esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Methodology
### Sub-Pixel Corner Localization  
According to the existing techniques discussed in Section 2.3, since a real region \(R\) is detected with a known corner position \(c_{\mathrm{p}}=[u_{\mathrm{p}},v_{\mathrm{p}}]\) at pixel level, the ideal model, \(C_{\mathrm{s}}\), most similar to \(R\) (the highest PSNR), can be found by determining  
\[\underset{\mu,v,\alpha,\beta,\lambda,\sigma,\
u}{\mathrm{argmin}}\left[\sum_ {i=-\tau}^{+\tau}\sum_{j=-\tau}^{+\tau}\left(\varepsilon_{i,j}\right)^{2} \right],\;\mathrm{with}\;\varepsilon_{i,j}=C_{\mathrm{s}}(i+\mu,j+v)-R\big{(}i +u_{\mathrm{p}},j+v_{\mathrm{p}}\big{)}, \tag{7}\]  
where \(\mu\) and \(v\) form a vector \(\mathbf{d}\) from the ideal corner position to the center of \(C_{\mathrm{s}}\). It is evident that the closed expression of \(C_{\mathrm{f}}\) is required to address the above optimization by common means, e.g., the Gauss-Newton method. Despite the fact that Equation (4) cannot be directly analyzed by anti-derivatives, it is approximately evaluated by separating the Gaussian kernel and using integration by parts, given as  
\[C_{\mathrm{f}}(u,v)=\mathrm{erf}\left[\frac{\chi(\alpha,u,v)}{\sqrt{2}\sigma }\right]\mathrm{erf}\left[\frac{\chi(\beta,u,v)}{\sqrt{2}\sigma}\right]+ \Delta(u,v), \tag{8}\]  
\[\Delta(u,v)\approx\left(1-\frac{4\theta_{1}}{\pi}\right)\left\{1-\mathrm{erf }^{2}\left[\sqrt{\frac{\delta_{1}\chi^{2}(\theta_{2},\mu,v)+\delta_{2}\chi^{ 2}\left(\frac{\pi}{2}+\theta_{2},\mu,v\right)}{2\sigma^{2}}}\right]\right\}, \;\mathrm{with} \tag{9}\]  
where \(\Delta(u,v)\) is the integral remainder term, \(\mathrm{erf}(x)\) denotes the Gaussian error function, and \(\theta_{1}\) and \(\theta_{2}\) are also known as the angles of shear and rotation in image plane. The corner model, approximated in Equations (8) and (9), share a high similarity with the ideal one in Equation (4), due to an effective estimation and compensation of \(\Delta(u,v)\) (Figure 2).  
However, there is still a lack of the closed form for the Gaussian error function; an accurate but expensive way is replacing it by piecewise polynomials [27]. Considering that most applications utilize 8-bit gray images (256 gray-levels), this replacement should be a balance between the computational accuracy and efficiency. Alternatively, a low-cost approximation \(\tanh(\alpha x)\) is used, and leads to an acceptable result by selecting a suitable value for the coefficient \(\rho\) (Figure 3).  
Finally, Equation (7) can be achieved using a linear optimization in iterations. \(\mu\) and \(v\) are initialized to 0 and \(\sigma\) to 1. \(\alpha\) and \(\beta\) are initialized based on edge extraction [28]. \(\kappa\) and \(\lambda\) are initialized using the gray values in the black and white areas close to \(c_{\mathrm{p}}\). Generally, about 14 pixels are suitable for \(r\) with an overall consideration of the lens distortions, image noise, and computational efficiency. After sufficient iterations for the system convergence, sub-pixel corner \(c_{\rm s}\) can be calculated from  
\[c_{\rm s}=c_{\rm p}-\mathbf{d}. \tag{10}\]
