# A GNSS/5G Integrated Three-Dimensional Positioning Scheme Based on D2D Communication
## 3 Results
GNSS: The GNSS measurements are directly calculated to obtain the positions of the requesting nodes without any integration with the measurements from the 5G network. From Figure 5, it is clear that the proposed algorithm, which synthesizes the DBSCAN and PF, achieves the best performance towards the root-mean-square errors (RMSEs) compared to other algorithms. Compared to the GNSS positioning, the lowest improvement of the proposed algorithm in RMSE is nearly 20%, appearing in MU 2, and the highest is approximately 85%, appearing in MU 1. Besides the GNSS results, which contain no additional processing and act as one kind of measurement source in our proposed algorithm, the algorithm without DBSCAN performs the worst, and the algorithm without PF achieves better than that. It explains that the inaccurate position information of the cooperative nodes can cause large errors in the positions of the requesting nodes. Thus, if the known positions of the reference nodes for the requesting nodes are inaccurate, it is hard to obtain accurate positions of the requesting nodes. In this regard, the improvement of the PF in that case is limited. To analyze the effect of the TOA and RSS measurements in our proposed algorithm, we compare GITPA with three other situations:  
1. With TOA only: We only use TOA measurements to estimate the distances between the requesting nodes and the reference nodes, including the BSs and the cooperative nodes, which are further exploited in DBSCAN and PF processes in our proposed algorithm. 2. With RSS only: Similarly, the RSS measurements are solely exploited in the proposed algorithm. 3. GNSS: As mentioned above, the GNSS positioning results are directly added for comparison to illustrate the effect of TOA and RSS measurements more comprehensively. Figure 4: Distribution of the data points before (**a**) and after (**b**) the DBSCAN process based on the TOA measurements. Figure 6 illustrates the performance comparison between the proposed algorithm and the above three algorithms for the five requesting nodes. It is obvious that the proposed algorithm that utilizes both TOA and RSS measurements obtains the lowest RMSEs for all the requesting nodes, and the GNSS positioning obtains the highest. From Figure 6, we can see that there is no clear difference between the algorithms based on the TOA and RSS measurements separately, and these two algorithms achieve a little worse than the proposed algorithm. This is because the distance between a requesting node and its reference nodes may be long or short, and the TOA and RSS measurements affect the range estimation in an average way. Note that when there is limited measurement information or computational resources, it is also feasible to use only TOA or RSS measurements. Figure 5: Performance comparison between the proposed algorithm and other situations for the requesting nodes. Figure 6: Performance comparison between the algorithms based on different measurements for the requesting nodes. To analyze the performance of the proposed algorithm when the requesting node is moving, we plot Figure 7 to see the positioning results where the requesting node moves at a fixed linear velocity and angular velocity. As is shown in Figure 7, the blue chain dotted line represents the trajectory of the requesting node, the red solid line represents the positions calculated by our proposed algorithm and the black dashed line represents the positions from the GNSS measurements. It is clear that the red solid line nearly coincides with the blue chain dotted line, meaning that the error in the results of the proposed algorithm for a moving requesting node is small, and it proves that the proposed algorithm is also effective for the moving requesting nodes. Figure 8 shows the RMSEs with different numbers of the particles used in the PF process. We can see that the RMSE decreases as the number of the particles increases. As we know, more particles can result in better performance of the PF.