## 3 The Proposed Multiple-Signal Joint Estimation Method  
### Multiple-Signal Compact Coupled Filter Group Architecture  
The currently widely used multi-signal source-fusion method adopts a cascaded filter architecture. After the individual positioning results of each sensor are given, the positioning settlement results are fused according to a certain weighted algorithm. These types of methods process the observations according to the time sequence according to the sequential fusion strategy and only need to fuse and estimate the independent positioning results. The advantage of this fusion method is that the structure is flexible and the implementation complexity is low. However, the disadvantages of this type of method are also obvious. Ignoring a large amount of prior information may lead to a significant decrease in the accuracy of the estimation results. In order to entirely achieve joint estimation and high-precision measurement of GNSS and 5G signals, this paper proposes a tightly coupled filter group, whose architecture is shown in Figure 2. This method first filters the observations of each channel of the GNSS and 5G joint positioning terminal separately in the first group, and then fuses the observations of each signal source to give the optimal estimate of the GNSS and 5G joint positioning results in the second group. In the first group, UKF algorithm is utilized to predict GNSS observation and 5G observation respectively. In the second group, we adopt the Square Root Unscented stable filter algorithm proposed in next section, multiple GNSS and 5G measurement obtained from the first group are efficiently fused into the position estimation to ensure the high dependability positioning. Figure 2: GNSS and 5G joint positioning compact coupled filter group architecture. The first group utilizes UKF to estimate the observation of 5G and GNSS, a general algorithm of UKF can be founded in [18] and the state equation of the system can be expressed as  
\[ \begin{split}\mathsf{s}_{\text{GNSS6\& 5G}}[t_{k}]=[ \tau_{\text{GNSS}}[t_{k}],\tau_{\text{5 GBS}}[t_{k}],\vartheta_{\text{5 GBS}}[t_{k} ],\theta_{\text{5 GBS}}[t_{k}]\\ \Delta\tau_{\text{GNSS}}[t_{k}],\Delta\tau_{\text{5 GBS}}[t_{k}], \Delta\varphi_{\text{5 GBS}}[t_{k}],\Delta\theta_{\text{5 GBS}}[t_{k}]]^{T}\end{split}  \tag{12}\]  
where \(\tau_{\text{{GNSS}}}[t_{k}],\tau_{\text{5 GBS}}[t_{k}],\sigma_{\text{5 GBS}}[t_{k }],\theta_{\text{5 GBS}}[t_{k}]\) denote GNSS TOA, 5G TOA, azimuth angle and elevation angle, respectively. Furthermore, parameters \(\Delta\tau_{\text{{GNSS}}}[t_{k}],\Delta\tau_{\text{5 GBS}}[t_{k}],\Delta \varphi_{\text{5 GBS}}[t_{k}]\), \(\Delta\theta_{\text{5 GBS}}[t_{k}]\) denote the rate of change of the corresponding variables. In GNSS and 5G fusion positioning scenarios, there often exist a large number of NLOS channels, and the positioning results of direct integration of multiple signal sources may result in an unacceptable rise in location error. At present, the widely used NLOS error suppression methods are mainly divided into error compensation based on NLOS error distribution model and suppression methods based on observation screening. Due to the wide coverage of the spatio-temporal network composed of GNSS and 5G communication networks, the modeling complexity and cost of collecting NLOS errors are extremely high. In the method proposed in this paper, UKF is used in the first group to predict and update the observation and the change rate of 5G and GNSS, respectively, which provides the feasibility for using signal quality evaluation and observation screening algorithm to exclude the NLOS channel observation information and can prevent excessive NLOS errors from being introduced into the joint positioning results of the second group. The second group utilizes the SRUSF algorithm introduced in Section 3.2 to estimate the receiver's position, velocity, clock offset, and clock skew.