 \\
1250, 450, 300 & 967.86 & 1610.46 & 1858.18 & 3 & \(-1\) & 5 \\
1250, 450, 400 & 1152.0 & 1653.10 & 1874.07 & 3 & 8 & \(-8\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Error contributed by straightness motion errors.  
three sliders, is an important measuring part. Our future studies on error averaging effect will further explore the correlation between different error sources and the error transfer coefficient to establish an integrated error model to improve the accuracy of the developed PCMM.  
The authors are grateful for the financial support provided by the Natural Science Foundation of China (51475133, 51675157) and Natural Science Foundation of Anhui Province (1508085 MF122).  
[PERSON] and [PERSON] conceived, designed the instrument structure and wrote the paper; [PERSON] guided the instrument design and provided new ideas about the instrument structure; [PERSON] designed and produced the motion control system; [PERSON] finished the experiment and processed the obtained data.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
PCMM  
Parallel coordinate measuring machine  
3-PUU  
3 pairs of prismatic-universal-universal joints
# Data Privacy and Ethical Considerations in Database Management
## 3 Best Practices
### Ethical Considerations in Access Control  
Implementing access controls raises several ethical considerations:  
* Privacy vs. Utility: Balancing the need for data protection with the need for data access to perform necessary functions is an ongoing ethical challenge [54].
* Transparency: Organizations should be transparent about their access control policies to maintain trust with data subjects and stakeholders [55].
* Non-discrimination: Access control measures should be implemented in a way that does not unfairly discriminate against certain groups or individuals [56].
* Accountability: There should be mechanisms in place to ensure that those who access data are accountable for their actions [57].  
These ethical considerations underscore the importance of the thoughtful and fair implementation of access controls in database management.
## 2 Materials and Methods
### Evaluation of Ringing and Blurring Artifacts  
To evaluate the artifacts on the images according to the undersampling ratio (25%, 35%, and 45%), the information from the undersampled k-space lines used for CSAM was used as a mask, and it was applied to the k-space full sampling dataset for the human subject (Figure 2). For the 25%, 35%, and 45% undersampling ratios, SNRs were obtained by setting the region of interest (ROI) in the gray and white matter regions using ImageJ software (1.53e, National Institutes of Health, Bethesda, MD, USA).  
The k-space data for CSAM, CSAKS, and CSAKC in the brain phantom were reconstructed using the wavelet reconstruction algorithm [18; 19], setting the total variation (TV) to 0.001 and the L1 penalty to 0.001. The final CSA image was then obtained by averaging the three reconstructed subset images. Furthermore, averaged profiles and modulation transfer functions (MTFs) were obtained from the predefined ROIs in the CSAM, CSAKS, and CSAKC images, to evaluate their sharpness and spatial resolution characteristics [24; 25; 26].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Undersampling**} & \multicolumn{3}{c}{**CSAM Acquisition**} & \multicolumn{3}{c}{**CSAKS Acquisition**} & \multicolumn{3}{c}{**CSAKC Acquisition**} \\ \cline{2-9}  & **S1** & **S2** & **S3** & **S1** & **S2** & **S3** & **S1** & **S2** & **S3** \\ \hline
25\% & 193 & 193 & 193 & 291 & 116 & 116 & 291 & 116 & 116 \\
35\% & 268 & 268 & 268 & 448 & 116 & 116 & 448 & 116 & 116 \\
45\% & 346 & 346 & 346 & 579 & 116 & 116 & 579 & 116 & 116 \\ \hline \multirow{2}{*}{**Undersampling**} & \multicolumn{3}{c}{**CSAM Acquisition**} & \multicolumn{3}{c}{**CSAKS Acquisition**} & \multicolumn{3}{c}{**CSAKC Acquisition**} \\ \cline{2-9}  & **S1** & **S2** & **S3** & **S1** & **S2** & **S3** & **S1** & **S2** & **S3** \\ \hline
25\% & 193 & 193 & 193 & 291 & 193 & 193 & 291 & 291 & 291 \\
35\% & 268 & 268 & 268 & 448 & 268 & 268 & 448 & 448 & 448 \\
45\% & 346 & 346 & 346 & 579 & 346 & 346 & 579 & 579 & 579 \\ \hline \hline \end{tabular}  
Acquisition and reconstruction indicate the number of k-space lines to be acquired and reconstructed, respectively. Abbreviations: s1, subset 1; s2, subset 2; s3, subset 3.  
\end{table}
Table 1: Number of k-space lines for MRI data acquisition and reconstruction in CSA techniques.
