## 3 The Proposed Multiple-Signal Joint Estimation Method
### Square Root Unscented Stable Filter
In addition, it can be seen that the correlation coefficient of SRUKF is significantly higher than other methods, which reflects the advantage of adding a stabilized coefficient in the state prediction covariance during the updating process. Figure 8 shows a scene where GNSS signals are severely blocked, such as an urban canyon or an indoor environment. Only two GNSS satellites can be seen, and elevation is distributed between 10\({}^{\circ}\) and 30\({}^{\circ}\). The RMSE of EKF, MRAKF, UKF, SRUKF VBHUKF, and SRUKF is significantly larger than that in Figure 7 and the correlation coefficient sharply is reduced as well. However, the proposed SRUKF remains the optimal algorithm and is about 9% better than the suboptimal SRUKF algorithm. Figure 6: GNSS-5G hybrid positioning with slight occlusion. (**a**) Sky plot (**b**) Taylor diagram. Figure 7: GNSS-5G hybrid positioning with moderate occlusion. (**a**) Sky plot (**b**) Taylor diagram. As can be seen in Figures 6-8, the SRUSF algorithm proposed in this paper outperforms other methods in all three typical scenarios: slight occlusion, moderate occlusion, and severe occlusion of satellite signals. In the scenario with slight occlusion, the performance of each positioning algorithm is close because of the sufficient number of visible signal sources. The SRUSF algorithm has the most obvious advantage in the scene with moderate occlusion, and the RMSE of the output is about 18% higher than that of the suboptimal SRUKF algorithm, and the data correlation coefficient is also the largest. In the scene with severe occlusion, the RMSE of each algorithm increases significantly, and the correlation coefficient decreases at the same time, but the performance of the SRUSF algorithm is still superior to that of the other algorithms. On the whole, the output results of SRUSF based on the square root of covariance are more stable. SRUSF innovatively introduces the stabilized coefficient to predict the covariance matrix of the error, which further prevents the divergence of filtering results and increases the dependability of the output. The multiple-signal joint estimation method based on SRUSF algorithm is more suitable for GNSS and 5G hybrid positioning because of the more reliable and dependable state estimation results. ## 5 Discussion

The potential real-world applications of this article can be divided into the following three aspects. Firstly, enhanced localization and tracking: this research can be widely applied to scenarios requiring high-precision positioning. Through the integration of 5G New Radio (NR) Release 17 and GNSS, a positioning accuracy of 0.2 m can be achieved in indoor and outdoor environments, which will provide essential support for human activity trajectory recognition and robot navigation. Secondly, smart manufacturing: the integration of 5G and GNSS will offer paramount advantages in smart factory scenarios. This could enable factory nodes and robots to seamlessly navigate, coordinate, and map the environment, which is conducive to fulfilling the demand of ultra-reliability, ultra-low latency, and massive connectivity often encountered in smart factory scenarios. Finally, vehicle-to-everything (V2X): autonomous vehicles are expected to fundamentally change the transportation industry, increasing highway capacity and traffic flow and hopefully reducing accidents. The integration of 5G and GNSS could provide environmental information to support fast vehicle platooning, secure and seamless access, and simultaneous localization and mapping. In this paper, a multiple-signal joint estimation method for GNSS-5G hybrid positioning in a highly dependable spatio-temporal network is proposed. A multiple-signal compact coupled filter group architecture is presented to fuse the measurements of GNSS and 5G. This filter group first filters the observations of each channel of the GNSS-5G joint positioning terminal separately and then fuses the observations of each signal source to give the optimal estimate of the GNSS-5G joint positioning results.