## 2 Materials and Methods
### Data Treatment  
Microsoft Excel 2010 software (Microsoft, Redmond, WA, USA) with the XLSTAT add-on was used for calculations. Transient signals were registered for the selected isotopes (see Table 2) during each measurement cycle. The intensities of blank signals for carrier gas (Ar) flow rates were registered for each isotope individually for 20 s before the start of ablation. These were used to calculate the mean of the instrumental blank (mean/BLANK/) and SD (SD/BLANK/). Mean/BLANK/ values were subtracted from the signals registered during ablation of the samples. Spikes, defined as single raw data intensities higher than  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**ICP-MS** & **LA-ICP-MS** & **ICP-MS**[68] \\ \hline RF power & 1350 W & 1350 W \\ Carrier gas flow rate (Ar) & 0.9 L/min & 0.9 L/min \\ Dwell time & 5 ms & 50 ms \\ Readings & 12,000 & 3 \\ Sweeps & 1 & 1 \\ Replicates & 1 & 3 \\  & \({}^{13}\)C, \({}^{23}\)Na, \({}^{26}\)Mg, \({}^{27}\)Al, \({}^{31}\)P, \({}^{32}\)S, & \({}^{23}\)Na, \({}^{24}\)Mg, \({}^{39}\)K, \({}^{43}\)Ca, \({}^{57}\)Fe, \\ Monitored isotopes: & \({}^{34}\)S, \({}^{35}\)Cl, \({}^{39}\)K, \({}^{44}\)Ca, \({}^{57}\)Fe, \({}^{65}\)Cu, & \({}^{63}\)Cu, \({}^{62}\)Zn, \({}^{82}\)Se, \({}^{88}\)Sr, \({}^{208}\)Pb \\  & \({}^{66}\)Zn, \({}^{78}\)Se, \({}^{88}\)Sr, \({}^{202}\)Hg, \({}^{208}\)Pb & \\ \hline \hline
**Laser Ablation** & & \\ Ablation mode & multi-line ablation & \\ Number of ablation lines & 15 & \\ Laser energy & 0.5 mJ & \\ Laser shot frequency & 20 Hz & \\ Spot size & 100 μm & \\ Space between lines & 100 μm & \\ Scan rate & 50 μm/s & \\ Shutter delay & 20 s & \\ Ablation time per sample & 1020 s & \\ \hline \hline \end{tabular}
\end{table}
Table 2: LA-ICP-MS instrumental conditions.  
the means of two neighboring data values, were removed and replaced with the mean of the neighboring values. Isotope \({}^{13}\)C was selected as the internal standard (IS). Limits of quantitation (LOQ) were calculated for each element, based on the formula recommended by IUPAC [70]: LOQ = mean\({}_{\text{/BLANK/}}\) + 10 SD\({}_{\text{/BLANK/}}\); from the list of monitored isotopes (Table 2), only the information about the elements presenting signal intensities above the LOQ (C, Na, Mg, Al, P, S, Cl, K, Ca, Fe, Cu, and Zn) in all samples was subjected to further analysis. Statistical analysis was performed using analysis of variance (ANOVA), preceded by checking the normal distribution with the Shapiro-Wilk test and homoscedasticity with [PERSON]'s test. In cases of statistically significant differences (\(p\)-value below 0.05), [PERSON]'s post hoc-test was performed in order to compare which groups differed from each other.
## 2 Materials and Methods
### Flux Partitioning in Forest Strata  
In this study, fluxes were analyzed at levels limited to the heights at which the EC system sensors were installed, as follows:  
* Ecosystem: the LE, H, and NEE fluxes were obtained by the EC system at height of 32 m;
* Understory: the LE, H, and NEE fluxes were obtained by the EC system at height of 11 m;
* Overstory: the LE, H, and NEE fluxes were calculated by subtracting the understory fluxes from the ecosystem fluxes, respectively.  
In the overstory, 90% of the biomass volume covers almost all canopies of the largest trees [27]. The remaining biomass (10%) is located below 11 m in height (undersory) and is composed of smaller vegetation and the soil surface.  
Evapotranspiration (ET), in mm day\({}^{-1}\), was estimated using daily LE (in W m\({}^{-2}\)) multiplied by the conversion factor of 0.0353. ET represents the sum of two distinct processes: evaporation (E) and transpiration (T). Overstory ET represents the transpiration process of the canopy and evaporation of intercepted precipitation and dew. In the understory, however, ET is formed by a combination of surface evaporation and lower biomass transpiration.  