## 2 Related Work
### Multi-Mode Two-Step Floating Catchment Area Method  
Considering the practical scenario where individuals utilize different transportation modes, the traditional 2 SFCA method's assumptions are limited. For instance, residents may prefer public transportation due to traffic congestion and parking difficulties, and low-income groups may use cars less frequently. Ignoring these differences can introduce errors in accessibility analysis. Based on this, [PERSON] [20] proposed the MM-2 SFCA method, which categorizes the population at the demand points and calculates the supply-demand ratio \(R_{j}\) and accessibility \(A_{i}\) for each demand point according to different population categories. The supply-demand ratio \(R_{j}\) for supply point \(j\) is calculated as follows:  
\[R_{j}=\frac{S_{j}}{\sum_{k\in\{d_{kj}(M_{1})\leq d_{0}(M_{1})\}}P_{k,M_{1}}+ \sum_{k\in\{d_{kj}(M_{2})\leq d_{0}(M_{2})\}}P_{k,M_{2}}+\cdots+\sum_{k\in\{d_ {kj}(M_{n})\leq d_{0}(M_{n})\}}P_{k,M_{n}}}, \tag{3}\]  
where \(M\) represents the transportation mode, and the population \(P_{k}\) at demand point \(k\) is divided into \(n\) subgroups according to \(n\) transportation modes \(\{M_{1},M_{2},\ldots,M_{n}\}\); \(d_{kj}(M_{n})\) is the time from demand point \(k\) to supply point \(j\) under mode \(M_{n}\); and \(d_{0}(M_{n})\) is the search radius under mode \(M_{n}\). That is, multiple search radius areas are drawn according to the transportation modes, and the sum of the travel population within the corresponding area is considered the demand for service \(S_{j}\).  
The overall accessibility \(A_{i}\) of demand point \(i\) under multiple transportation modes is calculated as follows:  
\[A_{i}=\frac{P_{i,M_{1}}\sum_{j\in d_{ij}(M_{1})\leq d_{0}(M_{1})}R_{j}+P_{i,M_ {2}}\sum_{j\in d_{ij}(M_{2})\leq d_{0}(M_{2})}R_{j}+\cdots+P_{i,M_{n}}\sum_{j \in d_{ij}(M_{n})\leq d_{0}(M_{n})}R_{j}}{\sum_{v=1}^{n}P_{i,M_{v}}}. \tag{4}\]  
\(A_{i}\) is not simply the sum of all \(R_{j}\) within supply point \(i\) but rather a weighted sum based on the size of each \(P_{k}\) subgroup within the search radius of each facility, which is then summed to calculate the overall accessibility of demand point \(i\).  
The MM-2 SFCA method enhances the rationality of accessibility modeling by supporting multiple transportation modes through the classification of resident populations at demand points.
# Insights into the Issue of Deploying a Private LoRaWAN
## 4 Experimental and Analytical Results
### Deployment Ease Evaluation
#### 4.3.1 Deployment Costs Evaluation  
This section briefly speculates on the costs of the private and the public network. However, an accurate analysis is strongly affected by the business practices and costs in each region and thus is beyond the scope of this paper. We include this analysis to support the evaluation of private and public networks; and to show the main differences in the nature of the costs they inquire. Moreover, this section might also serve for future estimation in specific use cases by application developers. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Security Procedure** & **LoRaWAN 1.0.x** & **LoRaWAN 1.1.x** \\ \hline Key establishment & OTAA/ABP & Added the second root key and enhanced key derivation \\ \hline Authentication & 64 b/128 b keys & Improved anti-replay technique \\ \hline Key update & Only session key & Session key enhanced by the rejoin procedure \\ \hline Encryption & AES\({}_{\text{CTR}}\)-128 & AES\({}_{\text{CCM}}\)-128 and enhanced data confidentiality at the application layer \\ \hline Data integrity & 32 b MIC & Provided by AES-CCM (2 CMAC functions) \\ \hline Data obtained from the standard specification [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 4  
The costs of technology and solution are based on two types of costs: (i) CAPEX (capital expenditures); and (ii) OPEX (operating expense). The list of items which form the CAPEX costs is displayed in Table 5. Together, these items make up the total CAPEX costs:  
\[ \begin{split}\sum C_{\text{capex}}=C_{\text{prop}}+C_{\text{sus}}+C _{\text{bld}}+\\ +C_{\text{res}}+C_{\text{cap-oth}}-C_{\text{dis}}-C_{\text{sell}}.\end{split}  \tag{2}\]  
The CAPEX of a private network highly depends on the size of the network. Based on our experiences, the CAPEX costs of private network are considered to be higher than public network costs due to the high \(C_{\text{prop}}\) and \(C_{\text{cap-oth}}\). The list of items which form the OPEX is displayed in Table 6.  
