# A New Hybrid Positioning Method by Fusion of BDS and 5G Signal Using the Particle Swarm Method
## 4 Performance Analysis  
### Algorithm Simulation Performance Test  
To verify the performance of the MOPSO-TOA/TDOA algorithm in the BDS-5G joint solution system, the convergence of the algorithm in the X, Y, and Z directions was verified using BDS satellite data and 5G base station data. In the selection of the initializationparameters, since the coordinates of the 5G base station are known, 5G base station position coordinates were selected for the initial position of iteration so that the algorithm could reach the convergence state faster. The test platform was MATLAB 2019 (a). Considering the complex environment and the insufficient number of visible satellites, at least four objective function equations were required to solve the position. The target equation set composed of two satellites and two 5G base stations were selected for testing. The four objective equations are as follows:  
\[\left\{ \begin{array}{l}f_{1}(x,y,z)=\|\rho_{1}-\sqrt{\left(x_{s1}-x\right)^{ 2}+\left(y_{s1}-y\right)^{2}+\left(z_{s1}-z\right)^{2}}-\delta\|\\ f_{2}(x,y,z)=\|\rho_{2}-\sqrt{\left(x_{s2}-x\right)^{2}+\left(y_{s2}-y\right) ^{2}+\left(z_{s2}-z\right)^{2}}-\delta\|\\ f_{3}(x,y,z)=\|c\Delta t_{n}-\sqrt{\left(x_{b3}-x\right)^{2}+\left(y_{b3}-y \right)^{2}+\left(z_{b3}-z\right)^{2}}-d_{1}\|\\ f_{4}(x,y,z)=\|c\Delta t_{n}-\sqrt{\left(x_{b4}-x\right)^{2}+\left(y_{b4}-y \right)^{2}+\left(z_{b4}-z\right)^{2}}-d_{1}\|\end{array} \right. \tag{10}\]  
Through a parameter modification test, when the number of particles of the multiobjective particle filter algorithm is set to 100, the inertia factor is set to 0.8, and the speed factor is set to 0.1, the algorithm can converge quickly and obtain the optimal result. The value of the objective function changed with the number of iterations, as shown in Figure 2. The figure contains four objective functions. In the early iteration process, the particles were in the search state, and the results of each objective function changed significantly. When iterating to 50 values approximately 100 times, each objective function converged, and the error of the calculated position result is shown in Figure 3. When iterating 100 times, the multiobjective particle positioning algorithm obtained the optimal solution. ### Algorithm Simulation Performance Test  
To compare the performance of the proposed MOPSO-TOA/TDOA algorithm and the traditional Kalman filtering fusion algorithm, outdoor field tests were used to verify the performance. The main streets in an urban environment were selected, and BeiDou satellite signals and 5G base station signals were received simultaneously. The two algorithms were used to calculate the location of the received data, and the algorithm convergence time and location accuracy were compared. The test terminal adopted the BDS-5G signal positioning terminal jointly developed by the Beijing University of Posts and Telecommunications and Hwa Create Corporation, which can simultaneously receive satellite pseudorange, coordinates, 5G ranging, and other observation information for joint positioning real-time solutions. The receiving terminal is shown in Figure 3(a). Two hundred complex environment test sites near a city street were selected as test sites. The test route is shown in Figure 3(b). The red location mark represents the test point. The Sinan k708 full-frequency high-precision positioning GNSS board and CTI E91 are the reference real coordinates to provide the authority positioning truth value. The convergence time and accuracy of the algorithm were compared and analyzed. As shown in Figure 3(c),d, 200 test points on urban roads were measured. The red curve represents the error between the position calculated by the MOPSO-TOA/TDOA algorithm and the real position, and the blue curve represents the error between the position calculated by the Kalman filtering fusion algorithm and the real position.