To partition the NEE between ecosystem respiration (RE), which represents the respiration from vegetation and soil (i.e., autotrophic and heterotrophic respiration), and gross primary production (GPP), we used the methodology described by [PERSON] et al. [43] using the REddyProc package (version 1.2.2) [44], based on the nighttime approach [45]. We obtained the RE from the nonlinear relationship proposed by [PERSON] and [PERSON] [46], parameterized during the nighttime period with the air temperature (Tair), as follows:  
\[\mathrm{RE}=\mathrm{rb}\,\exp\left[\mathrm{E}_{0}\left(\frac{1}{\mathrm{T}_{ \mathrm{ref}}-\mathrm{T}_{0}}-\frac{1}{\mathrm{Tair}-\mathrm{T}_{0}}\right)\right] \tag{3}\]  
where \(\mathrm{rb}\) is the respiration value at the reference temperature (\(\mathrm{T}_{\mathrm{ref}}\)), \(\mathrm{E}_{0}\) is the activation energy, \(\mathrm{T}_{0}\) is \(-46.02\)\({}^{\circ}\mathrm{C}\) as obtained by [PERSON] and [PERSON] [46], and \(\mathrm{T}_{\mathrm{ref}}\) is \(10\)\({}^{\circ}\mathrm{C}\). Equation (3) was extrapolated to the daytime period based on the \(\mathrm{rb}\) and \(\mathrm{E}_{0}\) parameters collected during the night period. Then, GPP was calculated as the residual between NEE and RE during the daytime. This procedure was conducted with the NEE flux calculated by the EC system at both 11 m and 32 m heights. We analyzed each level as follows:  
* Ecosystem: the RE and GPP from partition of NEE obtained by the EC system at a 32 m height;
* Understory: the RE and GPP from partition of NEE by the EC system at an 11 m height;
* Overstory: the RE and GPP were obtained by subtracting the ecosystem's RE and GPP from the understory's RE and GPP, respectively.  
In this study, the fluxes estimated for the overstory represent processes occurring in the canopy, while the fluxes estimated for the understory represent processes occurring in the vegetation and soil below the canopy.
###### Abstract  
The brain takes the vital role in human physiological and psychological activities. The precise understanding of the structure of the brain can supply the material basis for the psychological behavior and cognitive ability of human beings. In this study, a fast molecular fingerprint analysis of mouse brain tissue was performed using surface-enhanced Raman scattering (SERS) spectroscopy. A nanohybrid consisting of flake-like black phosphorus (BP) and Au nanoparticles (BP-AuNSs) served as the novel SERS substrate for the spectral analysis of brain tissue. BP-AuNSs exhibited outstanding SERS activity compared to the traditional citrate-stabilized Au nanoparticles, which could be largely ascribed to the plentiful hot spots formed in the BP nanosheet. Rapid, full-scale and label-free SERS imaging of mouse brain tissue was then realized with a scanning speed of 56 ms per pixel. Fine textures and clear contour were observed in the SERS images of brain tissue, which could be well in accordance with the classical histological analysis; however, it could avoid the disadvantages in the processing procedure of tissue section. Additionally, the SERS spectra illustrated plentiful biochemical fingerprint of brain tissue, which indicated the molecular composition of various encephalic regions. The SERS difference spectrum of the left versus right hemisphere revealed the biochemical difference between the two hemispheres, which helped to uncover the psychological and cognitive models of the left and right hemispheres.  
surface-enhanced Raman scattering; black phosphorus; mouse brain; label-free imaging; fingerprint analysis +
Footnote †: journal: Applied Sciences
## 6 Future Directions  
1. Scaling up from Cement Paste to Concrete: The research in this study focuses on the cement paste level. In the next study, it will be necessary to further scale up to the mortar and concrete level by considering the influence of aggregates. The interfacial transition zone (ITZ) has a higher porosity than the paste matrix part and may become a weak zone in terms of strength and durability. In addition, differential shrinkage is also one of the important issues related to the volume stability of concrete structures, and it needs to be further studied by combining hydration models, strength models, and concrete structure design specifications.
2. Enhancing Durability Assessment: The authors focused on the hydration kinetics, strength, and CO\({}_{2}\) emissions of cement-quartz powder blends without specific durability tests. Future work could include capillary absorption tests to assess durability, addressing the challenges of traditional labor-intensive methods. For this purpose, leveraged automated weight measurement [29] and computer vision techniques [30] for the liquid absorption analysis of construction materials should be used.
* Long-Term Strength Prediction: This study focused on the strength prediction of cement-quartz powder concrete before 28 days of age. The linear relationship between reaction degree and compressive strength may not hold for all concrete systems, especially for later-age strength gain driven by the continued hydration of unhydrated cement particles. In order to predict the strength at longer ages, other strength prediction models, such as the gel/space ratio model [17], need further study.
* Comprehensive Sustainability Assessment Beyond CO2 Emissions: The sustainability analysis focuses primarily on CO2 emission reduction. For a comprehensive sustainability assessment, other environmental impacts, such as embodied energy, resource depletion, or waste management, require further study. These environmental impacts can be calculated based on concrete mix proportions and life cycle analysis [31].  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15041923/s1](https://www.mdpi.com/article/10.3390/app15041923/s1)]([https://www.mdpi.com/article/10.3390/app15041923/s1](https://www.mdpi.com/article/10.3390/app15041923/s1)), Figure S1: Chemically bound water contents for plain cement.  
