# 1D-CLANet: A Novel Network for NLoS Classification in UWB Indoor Positioning System
## 3 Theoretical Analysis  
As shown in Figure 2, we take a 3-anchor positioning model as an example. Assume the coordinates of each anchor are known and denoted as \((x_{1},y_{1})\), \((x_{2},y_{2})\), \(\ldots\), \((x_{n},y_{n})\) where \(n=3\) in Figure 2. The coordinates of the tag to be determined are denoted as (\(x\),\(y\)). The distances from the tag to each anchor, measured by the UWB device using ToF, are \(d_{1},d_{2},\ldots,d_{n}\). This yields a system of nonlinear equations for the distances from the tag to each anchor: \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Category** & **Advantage** & **Shortcoming** & **Related Methods** \\ \hline \multirow{4}{*}{Traditional NLoS identification methods} & Distance-based methods & The identification principle is simple, and the computational efficiency is high & The identification accuracy is easily affected by fluctuations in distance information & Kurtosis [20] \\  & Distance-based methods & The NLoS identification performs well in static, well-mapped, known indoor environments & It requires extensive data and cannot identify dynamic obstacles causing NLoS & MKF [23] \\ \hline \multirow{4}{*}{Channel features-based methods} & Machine learning-based methods & It offers higher accuracy than traditional methods and greater efficiency than deep learning methods & Collecting a representative UWB channel feature dataset is challenging, and ML models often struggle with generalization in NLoS identification, leading to reduced accuracy & SVM [24, 26] \\  & Machine learning-based methods & It offers higher accuracy than traditional methods and greater efficiency than deep learning methods & Collecting a representative UWB channel feature dataset is challenging, and ML models often struggle with generalization in NLoS with generalization in NLoS identification, leading to reduced accuracy & SVM [24, 26] \\  & Machine learning-based methods & It offers higher accuracy than traditional methods and greater efficiency than deep learning methods & Collecting a representative UWB channel feature dataset is challenging, and ML models often struggle with generalization in NLoS identification, leading to reduced accuracy & SVM [24, 26] \\  & Channel feature-based NLoS identification & \multirow{2}{*}{NLoS deep feature extraction and scene recognition excel, with no need for manual feature extraction and strong robustness} & Research on NLoS & MLP [29] \\  & & NLoS attention and scene & multi-class classification is & CNN [30] \\  & Deep learning-based methods & recognition excel, with no need for manual feature extraction and strong robustness & limited, and complex & LSTM [31] \\  & & need for manual feature extraction and strong robustness & models with attention & HOCNN [32] \\  & & & mechanisms require costly & BiLSTM-CNN [33] \\  & & & hardware and may lack & ECA-ResNet [34] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of UWB NLoS identification methods. Square both sides of each equation in Equation (1) and subtract the subsequent \(n\) equations from the first equation. Combine the terms containing \(x\) and \(y\), and express the resulting equations in matrix form:  
\[ \begin{bmatrix}2(x_{1}-x_{n})2(y_{1}-y_{n})\\ 2(x_{2}-x_{n})2(y_{2}-y_{n})\\ \ldots\\ 2(x_{n-1}-x_{n})2(y_{n-1}-y_{n})\end{bmatrix}\begin{bmatrix}x\\ y\end{bmatrix} = \begin{bmatrix}d_{n}^{2}-d_{1}^{2}+x_{1}^{2}-x_{2}^{2}+y_{1}^{ 2}-y_{n}^{2}\\ d_{n}^{2}-d_{2}^{2}+x_{2}^{2}-x_{n}^{2}+y_{2}^{2}-y_{n}^{2}\\ \ldots\\ d_{n}^{2}-d_{n-1}^{2}+x_{n-1}^{2}-x_{n}^{2}+y_{n-1}^{2}-y_{n}^{2}\end{bmatrix}  \tag{2}\]  
Simplify the above equations to the form \(A_{ls}X=B_{ls}\), where \(A_{ls}\) and \(B_{ls}\) are given by  
\[A_{ls}= \begin{bmatrix}2(x_{1}-x_{n})2(y_{1}-y_{n})\\ 2(x_{2}-x_{n})2(y_{2}-y_{n})\\ \ldots\\ 2(x_{n-1}-x_{n})2(y_{n-1}-y_{n})\end{bmatrix}  \tag{3}\]  
\[B_{ls}=