Together these items result in the total OPEX costs:  
\[ \begin{split}\sum C_{\text{opex}}=t\cdot(C_{\text{fee}}+C_{\text {enr}}+C_{\text{rent1}}+\\ +C_{\text{rent2}}+C_{\text{ope-oth}}),\end{split}  \tag{3}\]  
where \(t\) is the application horizon in years. The OPEX of both networks highly depends on the size of the network. Moreover, the OPEX costs of a private network are considered to be lower than the public network costs, because most of the applications, such as smart grid, smart city, smart home, and others, are considered to be included in the functional user's infrastructure without any need to build new ones. However, the OPEX costs of the private network will markedly increase if no infrastructure is provided.
## 3 Materials and Methods  
### Particles Used to Prepare TFME Coatings  
In this study, thin-film microextraction coatings were prepared using 4 different types of silica particles bonded to octadecyl ligands and end-capping groups. Macherey Nagel(tm) NUCLEEDUR(r) C\({}_{18}\) Htec (henceforth referred to as \"5 um particles\"), Phenomenex(tm) Luna(tm) C18(2) (\"10 um particles\"), and Macherey-Nagel(tm) CHROMABOND(tm) C\({}_{18}\)ec (\"45 um particles\") were all end-capped with trimethylsilane, and Phenomenex(tm) Synergti(tm) Hydro-RP (\"10 um polar end-capped particles\") was end-capped with a polar ethanol group [40]; see Figure 2 for visualization.  
Additionally, apart from the differences in end-capping type, important particle parameters included the particles' size, pore diameter, specific surface area, and total carbon load (see Table 2 for more details).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Desorption** & **10 μm Polar** & **5 μm** & **10 μm** & **45 μm** \\
**Solvent** & **End-Capped Particles** & **Particles** & **Particles** & **Particles** \\ \hline \multirow{6}{*}{logD at pH = 7.4} & DS1a & 0.780 (0.000) & 0.796 (0.000) & 0.768 (0.000) & 0.576 (0.001) \\  & DS1n & 0.767 (0.000) & 0.794 (0.000) & 0.752 (0.000) & 0.568 (0.001) \\  & DS1b & 0.787 (0.000) & 0.743 (0.000) & 0.677 (0.000) & 0.547 (0.002) \\  & DS2a & 0.782 (0.000) & 0.728 (0.000) & 0.708 (0.000) & 0.513 (0.004) \\  & DS2n & 0.739 (0.000) & 0.756 (0.000) & 0.698 (0.000) & 0.495 (0.005) \\  & DS2b & 0.731 (0.000) & 0.763 (0.000) & 0.641 (0.000) & 0.498 (0.005) \\  & DS3a & 0.784 (0.000) & 0.792 (0.000) & 0.769 (0.000) & 0.618 (0.000) \\  & DS3n & 0.646 (0.000) & 0.612 (0.000) & 0.615 (0.000) & \\  & DS3b & 0.726 (0.000) & 0.683 (0.000) & 0.629 (0.000) & 0.518 (0.003) \\ \hline \multirow{6}{*}{(strongest acidic)} & DS1a & & & & 0.602 (0.004) \\  & DS1b & & & & 0.551 (0.010) \\  & DS2a & & & & 0.593 (0.005) \\  & DS2b & & & & 0.565 (0.008) \\  & DS3b & & & & 0.600 (0.004) \\ \hline \multirow{6}{*}{(strongest basic)} & DS1a & & \(-\)0.486 (0.009) & \(-\)0.515 (0.005) & \\  & DS2a & \(-\)0.525 (0.004) & & \(-\)0.517 (0.005) & \\  & DS2n & \(-\)0.497 (0.007) & \(-\)0.488 (0.008) & \(-\)0.502 (0.007) & \\  & DS3a & \(-\)0.513 (0.005) & \(-\)0.545 (0.003) & \(-\)0.516 (0.005) & \\ \hline \multirow{6}{*}{H donors} & DS1a & \(-\)0.493 (0.008) & \(-\)0.480 (0.010) & \(-\)0.489 (0.008) & \(-\)0.590 (0.001) \\  & DS1n & \(-\)0.498 (0.007) & \(-\)0.525 (0.004) & \(-\)0.531 (0.004) & \(-\)0.621 (0.000) \\  & DS1b & \(-\)0.544 (0.003) & \(-\)0.585 (0.001) & \(-\)0.621 (0.000) & \(-\)0.619 (0.000) \\  & DS2a & \(-\)0.526 (0.004) & \(-\)0.536 (0.003) & \(-\)0.513 (0.005) & \(-\)0.611 (0.001) \\ \cline{1-1}  & DS2n & \(-\)0.529 (0.004) & \(-\)0.540
###### Abstract  
This paper presents the experimental analysis of the effects of simulated hydrocarbon fire exposure on the mechanical properties and the heat transmission in fiber-reinforced self-compacting concrete, FR-SCC. For that purpose, 300-mm thick, and 1200-mm square-shaped slabs were cast. Basalt and polyvinyl alcohol (PVA) fibers were added using the content of 1, 1.5, and 2% in self-compacting concrete. For