## 3 Data Collection and Experiment Analysis
### Outliers Detection for the Offline Data Based on K-Means
#### 3.2.2 Analysis of Positioning Results  
In order to validate the correctness of the clustering results, we execute the DGNSS/INS tightly coupled positioning algorithm to conduct comparative experiments. Figure 9 demonstrates the comparison of the 3D position of the vehicle obtained by different positioning methods, where the red solid line is the ground reference value of the vehicle on the ground. This paper takes the starting point of the vehicle as the origin of the site-centric coordinate system. From Figure 9, we can recognize that the tightly coupled positioning result without multipath/NLOS observation processing deviates more from the reference coordinate value. Furthermore, the result without the height cut-off elevation angle has the most serious position deviation. The deviation in the starting position from the reference value causes an adverse influence on the positioning accuracy. Figure 8: Four feature value distribution pattern diagrams when the \(k\) value is 5. Since the multipath/NLOS observations are not eliminated in complex urban scenarios, it makes the tightly coupled observation equation unreliable. It can also be concluded that installing the satellite cut-off elevation angle can suppress the influence of multipath/NLOS observations to a certain extent. However, the overall positioning performance of the GNSS/INS tightly coupled system is still unsatisfactory, especially in the vertical direction. However, after using the K-means clustering algorithm to identify and exclude multipath/NLOS observations, the positioning results are significantly ameliorated, and the deviation level from the true value becomes small. Moreover, even if the satellite cut-off elevation angle is set to 0\({}^{\circ}\), the position solution of this method hardly changes. This phenomenon indicates that the cut-off elevation angle of most LOS observations in the scenario identified by the clustering algorithm are above 15\({}^{\circ}\). However, it does not mean that all satellite observations above 15\({}^{\circ}\) come from LOS signal reception. The above experiments also reveal that simply relying on setting the cut-off elevation angle cannot improve the positioning accuracy of GNSS/INS tightly coupled system, and even destroy its satellite geometry, which is proved and expounded in detail by [PERSON] et al. (2020). The LOS signal identification method proposed in this paper sufficiently considers the influence of the four feature parameters on the properties of GNSS signals with higher reliability. Furthermore, this paper calculates the RMS of the position error for the above positioning method, as shown in Table 3. The experimental results show that the positioning accuracy is 0.63 m in the horizontal direction and as high as 6.50 m in the vertical direction without multipath/NLOS observation processing (the cut-off elevation angle is set to 15\({}^{\circ}\)). After excluding the multipath/NLOS observations, the GNSS/INS tightly coupled positioning accuracy is improved by 16% and 85% in the horizontal and vertical directions, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Positioning Scheme**} & \multicolumn{5}{c}{**RMS/m**} \\ \cline{2-5}  & **E** & **N** & **U** & **2D** \\ \hline INS/DGNSS (ele \(\geq\) 15\({}^{\circ}\)) & 0.33 & 0.53 & 6.50 & 0.63 \\ INS/DGNSS (ele \(\geq\) 0\({}^{\circ}\)) & 0.32 & 2.75 & 11.57 & 2.76 \\ INS/DGNSS + K-means (ele \(\geq\) 15\({}^{\circ}\)) & 0.37 & 0.38 & 0.98 & 0.53 \\ INS/DGNSS + K-means (ele \(\geq\) 0\({}^{\circ}\)) & 0.38 & 0.38 & 0.98 & 0.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy comparison of positioning results for different tightly coupled schemes. Figure 9: 3D position comparison of positioning results of different tightly coupled schemes. respectively.