* B.Y.: writing--original draft, methodology, investigation; X.-Y.W.: data curation, writing--original draft, supervision, funding acquisition. All authors have read and agreed to the published version of the manuscript.  
* This work was supported by a National Research Foundation of Korea grant funded by the Korean government (MSIT) (No. RS-2023-00208720).  
* Not applicable.  
* The data presented in this study are available from the corresponding author upon reasonable request.  
* The authors declare no conflicts of interest.
# Quantum Multi-User Broadcast Protocol for the \"Platform as a Service\" Model
## 4 Analysis
### Analysis of Security under Typical Attack
#### 4.4.2 Attack via Ancilla Particle  
We suppose [PERSON] intercepts the particle sent by [PERSON], which will be entangled with an ancilla \(\ket{e}\) prepared by [PERSON]. The unitary transformation that is implemented on [PERSON]'s particle \(E\) does not change the state of single photons [27].  
\[\begin{split} E\otimes\ket{0e}&=a\ket{0e_{0}}+b\ket{1 e_{0}1}\,,\\ E\otimes\ket{1e}&=b^{\prime}\ket{0e_{0}}+a^{\prime} \ket{1e_{0}1}\,,\\ E\otimes\ket{+e}&=\frac{1}{2}[\ket{+}(a\ket{e_{0}} +b\ket{e_{0}1}+b^{\prime}\ket{e_{10}}+a^{\prime}\ket{e_{11}})+\ket{-}(a\ket{e_{ 0}})-b\ket{e_{01}}+b^{\prime}\ket{e_{10}}-a^{\prime}\ket{e_{11}}],\\ E\otimes\ket{-e}&=\frac{1}{2}[\ket{+}(a\ket{e_{0}} +b\ket{e_{0}1}-b^{\prime}\ket{e_{10}}-a^{\prime}\ket{e_{11}})+\ket{-}(a\ket{e_{ 0}})-b\ket{e_{01}}-b^{\prime}\ket{e_{10}}+a^{\prime}\ket{e_{11}}],\end{split} \tag{18}\]  
where the unitary transformation \(E\) can be written as  
\[E=\begin{pmatrix}a&b^{\prime}\\ b&a^{\prime}\end{pmatrix}, \tag{19}\]  
where \(\ket{a}^{2}=\ket{a^{\prime}}^{2}\), \(\ket{b}^{2}=\ket{b^{\prime}}^{2}\), and \(\ket{a}^{2}+\ket{b}^{2}=1\). Thus, the probability of [PERSON] being detected is  
\[P_{e}=\ket{b}^{2}=1-\ket{a}^{2}=\ket{b^{\prime}}^{2}=1-\ket{a^{\prime}}^{2}, \tag{20}\]  
the eavesdropping brings a certain amount of error rate, and it must be detected.  
According to the information theory, the amount of maximum accessible information in quantum system is limited by _Holevo_ limit:  
\[\chi(\psi)=S(\psi)-\sum_{i}p_{i}S(\psi_{i}), \tag{21}\]  
where \(S(\psi)\) is the von Neumann entropy of state \(\psi\), \(\psi=\sum_{i}p_{i}\psi_{i}\), and \(\psi_{i}\) is a state prepared in probability \(p_{i}\). If communicating parties prepare states \(\ket{0}\), \(\ket{1}\), \(\ket{+}\) and \(\ket{-}\), then the information entropy \(H(p)=-\sum_{i}p_{i}log_{2}p_{i}=2\). Thus the von Neumann entropy of Eve [27] is \(S(\psi^{\prime})=0<H(P)\). It seems that [PERSON] cannot obtain the complete information of photons in our protocol.
# Multiscale Superpixelwise Locality Preserving Projection for Hyperspectral Image Classification
## 3 Proposed Method
### Divide-and-Conquer-Based LPP Classification  
As local homogeneities on an HSI manifold can be reflected with superpixels, performing an LPP in each superpixel with a superpixel specific projection is expected to preserve the spatially local geometric structure of the data well.  
