## 1 Introduction
Firstly, GNSS positioning  
Figure 1: Scenario of GNSS-5G hybrid positioning in a high-dependability spatio-temporal network. results are dominant, and 5G base stations are utilized as communication means to transmit GNSS-enhanced information [13; 14]; secondly GNSS positioning signals are blocked or suffer from significant errors, and the positioning result of 5G PRS signal is dominant [11]; thirdly the positioning terminal can receive the GNSS signal and the 5G positioning signal at the same time and can obtain the positioning result through the fusion of the two signals [8; 9; 10; 12]. Therefore, the fusion positioning algorithm has become a research hotspot [2; 12]. The Extended Kalman Filter (EKF)-based algorithm is a widely used filtering algorithm that approximates nonlinear dynamics by linearizing system states and measurements. EKF has been extensively applied in GNSS and multi-sensor integration [15; 16; 17]. However, the linearization approximation of EKF for nonlinear systems and noise may lead to the growth of estimation errors. [PERSON] et al. [9] proposed a hybrid sequential-fusion Multiple-Rate Adaptive Kalman Filter (MRAKF) for GNSS-5G hybrid positioning, which is able to adaptively adjust the observation noise covariance matrix. MRAKF can manage the large dynamic range of the measurement noise uncertainty and prevent the decrease in the positioning accuracy. [PERSON] et al. [18] proposed an Unscented Kalman Filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state estimation. Through the utilization of a set of unscented transformation points to represent the mean and covariance of the state distribution, the state of nonlinear systems can be estimated with improved precision. Nevertheless, there is a drawback with filter divergence in the estimation of the state of high-dimensional systems. In GNSS and 5G fusion, the number of observation data is substantial, and the EKF calculation Jacobian matrix is intricate. Many researchers [19; 20; 21] have utilized a federated filter algorithm based on the Unscented Kalman Filter to improve the accuracy of low-cost Strapdown Inertial Navigation Systems (SINSs). The Square Root UKF (SRUKF) [23; 24; 25] is a modified form of UKF, the filter of which is initialized by calculating the matrix square root of the estimation-error covariance, which is proved to provide a better numerical stability. [PERSON] et al. [26] proposed a modified UKF algorithm called a Variational Bayesian-based Unscented Kalman Filter (VBHUKF). Adaptation is achieved by estimating the time-varying observation noise covariance based on Variational Bayesian approximations. The proposed method has better filtering consistency than the standard UKF, and the VBHUKF filter performs better when the observation noise covariance is time-varying and there are outliers in the observation data. The main contributions of this paper can be summarized as follows. We have proposed a multiple-signal, compact, coupled filter group architecture and a Square Root Unscented Stable Filter algorithm as a solution to the issues in the GNSS-5G hybrid network that the number of available signal sources fluctuates rapidly, the estimation stability of multi-scale and multi-type signals is poor, and dependable positioning is difficult. We have added an additional positive definite parameter to guarantee positive estimation-error covariance. Ultimately, the high-confidence joint positioning of GNSS and 5G is realized, and the divergence of fusion positioning results caused is avoided with abnormal observation data. The remainder of this paper is organized as follows. Section 2 briefly introduces the GNSS-5G hybrid positioning system model. Section 3 describes the proposed multiple-signal joint estimation method in detail, including a multiple-signal, compact, coupled filter group architecture and the realization of a Square Root Unscented stable filter.