investigating the heat transmission within 300-mm thick slabs, five external thermocouples were installed at the unexposed face to the fire of the slabs. Similarly, eleven internal thermocouples were installed at an interval of 25 mm throughout the slab thickness. It has been found that fibers have shown better insulation than the controlled concrete; the unexposed to fire surface of FR-SCC showed temperatures lower by ten degree Celcius than the controlled concrete. Compressive strength results showed that fiber addition caused a higher reduction in strength because of softening and stiffness reduction due to high-temperature exposure. After 120 min of fire exposure, basalt fibers caused an average reduction of 30% in the compressive strength, and PVA fibers caused an average reduction of 25%. Whereas, the addition of fibers improved the split cylindrical tensile strength even after exposure to 120 min of fire exposure in comparison with the unreinforced samples.  
fiber-reinforced self-compacting concrete; basalt fibers; PVA fibers; compressive strength; tensile strength; hydrocarbon fire; thermal performance
# Upscaling Gross Primary Production from Leaf to Canopy for Potato Crop (_Solanum tuberosum_ L.)
## 2 Materials and Methods
### Microclimate and Eddy Covariance (EC) Measurements  
Net carbon exchange and microclimatic variables were continuously recorded using the EC technique. The equipment was installed on 3 February 2021 (12 days post planting, DPP), and the measurements were taken until the end of the canopy life cycle on 9 June 2021 (138 DPP). The EC tower included an IRGASON with an open-path gas analyzer (EC 150, Campbell Scientific, Inc., Logan, UT, USA) and a 3D sonic anemometer (CSAT3A, Campbell Scientific, Inc., Logan, UT, USA). Both are operated by a separate electronic module (EC100, Campbell Scientific, Inc., Logan, UT, USA). The EC tower and additional sensor configuration are described by [8].
## 3 ULFO Suppression Control Method for Hydropower and PV
### PV Active Power Additional Controller  
The control structure of the PV generator after adding the active additional controller designed in this paper is shown in Figure 7:  
The structure of the PV power controller is shown in Figure 7. The structure of the PV active power additional controller includes three parts: filtering, adaptive proportional coefficient, and limiting. The mathematical expressions of filtering and adaptive proportional coefficient are as follows:  
\[G_{CPV}(s)=K\frac{sT_{f}}{1+sT_{f}} \tag{15}\]  
The input of the controller is selected as \(-\Delta\omega\), which is the deviation between the system reference frequency and the actual frequency. When the actual frequency of the system increases, the active power reference value (\(P^{r}\),\(w\)) of the PV power controller decreases through the active power additional controller link, thereby reducing the active power output. When the actual frequency of the system decreases, the active power output of PV will increase, thereby achieving oscillation suppression. The following describes in detail the principle of PV participating in oscillation suppression.  
The active power balance formula of the system is as follows:  
\[\Delta P_{e}+\Delta P_{PV}=\Delta P_{L} \tag{16}\]  
where \(\Delta P_{e}\) is the electromagnetic power deviation of the system, \(\Delta P_{PV}\) is the output active power deviation of the PV, and \(\Delta P_{L}\) is the active load deviation of the system. If the load is considered as a constant impedance load and its frequency adjustment effect is ignored, then the active load deviation \(\Delta P_{L}\) = 0, and Equation (16) can be rewritten as:  
\[\Delta P_{e}=-\Delta P_{PV} \tag{17}\]  
Figure 6: The damping torque coefficient changes with frequency before and after adding the controller.  
Figure 7: Control structure of the PV generator with active power additional controller.  
