# An NLOS Ranging Error Mitigation Method for 5G Positioning in Indoor Environments
## 3 The Proposed NLOS Mitigation and SRUKF-Based Location Estimation Method for 5G Positioning
### 5G NLOS Measurement Identification and Classification Method
When assuming the weight values \(w_{k}\) for the above features \(f_{k}\) regarding the channel classification, the combination importance of \(\alpha\) classification features can be viewed as a fuzzy set \(W\) in the feature domain \(\hat{F}\). The evaluation result is defined as a fuzzy set \(\hat{S}=\left\{s_{x}^{i}\right\}_{x=1}^{\left(s_{x}^{i}\in[0,1]\right)}\) in domain D, which can be obtained through the following fuzzy transformation:  
\[\hat{S}=W\cdot R \tag{30}\]  
\[W=\{w_{k}\}_{k=1}^{a}\text{, subject to }\left\{ \begin{array}{l}0\leq w_{k} \leq 1\\ \sum_{x=1}^{a}w_{k}=1.\end{array} \right. \tag{31}\]  
\(R\) can be expressed in matrix form as \([\tau_{xx}]\). In this article, the fuzzy operation operation can be regarded as the inner product of two vectors. \[s_{x}^{i}=\sum_{k=1}^{p}(w_{k}r_{kx}) \tag{32}\]  
The sampling data that achieve the maximum value in the evaluation result S are considered the data closest to the real-time measurements. The corresponding \(\hat{F}\) can be represented as \(F_{\text{best}}\). A new local dataset \(D_{\text{best}}=\left\{F_{\text{best}}^{i},\Delta d_{\text{best}}^{i},l_{ \text{best}}^{i},s_{\text{best}}^{i}\right\}_{i=1}^{p}\) can be generated, where \(\Delta d^{i}\) represents the ranging error, and \(l_{\text{best}}^{i}\) represents the current true channel condition. We identified the propagation channel of online measurements as one of the sample channels in \(D_{\text{best}}\) or a mixture of multiple sample channels. When NLOS phenomena are determined, we can further predict the NLOS ranging error using the same method. There is an upper limit on the representative number of channels, and the threshold can be expressed as  
\[s_{\text{best}}^{i}<\beta,\forall i,i\in\{1,2,\dots,p\} \tag{33}\]  
According to Equation (33), if the volume of the real-time test data exceeds the discrimination capability of this method, it is necessary to discard all data to avoid outliers that deviate significantly from the local data. Subsequently, the implementation of the NLOS identification and suppression method is as follows:  
\[ \begin{cases}\text{nlos},\tilde{d}=\hat{d}-\Delta d_{\text{best}}^{i}\,,& \text{when }\hat{l}=l_{\text{best}}^{i}<0\\ \text{los},\tilde{d}=\hat{d},&\text{when }\hat{l}=l_{\text{best}}^{i}>0.\end{cases}  \tag{34}\]If the above conditions cannot be met, then the positioning channel at this time can be divided into a combination of multiple channels, and these channels all meet the condition  
\[s_{\mathrm{best}}^{i}\geq\beta,i\in\{1,2,\ldots,p\} \tag{35}\]  
The NLOS suppression method can be denoted as  
\[\left\{ \begin{array}{c} NLOS,\tilde{d}=\hat{d}-\sum\left(\frac{s_{\mathrm{ best}}^{i}}{\mathrm{s}\hat{d}}\Delta d_{\mathrm{best}}^{i}\right),\text{ when}\\ \hat{l}=\sum\left(\frac{s_{\mathrm{best}}^{i}}{\mathrm{s}\hat{d}}l_{\mathrm{ best}}^{i}\right)<0\\ \text{LOS, }\tilde{d}=\hat{d},\text{ when }\hat{l}=\sum\left(\frac{s_{\mathrm{ best}}^{i}}{\mathrm{s}\hat{d}}l_{\mathrm{best}}^{i}\right)\geq 0,\end{array} \right. \tag{36}\]  
where  
\[\Psi=\sum s_{\mathrm{best}}^{i},\text{ subject to }s_{\mathrm{best}}^{i} \geq\beta \tag{37}\]