## 4 Discussion  
Multipath effects and NLOS signals are the main factors restricting the accuracy and reliability of GNSS/INS positioning, especially in challenging environments such as urban canyons, shaded trees, etc. Therefore, given the interference of multipath/NLOS signals, this paper proposes an outliers detection method composed of an offline learning system and an online learning system for GNSS/INS tightly coupled positioning in urban areas. We believe that GNSS signals in complex environments are generally divided into three categories: LOS, multipath, and NLOS signals. Each type of signal has a certain internal relationship with the four feature parameters of satellite elevation angle, carrier-to-noise ratio, pseudorange residual, and pseudorange rate consistency. According to this characteristic, K-means algorithm is used for signal clustering. When the sample is closest to one of the cluster centers, it is classified into this class. In an offline system, the K-means clustering algorithm is employed to detect observation outliers and construct an offline training set with labels, without resorting to 3D building model and external sensor. On this basis, due to the good scalability of the K-means clustering algorithm, the above-mentioned model is then utilized to identify multipath/NLOS signals on the online observation dataset for real-time positioning.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Positioning Scheme**} & \multicolumn{4}{c}{**RMS/m**} \\ \cline{2-5}  & **E** & **N** & **U** & **2D** \\ \hline INS/DGNSS (\(\text{ele}\geq 15^{\circ}\)) & 0.53 & 0.54 & 2.79 & 0.75 \\ INS/DGNSS + K-means (\(\text{ele}\geq 15^{\circ}\)) & 0.53 & 0.25 & 1.66 & 0.59 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Accuracy comparison of positioning results for different tightly coupled schemes.  
Figure 14: 3D position comparison of positioning results of different tightly coupled schemes.  
As can be seen from Figures 11 and 12, after excluding GNSS observation outliers, the number of satellites participating in the position calculation decreases, and the GDOP value has generally increased. Yet, despite this, the positioning accuracy has been improved. However, while ensuring the positioning accuracy, the continuity of the dynamic positioning results is also crucial. Although correct outlier detection and exclusion can effectively improve the performance of positioning results, it must be admitted that directly removing abnormal observations will reduce the number of available GNSS satellites and weaken the satellite geometric distribution. This will reduce the positioning performance to a certain extent, especially when the number of available satellites is small. Therefore, it is not advisable to blindly pursue positioning accuracy and lose a large number of original valid epochs, but there will certainly be more space for optimizing signal selection when the available GNSS constellations are enough.  
Unfortunately, although this paper has made some meaningful explorations in multi-path/NLOS detection and elimination, the above research work still needs to be further improved because of the complexity of multipath/NLOS signals, for example, using more GNSS/INS observation data to establish offline label datasets, so that the training set covers more scenarios and satellite constellations, and improves the generalization ability of the classification model. In addition, based on different anomaly distribution assumptions, a more suitable detection method for observation outliers is pursued under the condition of ensuring positioning accuracy. We have also made preparations for this and will further study it in the future.