Our method utilizes the region covariance descriptor to construct the graph for an LPP. The descriptor can yield spectral-spatial covariance features more robust to noise and spectral variabilities than the spectral feature [26; 27; 28]. More specifically, we characterize pixels with their region covariance descriptors, calculate the pairwise distances among pixels in a superpixel with Log-Euclidean distance metric, find the nearest neighbors of the pixels in a superpixel, and compute their similarities as  
\[\mathbf{W}_{ij}=\begin{cases}e^{-\frac{d_{LE}(\mathbf{C}_{i},\mathbf{C}_{j})^ {2}}{2\sigma^{2}}},&\text{if}\quad\mathbf{C}_{i}\in\text{N}(\mathbf{C}_{j}) \quad\text{or}\quad\mathbf{C}_{j}\in\text{N}(\mathbf{C}_{i})\\ 0,&\text{otherwise}\end{cases} \tag{9}\]  
where \(\text{N}(\mathbf{C}_{i})\) denotes the neighbors of \(\mathbf{C}_{i}\). Then, we run an LPP on each superpixel.  
After performing the dimensionality reduction on the HSI with \(2P+1\) different segmentation scales, we classify the obtained low-dimensional data on each scale, and then majority voting decision fusion is utilized to aggregate the results from all the scales. Suppose that the classification result on the \(j\)th scale for a pixel is \(l_{j}\). Then, the score for the \(i\)th class is  
\[N(i)=\sum_{j=1}^{2P+1}I(l_{j}=i) \tag{10}\]  
where \(I(l_{j}=i)=\begin{cases}1,&\text{if}\quad l_{j}=i\\ 0,&\text{otherwise}\end{cases}\) denotes an indicator function. The final classification result is achieved by  
\[l=\operatorname*{arg\,max}_{i\in\{1,2,\cdots,L\}}N(i) \tag{11}\]  
where \(L\) is the number of all possible classes. The flowchart of our proposed MSuperLPP for HSI classification is shown in Figure 1, and the connected performing steps can be found in Algorithm 1.  
```
0: HSI \(\mathcal{X}\in\mathbb{R}^{W\times H\times D}\); scale set \(N_{sp}=\{N_{i}|i=1,2,\cdots,S\}\) obtained by (8); window size \(s=w\times h\). Extract spectral-spatial covariance features using (5) and perform PCA to extract the first principle component \(I_{f}\). for\(i\)=1 to \(S\)do  Segment \(\mathcal{X}\) into \(N_{i}\) homogeneous subregions using ERS with \(I_{f}\); for\(j\)=1 to \(N_{i}\)do  Perform LPP in each subregion \(\widehat{R}_{j}\), where the spectral-spatial covariance features are used to search for the \(k\) nearest neighbors. endfor  Combine the low-dimensional features of all the subregions on the same scale to form the low-dimensional data on this scale. Perform classification on the scales \(i\) to get preliminary output \(T_{i}\). endfor  Aggregate the classification results \(T_{i}(i=1,2,\cdots,S)\) using (10) and (11). Output: Final classification result \(T\).
```  
**Algorithm 1**MSuperLPP
# Guard Band Protection Scheme to Facilitate Coexistence of 5G Base Stations and Radar Altimeters
## 2 Modelling for Guard Band Protection and Analysis
### ACS and ACIR  
The ACS of radar altimeters is detailed in [4], indicating that the filter attenuation of the radar altimeter system is proportional to 24 dB per octave, reaching a maximum of 40 dB. Figure 6 depicts the ACS of radar altimeters against frequency.  
Given that the guard band represents the frequency separation between the edges of the radar altimeter channel and base station channel, the offset frequency is used to compute the ACS of radar altimeters with guard band protection as  
\[\mathrm{f_{offset}}=\frac{1}{2}\mathrm{BW_{BS}}+\mathrm{GB}. \tag{16}\]  
where \(BW_{\mathrm{BS}}\) is the channel bandwidth of the 5G base station, and \(GB\) denotes the bandwidth of the guard band.  
Leveraging the calculations of ACLR and ACS, we investigate the ACIR vs. the guard band, ranging from 0 to 200 MHz in increments of 5 MHz (Figure 7). According to the spectrum allocation of South Korea, 200 MHz is the maximum buffering frequency. The ACIR increases with the expansion of the guard band. Notably, the ACIR exhibits abrupt changes when the guard band reaches 50 MHz and 150 MHz but not at other values. Contrary to expectations, the ACIR values with and without filtering exhibit no significant differences, as highlighted in red. This is because most radar altimeter designs originated in the 1990s, a period when mobile communication primarily operated within the 2 GHz range, with only minimal satellite downlink signals above 3 GHz. Consequently, radar altimeters were not initially designed to contend with the widespread presence of high-power mobile communications. During that era, high-performance filters were not commonly integrated into the receivers of radar altimeter systems. The subpar out-of-band power emission performance of radar altimeters led to a series of nonlinear responses. Therefore, although the ACLR performance is improved by using a filter, the improvement is not significant.  