Combining Equation (16), damping torque calculation Equation (14), and generator rotor motion Equation (1), the calculation equation of the system damping ratio (\(\xi\)) can be obtained:  
\[T_{\mathrm{J}}s^{2}\Delta\delta+(D_{T}+K+D)\Delta\omega+\omega_{0}S_{T}\Delta \delta=0 \tag{18}\]  
Solving the above formula can produce the mathematical expression of \(\xi\):  
\[\xi=\frac{D_{T}+K+D}{2\sqrt{T_{\mathrm{J}}\omega_{0}S_{T}}} \tag{19}\]  
It can be seen from the above formula that the proportional coefficient of PV active power additional control (\(K\)) is positively correlated with the system damping ratio (\(\xi\)). When it increases, the system damping ratio can also be improved, which proves that the PV active power additional controller is effective in suppressing ULFO by increasing system damping.
## 4 Mathematical Model
### Thermal Balance on the External Glazing Surface  
On the outer glazing surface, the heat transfers by both radiation and convection are considered (Equation (1)). These superficial heat transfers are linearized using the gray surfaces hypothesis in longwave radiation. In this case, the following expression for the thermal balance at the outer solar wall is thus obtained:  
\[\phi_{g}|_{x=0}=\alpha_{g}Q_{glob,vert}+Q_{r}+Q_{conv} \tag{1}\]  
where \(Q_{glob,vert}\) is the vertical global solar flux on the outer surface of the double glazing; this flux is the sum of the various components of the incident solar radiation that reaches the surface of the double glazing (direct, diffuse and reflected radiation).  
\(Q_{r}\) is the balance of longwave radiation exchanges between the surface of the double glazing and its external environment (ground environment and celestial vault); this total flux is given by the following equation:  
\[Q_{r}=h_{r,sky}(T_{sky}-T_{g,ext})+h_{r,gro}(T_{gro}-T_{g,ext}) \tag{2}\]  
where:  
\[h_{r,sky}=\frac{\sigma\left(T_{sky}^{2}+T_{g,ext}^{2}\right)\left(T_{sky}+T_{ g,ext}\right)}{1/\varepsilon_{g,ext}+1} \tag{3}\]  
\[h_{r,gro}=\frac{\sigma\left(T_{gro}^{2}+T_{g,ext}^{2}\right)\left(T_{gro}+T_{ g,ext}\right)}{1/\varepsilon_{g,ext}+1} \tag{4}\]  
\(h_{r,sky}\) and \(h_{r,gro}\) are the radiative heat transfer coefficients on the outer surface of the double glazing. \(h_{r,sky}\) and \(h_{r,gro}\) are calculated based on the fluctuation between the sky temperature, the outside air temperature (\(T_{sky}\), \(T_{gro}\)) and the glass temperature (\(T_{g,ext}\)).  
\(Q_{conv}\) is the convective heat transfer at the outer surface of the double glazing with the outside air; it is calculated by the following equation:  
\[Q_{conv}=h_{c,g}\left(T_{env}-T_{g,ext}\right) \tag{5}\]  
Figure 7: Diagram of a composite Trombe wall model using the Dymola/Modelica software.  
The convective heat transfer coefficient at the outer surface of the double glazing is then calculated by the correlation [60]:  
\[h_{c,g}=\frac{2\times 0.86\lambda_{f}\left(Re^{1/2}\right)\left(Pr^{1/3}\right)}{H+W} \tag{6}\]  
where:  
\[Re=\frac{V\left(H+W\right)}{2v_{air}}\quad and\quad Pr=\frac{\mu_{air}c_{air}}{ \lambda_{air}} \tag{7}\]  
Hence, the thermal balance on the outer surface of the solar wall equipped with double glazing is:  
\[\phi_{g}|_{x=0}=\alpha_{g}Q_{glob,vert}+h_{r,sky}(T_{sky}-T_{g,ext})+h_{r,gro} (T_{gro}-T_{g,ext})+h_{c,g}\left(T_{env}-T_{g,ext}\right) \tag{8}\]
# A Unified Approach for the Control of Power Electronics Converters. Part II: Tracking
## 6 Numerical Examples
### Boost Inverter for Stand-Alone Applications
In particular, determining the state reference is complicated. The difficulty follows from the fact that the power balance Equation (21) must be satisfied by the reference signals, but only one control is now available. In addition, only the reference for the difference \(v_{C_{1}}(t)-v_{C_{2}}(t)\) is available, drastically complicating the determination of the reference signals. This motivates the approximated method introduced in the next section.