# A GNSS/5G Integrated Three-Dimensional Positioning Scheme Based on D2D Communication
## 3 Results  
In this section, we carry out several numerical simulations to evaluate the proposed algorithm. The simulation setup is as follows. Consider an urban cellular mobile radio environment with four BSs and 13 MUs, and the latter is composed of five requesting nodes and eight cooperative nodes. Meanwhile, GNSS satellites are available to provide the measurements for the MUs. We assume a default height of the BSs, denoted as \(h_{BS}=25\) m, and the height of the MUs satisfies \(1.5\) m \(\leq h_{MUL}\leq 22.5\) m. Hence, according to [31], the signal propagation model parameters for the propagation between the BS and the MUs can be obtained, i.e., \(A=22\), \(B=28\), \(C=20\) and \(\sigma_{SF}^{2}=4\) dB. In general, as the transmitting distance between two D2D users is below \(100\) m, to guarantee the QoS between the requesting nodes and the reference nodes to obtain reliable range measurements, we set the maximum distance between them as \(50\) m; \(\sigma_{t}^{2}=10^{-10}\) is set for the TOA measurements [39], and \(\sigma_{r,b}^{2}=4\times 10^{-14}\) and \(\sigma_{r,m}^{2}=10^{-14}\) are set for the RSS measurements [19]. In the DBSCAN process, the neighborhood parameters are \(\varepsilon=0.5\) and \(MinPts=10\). In fact, to achieve time synchronization in GNSS/5G integrated positioning, a one-way system proposed in [15] is exploited to provide a unified time system, and the ionospheric and tropospheric effect in GNSS can be significantly corrected according to the ephemeris of the satellites. Firstly, Figure 4 gives an intuitional impression of the effect of the DBSCAN, which shows the distribution of the data points before and after the DBSCAN process. Actually, those data points represent the calculated positions of the MUs based on the TOA measurements. As the result based on the RSS measurements is similar to Figure 4, it was omitted due to limited space. There are 13 MUs in the simulation, including five requesting nodes and eight cooperative nodes. An amount of 100 particles are used in the PF process. In Figure 4a, the calculated positions of each MU are represented by a single color, and we can see that some data points concentrate on a center and others are scattered. After the DBSCAN process, as Figure 4b shows, those scattered data points are all removed as outliers and the clusters are formed, where the cyan circles represent the data points, i.e., the calculated positions of the MUs, the red triangles represent the cluster centers, the magenta crosses represent the true positions of the requesting nodes, and the black squares represent the true positions of the cooperative nodes. It is obvious that after removing the outliers in the DBSCAN, the distance between the cluster centers and the true positions of the MUs is really short, which means the error of the results is small. It proves that the position uncertainty of the cooperative nodes can be significantly reduced, and the more accurate positions of the requesting nodes are obtained. Besides, there may be some error in the TOA and RSS measurements, according to which the positions that are calculated are also removed in the clustering. To evaluate the effect of DBSCAN and PF in our proposed algorithm, we compare GITPA with the following three situations:  
1. Without DBSCAN: As we know, the position information of the cooperative nodes is inaccurate. Specifically, here we use the inaccurate position information of the cooperative nodes with the GNSS and TOA/RSS measurements to calculate the positions of the requesting nodes by GITPAPF. In other words, we want to see how the inaccurate position information of the cooperative nodes influence the position results of the requesting nodes. 2. Without PF: Here, we only keep the clustering process based on DATM with the joint TOA/RSS method and output the mean value of the clusters as the final results for the positions of the requesting nodes. That is, we omit the PF process in this algorithm, and the performance of PF in the proposed algorithm can be demonstrated. 3.