Figure 5: Process flow of ACLR measurement with filter design.  
Figure 6: Adjacent channel selectivity of the radar altimeter.
# An NLOS Ranging Error Mitigation Method for 5G Positioning in Indoor Environments
## 2 Problem Description and System Model
In assuming that the terminal can completely strip the carrier from the received signal, the outputs of the early, prompt, and \(L\) correlators can be represented as follows:  
\[E=A^{m}\cdot R\bigg{(}\tau_{e}^{m}+\frac{d}{2}\bigg{)}+\alpha^{\text{NLOS}}A^{ n}\cdot R\bigg{(}\tau_{e}^{\text{NLOS}}+\frac{d}{2}\bigg{)} \tag{2}\]  
\[P=A^{m}\cdot R\big{(}\tau_{e}^{m}\big{)}+\alpha^{\text{NLOS}}A^{n}\cdot R\bigg{(} \tau_{e}^{\text{NLOS}}\bigg{)} \tag{3}\]  
\[L=A^{m}\cdot R\bigg{(}\tau_{e}^{m}-\frac{d}{2}\bigg{)}+\alpha^{\text{NLOS}}A^{ n}\cdot R\bigg{(}\tau_{e}^{\text{NLOS}}-\frac{d}{2}\bigg{)} \tag{4}\]  
where \(R\) represents the autocorrelation function, \(d\) represents the spacing between the early and late correlators, \(\tau_{e}^{m}=\hat{\tau}^{m}-\tau^{m}\) represents the code phase difference of the direct path signal, \(\tau_{e}^{NLOS}=\hat{\tau}^{NLOS}-\big{(}\tau^{LOS,n}+\tau^{NLOS}\big{)}\) is the code phase difference of the NLOS signal, and \(\hat{\tau}^{m}\) represents the estimated values of the ranging results. Here, we mainly consider the scenario of 2D positioning, but it can be extended to 3D positioning as needed. The estimated values of the ranging results at the terminal can be modeled as follows:  
\[\hat{d}_{m}=\left\{ \begin{array}{ll}d_{m}+\omega_{m},&\text{for LOS case}\\ d_{m}+\omega_{m}+\eta_{m},&\text{for NLOS case}\end{array} \right.,m=1,2, \cdots,M \tag{5}\]  
\[d_{m}=\sqrt{\big{(}x_{m}-x\big{)}^{2}+\big{(}y_{m}-y\big{)}^{2}} \tag{6}\]  
where \((x_{m},y_{m})\) and \((x,y)\) represent the coordinates of the 5G base station and the terminal, \(\hat{d}_{m}\) represents the estimated distance from the \(m\)th base station to the terminal, \(\omega_{m}\) denotes zero-mean Gaussian noise, and \(\eta_{m}\) is an NLOS error term. The ranging results from the M base stations are divided into two categories, \(\Phi_{LOS}\) and \(\Phi_{NLOS}\), representing line-of-sight and non-line-of-sight phenomena, respectively. \[\Phi_{LOS}=\Big{\{}\Big{(}x_{m},y_{m},\hat{d}_{m}\Big{)}:\hat{l}_{m}=1\Big{\}},\Phi_{NLOS}=\Big{\{}\Big{(}x_{m},y_{m},\hat{d}_{m}\Big{)}:\hat{l}_{m}=-1\Big{\}} \tag{7}\]  
where \(\hat{l}_{m}\) is the indicator of the channel state, \(1\) represents the LOS channel, and \(-1\) represents the NLOS channel. In an indoor environment, the terminal often needs to provide position estimation results in the presence of a mixture of LOS and NLOS ranging results. The optimal set of ranging results available for the user terminal to choose from can be denoted as  
\[\Phi=\Phi_{LOS}\cup\Phi_{NLOS}^{\prime}\text{ and }\Phi_{NLOS}^{\prime} \subseteq\Phi_{NLOS} \tag{8}\]  
Afterward, various methods can be used to provide position estimation values based on the ranging results. However, existing methods do not consider the incomplete identification of NLOS observations or incomplete suppression of NLOS errors. These residual NLOS errors can lead to a significant increase in positioning errors for 5G positioning.