## 3 The Proposed Multiple-Signal Joint Estimation Method
### Square Root Unscented Stable Filter
on the relationship between the number of positioning signals received and the positioning accuracy in the GNSS and 5G joint positioning system, as well as the influence of different fusion positioning algorithms on the results. Figure 5 presents the relationship between the positioning RMSE in the horizontal planes and the number of positioning signals. It can be seen that when the number of positioning signals received by the receiver increases from 3 to 10, the positioning errors of each fusion algorithm are significantly reduced. When the number of available positioning signals is further increased, the positioning accuracy is not greatly improved. Compared with the methods EKF, MRAKF, UKF, SRUKF, VBHUKF, and SRUSF, the performance of the proposed SRUSF algorithm is close to that of other methods, but the performance of the SRUSF algorithm is still better than the other methods, showing high numerical stability. (3) GNSS and 5G joint positioning performance in a typical environment

In order to further prove the superiority of the SRUSF algorithm proposed in this paper, three typical GNSS and 5G joint positioning scenarios are considered in this section, including the slight occlusion of satellite signals, the moderate occlusion of satellite signals, and the severe occlusion of satellite signals. We simulate different numbers of visible satellites and present the performance of various positioning algorithms in different environments. The 5G positioning base station can be arranged according to the requirements, assuming that the 5G base station is evenly distributed around the positioning receiver. An excessive number of base stations is not conducive to observing the impact of changes in the number of GNSS satellites on the positioning accuracy, so the number of 5G positioning base stations is set to four. We generate three sets of observation data with different accuracy levels, and the mean of the real positioning results is set to 0, and STDs are set to 0.5, 0.4, and 0.3 m. In the three typical scenarios, the sky plot and the Taylor diagram are given. In the sky plot, the blue circle represents the GNSS satellite, the number in the middle represents the satellite number, the purple hexagram represents the 5G positioning base station, and the number in the middle represents the base station number. The rings from the outside to the inside represent different elevation angles, ranging from 0 to 90 degrees, and the numbers on the outside of the outermost circle represent azimuth angles, ranging from 0 to 360 degrees. In the Taylor diagram, the red axis represents the STD of the positioning result, the green dashed line represents the RMSE of the positioning result, and the blue axis represents the correlation coefficient of the output result. Figure 6 shows the scene in which GNSS signals are slightly blocked. The geometric distribution of satellites is good, 10 GNSS satellites can be seen, the elevation distribution is between 10\({}^{\circ}\) and 80\({}^{\circ}\), and four 5G positioning base stations can be seen. The EKF algorithm performs the worst, and the STD and RMSE of the output results of MRAKF, UKF, SRUKF, VBHUKF, and SRUSF are very close to each other. The SRUSF proposed in this paper is about 7% higher than the

Figure 5: Positioning RMSE versus the number of positioning signals with different methods. suboptimal SRUKF algorithm, and the data consistency of SRUKF and SRUKF is obviously better than that of other methods. Figure 7 shows a scene in which GNSS signals are moderately obstructed, such as the entrance of a tunnel or the side of a tall building. The geometric distribution of satellites is poor, and six GNSS satellites can be seen. The RMSE of EKF, MRAKF, UKF, SRUKF, VBHUKF, and SRUKF deteriorated significantly compared with what is shown in Figure 6, but the increase in RMSE in SRUKF proposed in this paper is the least, which is 18% lower than the suboptimal SRUKF algorithm.